Photonuclear reactions on stable isotopes of cadmium and tellurium at bremsstrahlung end-point energies of 10−23 MeV

In order to learn more about how the population of nuclear shells affects unique aspects of the decay of excited nuclear states, it is interesting to investigate the photodisintegration of nuclei located close to the Z = 50 closed proton shell. The yields of different channels of the photodisintegration of isotopes in comparison with the ratio of the numbers of neutrons and protons in the nuclei can highlight the mechanisms of excitation and decay of nuclear states in the energy region between 10 and 50 MeV.

Cadmium (Z = 48) and tellurium (Z = 52) isotopes are suitable for investigations, as they have several stable isotopes under natural conditions, which allows to obtain the dependence of the yields of various reactions on the number of neutrons in a nucleus. The main decay channels of the giant dipole resonance (GDR) are the emission of neutrons or protons. Currently, an extensive database of experimental data on the photoneutron reactions in the stable isotopes of the natural mixture of cadmium and tellurium [1−22] is available. Nevertheless, these data are currently incomplete and lack a proper explanation. The proton channel, despite a small cross section of the (γ,p) reaction, is interesting in connection with the isospin splitting of the GDR [23].

Natural cadmium consists of eight stable isotopes with the following mass numbers and isotopic abundances: ¹⁰⁶Cd (1.25%), ¹⁰⁸Cd (0.89%), ¹¹⁰Cd (12.49%), ¹¹¹Cd (12.80%), ¹¹²Cd (24.13%), ¹¹³Cd (12.22%), ¹¹⁴Cd (28.73%), and ¹¹⁶Cd (7.49%). The photoneutron reaction cross sections σ(γ,n) + σ(γ, np) and σ(γ, 2n) as well as the total absorption cross section σ(γ, sn) = σ(γ,n) + σ(γ, np) + σ(γ, 2n) for a target from a natural mixture of cadmium isotopes were measured by using a beam of quasimonochromatic photons without separating the contributions from the reactions on individual isotopes [1]. The majority of photonuclear reaction data on cadmium isotopes have been obtained in experiments using bremsstrahlung photons. For example, the relative yields of multiparticle reactions on natural cadmium were studied using the end-point energy of 23 MeV [2, 3] and 55 MeV [4−6]; the flux-averaged cross section was determined using the end-point energies of 50 and 60 MeV [7]; isomeric ratios were determined using electron bremsstrahlung for the pairs ^115m,gCd [7−15] and ^104m,gAg [13].

Natural tellurium consists of eight stable isotopes with the following mass numbers and isotopic abundances: ¹²⁰Te (0.09%), ¹²²Te (2.55%), ¹²³Te (0.89%), ¹²⁴Te (4.74%), ¹²⁵Te (7.07%), ¹²⁶Te (18.84%), ¹²⁸Te (31.74%), and ¹³⁰Te (34.08%). Although all these isotopes can undergo photodisintegration via different reaction channels, only a few have been studied to date, such as photoneutron reactions [10−12,16−22]. The cross sections for the (γ, n) [22], (γ, n) + (γ, pn) [16] and (γ, 2n) + (γ, 2np) [16] reactions on the isotopes ^{120,124,126,128,130}Te induced by bremsstrahlung photons and positron annihilation in flight were determined by detecting neutrons in the energy range of the γ quantum (8.03−26.46 MeV). Isomeric ratios have been measured for the pairs ^119m,gTe [10, 17, 19, 20], ^121m,gTe [10, 11, 19, 20], ^123m,gTe [10, 18], ^127m,gTe [11,19, 21], and ^129m,gTe [10−12, 17,19, 21].

This study aimed to obtain new data on fundamental photonuclear reactions of cadmium and tellurium isotopes using a bremsstrahlung γ-radiation beam with energies between 10 and 23 MeV. We used TALYS-2.0 [24] and the combined model of photonucleon reactions (CMPR) [25] for simulations and the γ-activation method with bremsstrahlung photons from the electron accelerator to obtain our experimental data. Furthermore, the photoproton reaction product ¹¹¹Ag is a prospective medicinal isotope [26−29]; thus, examining the reaction yields is beneficial for both research and practical applications.

This paper is organized as follows. Sec. II describes the experimental set-up and procedures. Sec. III outlines the data analysis methods. In Sec. IV, the results for Cd and Te isotopes are presented and discussed. Sec. V presents the conclusions. Appendix A presents the tabulated experimental results, whereas Appendix B examines the TALYS options and GDR isospin splitting.

This experiment was conducted using the output electron beam of the MT-25 microtron [30]. The electron energies ranged from 10 to 23 MeV, with an energy step of 1 MeV. Table 1 lists the main experimental parameters. A tungsten radiator target, a common convertor material, was used to generate the γ-radiation. The tungsten target was thick enough (3 mm) to maximize the amount of photons in the energy range of the GDR, which dominates the photonuclear cross section between the nucleon separation threshold and 20−30 MeV. To eliminate the leftover electrons from the bremsstrahlung beam, a 30 mm thick aluminum absorber was positioned behind the tungsten converter. The Cd and Te targets were located perpendicular to the electron beam and 1 cm away from the converter. The target of natural cadmium had dimensions 10 mm×10 mm×0.5 mm (at 10−19 MeV) and 5 mm×5 mm×0.5 mm (at 20−23 MeV). The natural tellurium target in powder form was enclosed in aluminum foils in the form of a square envelope with sizes of 15 mm×15 mm×2 mm (at 10−15 MeV), 8 mm×8 mm×2 mm (at 16−19 MeV), and 6 mm×6 mm×2 mm (at 20−23 MeV).

In the trials, a bremsstrahlung flux generated in the tungsten converter was utilized to irradiate the metallic natural cadmium and tellurium samples. The fluctuations in the beam current were measured using a Faraday cup and calibrated ionization chamber in the beam, and subsequently recorded in a web-accessible database for future analysis by using LabView software and an analog-to-digital converter card. [31]. Along with the Faraday cup and ionization chamber, the beam current was determined by digitizing the electrical charge accumulated on the target. During irradiation, the electron current of the accelerator was measured using a Faraday cup. A 0.15-mm-thick copper monitor was positioned behind the irradiation target. The absolute value of the current was calculated by comparing the experimentally measured and theoretical yields at the monitor based on the ⁶⁵Cu(γ, n)⁶⁴Cu reaction. The experimental cross sections of the partial photoneutron reactions for the ⁶⁵Cu nucleus, obtained on quasimonoenergetic annihilation photon beams [32] using the neutron multiplicity sorting method, display considerable systematic uncertainties and do not satisfy the specially introduced objective physical data reliability criteria. We applied the corrected theoretical cross sections, which were used to evaluate the cross sections of the partial reactions by employing the experimental-theoretical approach [33]. The yield of the ⁶⁵Cu(γ, n)⁶⁴Cu reaction was determined using the expected cross section [33], and the bremsstrahlung spectrum was generated using Geant4 [34].

Once the radiation levels in the experimental hall were safe, the targets were transferred to a different measurement room and the induced activity in the irradiated target was measured. We used a high purity germanium (HPGe) γ-detector with a resolution of 16 keV at 1332 keV, together with standard measurement electronics and a 16K ADC/MCA (Multiport II Multichannel Analyser, CANBERRA). The energy and efficiency of the HPGe detector were calibrated using standard γ-ray sources. A detailed explanation of the γ-activation measurement method used in this study can be found in Refs. [35, 36].

The duration between the end of the irradiation process and beginning of the measurement was between 10 and 15 min, designated as the cooling period. The spectra of each sample were taken many times over a total of 0.5, 1, 12, and 24 h. Fig. 1 and Fig. 2 display the typical γ-ray spectra of the chemical products generated from ^natCd and ^natTe, respectively. A background spectrum (red line) is also shown in Fig. 1. Bremsstrahlung radiation with an end-point energy of 23 MeV was used to irradiate the samples.

Figure 1.  (color online) Spectra of residual activity of the irradiated sample of ^natCd (top-to-bottom) 3 h (a) and 4 days (b) after irradiation. The spectra measurement durations were 1 h (a) and 1 day (b), respectively.

Figure 2.  (color online) Spectra of residual activity of the irradiated sample of ^natTe (top-to-bottom) 6 h (a) and 11 days (b) after irradiation. The spectra measurement durations were 1 h (a) and 3 days (b), respectively.

The γ-ray spectra were processed using the DEIMOS32 code [37]. This code uses the Gaussian function to fit the count area of the full-energy peaks. The processed peaks were identified using the half-life of the residual nuclei, γ-ray energy, and intensity. The radionuclides were identified based on their different γ-ray energies and half-lives. Table 2 provides the key γ-ray energies and intensities used to compute the reaction product yield. The columns 4−5 in Table 2 contain the nuclear data from Ref. [38].

The half-lives of previously investigated radionuclides ranged from 20 min (¹¹⁵Ag) to 461.9 days (¹⁰⁹Cd) as well as from 69.6 min (^129gTe) to 164.2 days (^121mTe). To compute the radioactive half-lives and select the appropriate spectra for the activity of each isotope, γ-ray spectra were collected over a range of waiting times, from minutes to a day, after irradiation. The activity is typically measured using the highest intensity, well-separated, interference-free, and correctable γ-ray.

This experiment was carried out using the MT-25 microtron's output electron beam [30]. The electron energies ranged from 10 to 23 MeV, with an energy step of 1 MeV. Table 1 lists the main parameters of the experiments. To generate γ-radiation, a tungsten radiator target, a common convertor material, was employed. The tungsten target was thick enough (3 mm) to maximise the amount of photons in the energy range of the giant dipole resonance (GDR), which dominates the photonuclear cross section between the nucleon separation threshold and 20-30 MeV. To eliminate the leftover electrons from the bremsstrahlung beam, a 30 mm thick aluminium absorber was positioned behind the tungsten converter. The Cd and Te targets were located perpendicular to the electron beam and 1 cm away from the converter. The target of natural cadmium had dimensions 10×10×0.5 mm (at 10–19 MeV) and 5×5×0.5 mm (at 20–23 MeV). The natural tellurium target in a form of a powder in an aluminium foil in the form of a square envelope with a size of 15×15×2 mm (at 10-15 MeV), 8×8×2 mm (at 16-19 MeV) and 6×6×2 mm (at 20-23 MeV).

In the trials, a bremsstrahlung flux generated in the tungsten converter was utilised to irradiate metallic natural cadmium and tellurium samples. The fluctuations in beam current were measured using a Faraday cup and a calibrated ionisation chamber in the beam, and then recorded into a web-accessible database for use in the study with LabView software and an analog-to-digital converter card. [31]. Along with the Faraday cup and ionisation chamber, the beam current was determined by digitising the electrical charge accumulated on the target. During irradiation, the electron current of the accelerator was measured using a Faraday cup. A 0.15-mm-thick copper monitor was positioned behind the irradiation target. The absolute value of the current was calculated by comparison of experimentally measured and theoretical yields at the monitor on the basis of the ⁶⁵Cu(γ,n)⁶⁴Cu reaction. The experimental cross sections of the partial photoneutron reactions for the ⁶⁵Cu nucleus, obtained on quasimonoenergetic annihilation photon beams [32] using the neutron multiplicity sorting method display considerable systematic uncertainties and do not satisfy the specially introduced objective physical data reliability criteria. We used the corrected theoretical cross sections which were used to evaluate the cross sections of the partial reactions using their experimental-theoretical approach [33]. The yield of the ⁶⁵Cu(γ,n)⁶⁴Cu reaction was determined using the expected cross section [33], and the bremsstrahlung spectrum was generated using Geant4 [34].

Once the radiation levels in the experimental hall were safe, the targets were transferred to a different measurement room and the induced activity in the irradiated target was measured. We used a high purity germanium (HPGe) γ-detector with a resolution of 16 keV at 1332 keV, together with standard measurement electronics and a 16K ADC/MCA (Multiport II Multichannel Analyser, CANBERRA). The energy and efficiency of the HPGe detector were calibrated using standard γ-ray sources. A thorough explanation of the γ-activation measurement method used in this study can be found in [35,36].

The duration that elapsed between the end of the irradiation process and the beginning of the measurement was between 10 and 15 minutes, designated as the cooling period. The spectra of each sample were taken many times over a total of 0.5, 1, 12, and 24 hours. Fig. 1 and Fig. 2 display typical γ-ray spectra of the chemical products generated from the ^natCd and ^natTe, respectively. A background spectrum (red line) is also shown in Fig. 1. Bremsstrahlung radiation with end-point energy of 23 MeV was used to irradiate the samples.

Figure 1.  (color online) Spectra of residual activity of the irradiated sample of ^natCd (top-to-bottom) 3 h (a) and 4 days (b) after irradiation. The spectra measurement duration was 1 h (a) and 1 day (b), respectively

Figure 2.  (color online) Spectra of residual activity of the irradiated sample of ^natTe (top-to-bottom) 6 h (a) and 11 days (b) after irradiation. The spectra measurement duration was 1 h (a) and 3 days (b), respectively

The γ-ray spectra were processed using the DEIMOS32 code [37]. This code uses the Gaussian function to fit the count area of full-energy peaks. The processed peaks were identified using the half-life of residual nuclei, γ-ray energy, and intensity. The radionuclides were identified based on their different γ-ray energies and half-lives. Table 2 provides the key γ-ray energies and intensities used to compute the reaction product yield. Table 2's columns 4-5 contain nuclear data from Ref. [38].

The half-lives of previously investigated radionuclides ranged from 20 min (¹¹⁵Ag) to 461.9 days (¹⁰⁹Cd) as well as from 69.6 min (^129gTe) to 164.2 days (^121mTe). To compute radioactive half-lives and select appropriate spectra for each isotope's activity, γ-ray spectra were collected throughout a range of waiting times, from minutes to a day after irradiation. The activity is typically measured using the highest intensity, well-separated, interference-free, and correctable γ-ray.

This experiment was conducted using the output electron beam of the MT-25 microtron [30]. The electron energies ranged from 10 to 23 MeV, with an energy step of 1 MeV. Table 1 lists the main experimental parameters. A tungsten radiator target, a common convertor material, was used to generate the γ-radiation. The tungsten target was thick enough (3 mm) to maximize the amount of photons in the energy range of the GDR, which dominates the photonuclear cross section between the nucleon separation threshold and 20−30 MeV. To eliminate the leftover electrons from the bremsstrahlung beam, a 30 mm thick aluminum absorber was positioned behind the tungsten converter. The Cd and Te targets were located perpendicular to the electron beam and 1 cm away from the converter. The target of natural cadmium had dimensions 10 mm×10 mm×0.5 mm (at 10−19 MeV) and 5 mm×5 mm×0.5 mm (at 20−23 MeV). The natural tellurium target in powder form was enclosed in aluminum foils in the form of a square envelope with sizes of 15 mm×15 mm×2 mm (at 10−15 MeV), 8 mm×8 mm×2 mm (at 16−19 MeV), and 6 mm×6 mm×2 mm (at 20−23 MeV).

In the trials, a bremsstrahlung flux generated in the tungsten converter was utilized to irradiate the metallic natural cadmium and tellurium samples. The fluctuations in the beam current were measured using a Faraday cup and calibrated ionization chamber in the beam, and subsequently recorded in a web-accessible database for future analysis by using LabView software and an analog-to-digital converter card. [31]. Along with the Faraday cup and ionization chamber, the beam current was determined by digitizing the electrical charge accumulated on the target. During irradiation, the electron current of the accelerator was measured using a Faraday cup. A 0.15-mm-thick copper monitor was positioned behind the irradiation target. The absolute value of the current was calculated by comparing the experimentally measured and theoretical yields at the monitor based on the ⁶⁵Cu(γ, n)⁶⁴Cu reaction. The experimental cross sections of the partial photoneutron reactions for the ⁶⁵Cu nucleus, obtained on quasimonoenergetic annihilation photon beams [32] using the neutron multiplicity sorting method, display considerable systematic uncertainties and do not satisfy the specially introduced objective physical data reliability criteria. We applied the corrected theoretical cross sections, which were used to evaluate the cross sections of the partial reactions by employing the experimental-theoretical approach [33]. The yield of the ⁶⁵Cu(γ, n)⁶⁴Cu reaction was determined using the expected cross section [33], and the bremsstrahlung spectrum was generated using Geant4 [34].

Once the radiation levels in the experimental hall were safe, the targets were transferred to a different measurement room and the induced activity in the irradiated target was measured. We used a high purity germanium (HPGe) γ-detector with a resolution of 16 keV at 1332 keV, together with standard measurement electronics and a 16K ADC/MCA (Multiport II Multichannel Analyser, CANBERRA). The energy and efficiency of the HPGe detector were calibrated using standard γ-ray sources. A detailed explanation of the γ-activation measurement method used in this study can be found in Refs. [35, 36].

The duration between the end of the irradiation process and beginning of the measurement was between 10 and 15 min, designated as the cooling period. The spectra of each sample were taken many times over a total of 0.5, 1, 12, and 24 h. Fig. 1 and Fig. 2 display the typical γ-ray spectra of the chemical products generated from ^natCd and ^natTe, respectively. A background spectrum (red line) is also shown in Fig. 1. Bremsstrahlung radiation with an end-point energy of 23 MeV was used to irradiate the samples.

Figure 1.  (color online) Spectra of residual activity of the irradiated sample of ^natCd (top-to-bottom) 3 h (a) and 4 days (b) after irradiation. The spectra measurement durations were 1 h (a) and 1 day (b), respectively.

Figure 2.  (color online) Spectra of residual activity of the irradiated sample of ^natTe (top-to-bottom) 6 h (a) and 11 days (b) after irradiation. The spectra measurement durations were 1 h (a) and 3 days (b), respectively.

The γ-ray spectra were processed using the DEIMOS32 code [37]. This code uses the Gaussian function to fit the count area of the full-energy peaks. The processed peaks were identified using the half-life of the residual nuclei, γ-ray energy, and intensity. The radionuclides were identified based on their different γ-ray energies and half-lives. Table 2 provides the key γ-ray energies and intensities used to compute the reaction product yield. The columns 4−5 in Table 2 contain the nuclear data from Ref. [38].

The half-lives of previously investigated radionuclides ranged from 20 min (¹¹⁵Ag) to 461.9 days (¹⁰⁹Cd) as well as from 69.6 min (^129gTe) to 164.2 days (^121mTe). To compute the radioactive half-lives and select the appropriate spectra for the activity of each isotope, γ-ray spectra were collected over a range of waiting times, from minutes to a day, after irradiation. The activity is typically measured using the highest intensity, well-separated, interference-free, and correctable γ-ray.

This experiment was conducted using the output electron beam of the MT-25 microtron [30]. The electron energies ranged from 10 to 23 MeV, with an energy step of 1 MeV. Table 1 lists the main experimental parameters. A tungsten radiator target, a common convertor material, was used to generate the γ-radiation. The tungsten target was thick enough (3 mm) to maximize the amount of photons in the energy range of the GDR, which dominates the photonuclear cross section between the nucleon separation threshold and 20−30 MeV. To eliminate the leftover electrons from the bremsstrahlung beam, a 30 mm thick aluminum absorber was positioned behind the tungsten converter. The Cd and Te targets were located perpendicular to the electron beam and 1 cm away from the converter. The target of natural cadmium had dimensions 10 mm×10 mm×0.5 mm (at 10−19 MeV) and 5 mm×5 mm×0.5 mm (at 20−23 MeV). The natural tellurium target in powder form was enclosed in aluminum foils in the form of a square envelope with sizes of 15 mm×15 mm×2 mm (at 10−15 MeV), 8 mm×8 mm×2 mm (at 16−19 MeV), and 6 mm×6 mm×2 mm (at 20−23 MeV).

In the trials, a bremsstrahlung flux generated in the tungsten converter was utilized to irradiate the metallic natural cadmium and tellurium samples. The fluctuations in the beam current were measured using a Faraday cup and calibrated ionization chamber in the beam, and subsequently recorded in a web-accessible database for future analysis by using LabView software and an analog-to-digital converter card. [31]. Along with the Faraday cup and ionization chamber, the beam current was determined by digitizing the electrical charge accumulated on the target. During irradiation, the electron current of the accelerator was measured using a Faraday cup. A 0.15-mm-thick copper monitor was positioned behind the irradiation target. The absolute value of the current was calculated by comparing the experimentally measured and theoretical yields at the monitor based on the ⁶⁵Cu(γ, n)⁶⁴Cu reaction. The experimental cross sections of the partial photoneutron reactions for the ⁶⁵Cu nucleus, obtained on quasimonoenergetic annihilation photon beams [32] using the neutron multiplicity sorting method, display considerable systematic uncertainties and do not satisfy the specially introduced objective physical data reliability criteria. We applied the corrected theoretical cross sections, which were used to evaluate the cross sections of the partial reactions by employing the experimental-theoretical approach [33]. The yield of the ⁶⁵Cu(γ, n)⁶⁴Cu reaction was determined using the expected cross section [33], and the bremsstrahlung spectrum was generated using Geant4 [34].

Once the radiation levels in the experimental hall were safe, the targets were transferred to a different measurement room and the induced activity in the irradiated target was measured. We used a high purity germanium (HPGe) γ-detector with a resolution of 16 keV at 1332 keV, together with standard measurement electronics and a 16K ADC/MCA (Multiport II Multichannel Analyser, CANBERRA). The energy and efficiency of the HPGe detector were calibrated using standard γ-ray sources. A detailed explanation of the γ-activation measurement method used in this study can be found in Refs. [35, 36].

The duration between the end of the irradiation process and beginning of the measurement was between 10 and 15 min, designated as the cooling period. The spectra of each sample were taken many times over a total of 0.5, 1, 12, and 24 h. Fig. 1 and Fig. 2 display the typical γ-ray spectra of the chemical products generated from ^natCd and ^natTe, respectively. A background spectrum (red line) is also shown in Fig. 1. Bremsstrahlung radiation with an end-point energy of 23 MeV was used to irradiate the samples.

Figure 1.  (color online) Spectra of residual activity of the irradiated sample of ^natCd (top-to-bottom) 3 h (a) and 4 days (b) after irradiation. The spectra measurement durations were 1 h (a) and 1 day (b), respectively.

Figure 2.  (color online) Spectra of residual activity of the irradiated sample of ^natTe (top-to-bottom) 6 h (a) and 11 days (b) after irradiation. The spectra measurement durations were 1 h (a) and 3 days (b), respectively.

The γ-ray spectra were processed using the DEIMOS32 code [37]. This code uses the Gaussian function to fit the count area of the full-energy peaks. The processed peaks were identified using the half-life of the residual nuclei, γ-ray energy, and intensity. The radionuclides were identified based on their different γ-ray energies and half-lives. Table 2 provides the key γ-ray energies and intensities used to compute the reaction product yield. The columns 4−5 in Table 2 contain the nuclear data from Ref. [38].

The half-lives of previously investigated radionuclides ranged from 20 min (¹¹⁵Ag) to 461.9 days (¹⁰⁹Cd) as well as from 69.6 min (^129gTe) to 164.2 days (^121mTe). To compute the radioactive half-lives and select the appropriate spectra for the activity of each isotope, γ-ray spectra were collected over a range of waiting times, from minutes to a day, after irradiation. The activity is typically measured using the highest intensity, well-separated, interference-free, and correctable γ-ray.

The experimental yields of the reactions, Y_exp, were normalized to one electron of the accelerated beam incident on the bremsstrahlung target and calculated using the following formula:

where $ {S}_{p} $ is the full-energy-peak area; $ \varepsilon $ is the full-energy-peak detector efficiency; $ {I}_{\gamma } $ is the γ- emission probability; $ C\mathrm{_{abs}} $ is the correction for self-absorption of γ-rays in the sample; $ t\mathrm{_{real}} $ and $ t\mathrm{_{live}} $ are the real time and live time of the measurement, respectively; $ N $ is the number of atoms in the activation sample; $ {N}_{e} $ is the integral number of incident electrons; $ \lambda $ is the decay constant; $ t\mathrm{_{cool}} $ is the cooling time; and $ t\mathrm{_{irr}} $ is the irradiation time.

The experiment determined the yields Y_theor of the photonuclear reactions, which reflect the convolution of the photonuclear reaction cross section σ_i(E), and distribution density of the number of bremsstrahlung photons over the energy per electron of the accelerator W(E, E_γmax). The outcome of measuring the yield of isotope generation in all possible reactions on a natural mixture of isotopes is as follows:

where E_γmax is the kinetic energy of the electrons hitting the tungsten radiator, E is the energy of bremsstrahlung photons produced on the radiator, E_th is the threshold of the studied photonuclear reaction, η_i is the percentage of the studied isotope in the natural mixture, and the index i corresponds to the number of reactions contributing to the production of the studied isotope.

Figure 3 illustrates the distribution density of the number of bremsstrahlung photons W(E, E_γmax) per electron of the accelerator for accelerated electron energies from 10 to 23 MeV, determined using Geant4 for the bremsstrahlung target made of tungsten with a thickness of 3 mm.

Figure 3.  Distribution density of the number of bremsstrahlung photons at the energies of 10−23 MeV

The total and partial cross sections σ(E) of the photonuclear reactions on the cadmium and tellurium isotopes were estimated for monochromatic photons using the TALYS code [24] with standard parameters and CMPR [25]. The TALYS program examines all processes in the nucleus and transitions between the states. As a result, it is possible to calculate not only the total cross section of a photonuclear reaction but also the cross sections of reactions involving the production of certain states, particularly isomeric states. The standard (default) TALYS option uses the Simple Modified Lorentzian (SMLO) model for photon strength functions (PSFs). This model is used to calculate E1, M1, and upbend components, generally providing more accurate, temperature-dependent resonance shapes than those achieved with older models.

When compared with TALYS, the CMPR accurately considers the GDR isospin splitting, which is crucial for describing the proton decay channel. The basics of the GDR isospin splitting and some relevant CMPR results are presented in Appendix B. This Appendix also provides information on TALYS options as well as examples of comparison between the TALYS and CMPR results.

The yield measurement for a natural mixture of isotopes yields gives the amount of isotope produced in all potential reactions on the natural mixture. The primary problem of bremsstrahlung beam experiments is that the yield of photonuclear reaction depends on both the investigated cross section of the reaction σ_i(E) and the form of the bremsstrahlung spectrum W(E, E_γmax), which is often known with inadequate accuracy. The use of relative yields allows us to determine the dependency of the yield of photonuclear reactions on the maximal energy of bremsstrahlung under various experimental settings. The overall photon absorption cross section is not taken into account when calibrating the yield of one of the most likely reactions. The the most probable and well-studied ¹¹⁶Cd(γ, n)¹¹⁵Cd and ¹³⁰Te(γ, n)¹²⁹Te reactions were chosen as a primary reaction in case of cadmium and tellurium, respectively. In addition, there are no other channels (for example, (γ, 2n) reaction on heavier stable nuclei) for the product formation of ¹¹⁵Cd and ¹²⁹Te, as the nuclei ¹¹⁶Cd and ¹³⁰Te are the heaviest stable nuclei in the natural mixture of Cd and Te.

The theoretical values of the relative yields can be calculated using the following formula:

where η denotes the percentages of the ¹¹⁶Cd and ¹³⁰Te isotopes in the natural mixture of cadmium and tellurium isotopes, respectively. Owing to the assumption regarding the unchanged shape of the bremsstrahlung spectrum, the bremsstrahlung spectrum W(E, E_γmax) can be replaced by the photon production cross section σ(E, E_γmax) calculated using the Seltzer-Berger tables [39].

To represent the experimental photonuclear reaction data, the cross section per equivalent quantum σ_q, determined by the following expression, is used:

The cross section per equivalent quantum for a natural mixture of isotopes includes all possible channels of the final isotope production, where the percentage of initial nuclei is accounted for as follows:

The experimental points along the cross sections of the (γ, n) [22] and (γ, n) + (γ, pn) [16] reactions on the isotopes ^120,128,130Te were approximated by the Lorentz function, and the relative yields Y_rel and cross sections per equivalent quantum σ_q were calculated based on the least squares approximation. In Figs. 4−10, these points are indicated by open circles [22] and open rectangles [16], respectively.

Figure 4.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 11.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹²Cd(γ, p)¹¹¹Ag as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 12.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹³Cd(γ, p)¹¹²Ag as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 13.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁴Cd(γ, p)¹¹³Ag as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 14.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, p)¹¹⁵Ag as functions of bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 15.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹²⁰Te(γ, n)¹¹⁹Te as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [22] (open circles), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 16.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of the ¹²²Te(γ, n)¹²¹Te and ¹²³Te(γ, 2n)¹²¹Te reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 17.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe, and ¹²⁵Te(γ, 2n)^123mTe reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using TALYS code.

Figure 18.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using TALYS code.

Figure 19.  Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁸Te(γ, n)¹²⁷Te reaction as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [22] (open rectangles), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 20.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹³⁰Te(γ, n)¹²⁹Te as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [22] (open rectangles), and simulated values using the CMPR (solid line) and TALYS code (dashed lines).

Figure 21.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²³Te(γ, p)¹²²Sb and ¹²⁴Te(γ, np)¹²²Sb reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 22.  Ratio of the cross section per equivalent quantum $ \sigma_{q\mathrm{exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ for the ¹²³Te(γ, p)¹²²Sb reaction.

Figure 23.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 24.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹²⁸Te(γ, p)¹²⁷Sb as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 25.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹³⁰Te(γ, p)¹²⁹Sb as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 5.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁸Cd(γ, n)¹⁰⁷Cd as functions of the bremsstrahlung end-point energy from this study (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 6.  Relative yields (a) and cross section per equivalent quantum (b) of reactions ¹¹⁰Cd(γ, n)¹⁰⁹Cd and ¹¹¹Cd(γ, 2n)¹⁰⁹Cd as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 7.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions as functions of bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using TALYS code (dashed lines).

Figure 8.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, n)¹¹⁵Cd as functions of bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangles), and simulated values using the CMPR (solid line) and TALYS code (dashed lines).

Figure 9.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, p)¹⁰⁵Ag as functions of bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 10.  (color online) Cross section per equivalent quantum of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

The experimental yields of the reactions, Y_exp, were normalized to one electron of the accelerated beam incident on the bremsstrahlung target and calculated using the following formula:

where $ {S}_{p} $ is the full-energy-peak area; $ \varepsilon $ is the full-energy-peak detector efficiency; $ {I}_{\gamma } $ is the γ- emission probability; $ C\mathrm{_{abs}} $ is the correction for self-absorption of γ-rays in the sample; $ t\mathrm{_{real}} $ and $ t\mathrm{_{live}} $ are the real time and live time of the measurement, respectively; $ N $ is the number of atoms in the activation sample; $ {N}_{e} $ is the integral number of incident electrons; $ \lambda $ is the decay constant; $ t\mathrm{_{cool}} $ is the cooling time; and $ t\mathrm{_{irr}} $ is the irradiation time.

The experiment determined the yields Y_theor of the photonuclear reactions, which reflect the convolution of the photonuclear reaction cross section σ_i(E), and distribution density of the number of bremsstrahlung photons over the energy per electron of the accelerator W(E, E_γmax). The outcome of measuring the yield of isotope generation in all possible reactions on a natural mixture of isotopes is as follows:

where E_γmax is the kinetic energy of the electrons hitting the tungsten radiator, E is the energy of bremsstrahlung photons produced on the radiator, E_th is the threshold of the studied photonuclear reaction, η_i is the percentage of the studied isotope in the natural mixture, and the index i corresponds to the number of reactions contributing to the production of the studied isotope.

Figure 3 illustrates the distribution density of the number of bremsstrahlung photons W(E, E_γmax) per electron of the accelerator for accelerated electron energies from 10 to 23 MeV, determined using Geant4 for the bremsstrahlung target made of tungsten with a thickness of 3 mm.

Figure 3.  Distribution density of the number of bremsstrahlung photons at the energies of 10−23 MeV

The total and partial cross sections σ(E) of the photonuclear reactions on the cadmium and tellurium isotopes were estimated for monochromatic photons using the TALYS code [24] with standard parameters and CMPR [25]. The TALYS program examines all processes in the nucleus and transitions between the states. As a result, it is possible to calculate not only the total cross section of a photonuclear reaction but also the cross sections of reactions involving the production of certain states, particularly isomeric states. The standard (default) TALYS option uses the Simple Modified Lorentzian (SMLO) model for photon strength functions (PSFs). This model is used to calculate E1, M1, and upbend components, generally providing more accurate, temperature-dependent resonance shapes than those achieved with older models.

When compared with TALYS, the CMPR accurately considers the GDR isospin splitting, which is crucial for describing the proton decay channel. The basics of the GDR isospin splitting and some relevant CMPR results are presented in Appendix B. This Appendix also provides information on TALYS options as well as examples of comparison between the TALYS and CMPR results.

The yield measurement for a natural mixture of isotopes yields gives the amount of isotope produced in all potential reactions on the natural mixture. The primary problem of bremsstrahlung beam experiments is that the yield of photonuclear reaction depends on both the investigated cross section of the reaction σ_i(E) and the form of the bremsstrahlung spectrum W(E, E_γmax), which is often known with inadequate accuracy. The use of relative yields allows us to determine the dependency of the yield of photonuclear reactions on the maximal energy of bremsstrahlung under various experimental settings. The overall photon absorption cross section is not taken into account when calibrating the yield of one of the most likely reactions. The the most probable and well-studied ¹¹⁶Cd(γ, n)¹¹⁵Cd and ¹³⁰Te(γ, n)¹²⁹Te reactions were chosen as a primary reaction in case of cadmium and tellurium, respectively. In addition, there are no other channels (for example, (γ, 2n) reaction on heavier stable nuclei) for the product formation of ¹¹⁵Cd and ¹²⁹Te, as the nuclei ¹¹⁶Cd and ¹³⁰Te are the heaviest stable nuclei in the natural mixture of Cd and Te.

The theoretical values of the relative yields can be calculated using the following formula:

where η denotes the percentages of the ¹¹⁶Cd and ¹³⁰Te isotopes in the natural mixture of cadmium and tellurium isotopes, respectively. Owing to the assumption regarding the unchanged shape of the bremsstrahlung spectrum, the bremsstrahlung spectrum W(E, E_γmax) can be replaced by the photon production cross section σ(E, E_γmax) calculated using the Seltzer-Berger tables [39].

To represent the experimental photonuclear reaction data, the cross section per equivalent quantum σ_q, determined by the following expression, is used:

The cross section per equivalent quantum for a natural mixture of isotopes includes all possible channels of the final isotope production, where the percentage of initial nuclei is accounted for as follows:

The experimental points along the cross sections of the (γ, n) [22] and (γ, n) + (γ, pn) [16] reactions on the isotopes ^120,128,130Te were approximated by the Lorentz function, and the relative yields Y_rel and cross sections per equivalent quantum σ_q were calculated based on the least squares approximation. In Figs. 4−10, these points are indicated by open circles [22] and open rectangles [16], respectively.

Figure 4.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 11.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹²Cd(γ, p)¹¹¹Ag as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 12.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹³Cd(γ, p)¹¹²Ag as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 13.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁴Cd(γ, p)¹¹³Ag as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 14.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, p)¹¹⁵Ag as functions of bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 15.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹²⁰Te(γ, n)¹¹⁹Te as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [22] (open circles), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 16.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of the ¹²²Te(γ, n)¹²¹Te and ¹²³Te(γ, 2n)¹²¹Te reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 17.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe, and ¹²⁵Te(γ, 2n)^123mTe reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using TALYS code.

Figure 18.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using TALYS code.

Figure 19.  Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁸Te(γ, n)¹²⁷Te reaction as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [22] (open rectangles), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 20.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹³⁰Te(γ, n)¹²⁹Te as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [22] (open rectangles), and simulated values using the CMPR (solid line) and TALYS code (dashed lines).

Figure 21.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²³Te(γ, p)¹²²Sb and ¹²⁴Te(γ, np)¹²²Sb reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 22.  Ratio of the cross section per equivalent quantum $ \sigma_{q\mathrm{exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ for the ¹²³Te(γ, p)¹²²Sb reaction.

Figure 23.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 24.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹²⁸Te(γ, p)¹²⁷Sb as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 25.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹³⁰Te(γ, p)¹²⁹Sb as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 5.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁸Cd(γ, n)¹⁰⁷Cd as functions of the bremsstrahlung end-point energy from this study (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 6.  Relative yields (a) and cross section per equivalent quantum (b) of reactions ¹¹⁰Cd(γ, n)¹⁰⁹Cd and ¹¹¹Cd(γ, 2n)¹⁰⁹Cd as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 7.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions as functions of bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using TALYS code (dashed lines).

Figure 8.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, n)¹¹⁵Cd as functions of bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangles), and simulated values using the CMPR (solid line) and TALYS code (dashed lines).

Figure 9.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, p)¹⁰⁵Ag as functions of bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 10.  (color online) Cross section per equivalent quantum of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

The experimental yields of the reactions Y_exp were normalized to one electron of the accelerated beam incident on the bremsstrahlung target and calculated using the following formula:

where $ {S}_{p} $ is the full-energy-peak area; $ \varepsilon $ is the full-energy-peak detector efficiency; $ {I}_{\gamma } $ is the γ- emission probability; $ {C}_{abs} $ is the correction for self-absorption of γ-rays in the sample; $ {t}_{real} $ and $ {t}_{live} $ are the real time and live time of the measurement, respectively; $ N $ is the number of atoms in the activation sample; $ {N}_{e} $ is the integral number of incident electrons; $ \lambda $ is the decay constant; $ {t}_{cool} $ is the cooling time; and $ {t}_{irr} $ is the irradiation time.

The experiment determined the yields Y_theor of photonuclear reactions, which reflect the convolution of the photonuclear reactions cross section σ_i(E), and the distribution density of the number of bremsstrahlung photons over energy per one electron of the accelerator W(E, E_γmax). The outcome of measuring the yield of isotope generation in all possible reactions on a natural mixture of isotopes is as follows:

where E_γmax is the kinetic energy of electrons hitting the tungsten radiator, E is the energy of bremsstrahlung photons produced on the radiator, E_th is the threshold of the studied photonuclear reaction, η_i is the percentage of the studied isotope in the natural mixture, and the index i corresponds to the number of the reaction contributing to the production of the studied isotope.

Figure 3 illustrates the distribution density of the number of bremsstrahlung photons W(E, E_γmax) per one electron of the accelerator for accelerated electron energies from 10 to 23 MeV, determined using Geant4 for the bremsstrahlung target made of tungsten with a thickness of 3 mm.

Figure 3.  The distribution density of the number of bremsstrahlung photons at the energies of 10-23 MeV

The total and partial cross sections σ(E) of photonuclear reactions on cadmium and tellurium isotopes were estimated for monochromatic photons using the TALYS code [24] with standard parameters, and CMPR [25]. The TALYS program examines all processes in the nucleus and transitions between states. As a result, it is possible to calculate not only the total cross sections of photonuclear reactions, but also the cross sections of reactions involving the production of certain states, particularly isomeric states. The standard (default) TALYS option uses Simple Modified Lorentzian (SMLO) model for photon strength functions (PSF). This model is used to calculate E1, M1, and upbend components, generally providing more accurate, temperature-dependent resonance shapes than older models.

As compared with TALYS, the CMPR accurately takes into account the GDR isospin splitting, which is of a crucial importance for description of the proton decay channel. The basics of the GDR isospin splitting and some relevant CMPR results are presented in Appendix 2. This Appendix also provides the information on TALYS options as well as examples of comparison of TALYS and CMPR results

The yield measurement for a natural mixture of isotopes yields gives the amount of isotope produced in all potential reactions on the natural mixture. The primary problem of bremsstrahlung beam experiments is that the yield of photonuclear reaction depends on both the investigated cross section of the reaction σ_i(E) and the form of the bremsstrahlung spectrum W(E, E_γmax), which is often known with inadequate accuracy. The use of relative yields allows us to determine the dependency of the yield of photonuclear reactions on the maximal energy of bremsstrahlung under various experimental settings. The overall photon absorption cross section is not taken into account when calibrating the yield of one of the most likely reactions. The the most probable and well-studied ¹¹⁶Cd(γ,n)¹¹⁵Cd and ¹³⁰Te(γ,n)¹²⁹Te reactions were chosen as a primary reaction in case of cadmium and tellurium, respectively. Also there are no other channels (for example, (γ,2n) reaction on heavier stable nuclei) for product formation of ¹¹⁵Cd and ¹²⁹Te since the nuclei ¹¹⁶Cd and ¹³⁰Te are the heaviest stable nuclei in the natural mixture of Cd and Te, respectively.

Theoretical values of the relative yields can be calculated using the following formula:

where η is the percentage of the ¹¹⁶Cd and ¹³⁰Te isotopes in the natural mixture of cadmium and tellurium isotopes, respectively. Owing to the assumption on the unchanged shape of the bremsstrahlung spectrum, the bremsstrahlung spectrum W(E, E_γmax) can be replaced by the photon production cross section σ(E, E_γmax) calculated using Seltzer-Berger tables [39]:

To represent the experimental photonuclear reaction data, the cross section per equivalent quantum σ_q is used determined by the expression:

The cross section per equivalent quantum for a natural mixture of isotopes includes all possible channels of the final isotope production with account for the percentage of initial nuclei is:

The experimental points along the cross sections of the (γ,n) [22] and (γ,n) + (γ,pn) [16] reactions on the isotopes ^120,128,130Te were approximated by the Lorentz function, the relative yields Y_rel and cross sections per equivalent quantum σ_q were calculated based on the least squares approximation. In Fig. 4-10 these points are indicated by open circles [22] and open rectangles [16], respectively.

Figure 4.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 11.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹²Cd(γ, p)¹¹¹Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 12.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹³Cd(γ, p)¹¹²Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 13.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁴Cd(γ, p)¹¹³Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 14.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, p)¹¹⁵Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 15.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹²⁰Te(γ, n)¹¹⁹Te as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [22] (open circles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 16.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of the ¹²²Te(γ,n)¹²¹Te and ¹²³Te(γ,2n)¹²¹Te reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 17.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe and ¹²⁵Te(γ, 2n)^123mTe reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using TALYS code

Figure 18.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using TALYS code

Figure 19.  Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁸Te(γ, n)¹²⁷Te reaction as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [22] (open rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 20.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹³⁰Te(γ, n)¹²⁹Te as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [22] (open rectangles) as well as simulated values using the CMPR (solid line) and TALYS code (dashed lines)

Figure 21.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²³Te(γ, p)¹²²Sb and ¹²⁴Te(γ, np)¹²²Sb reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 22.  The ratio of the cross section per equivalent quantum $ \sigma _{qexp}^{nat}/\sigma _{qtheory}^{nat} $ for the ¹²³Te(γ, p)¹²²Sb reaction

Figure 23.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 24.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹²⁸Te(γ, p)¹²⁷Sb as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 25.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹³⁰Te(γ, p)¹²⁹Sb as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 5.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁸Cd(γ, n)¹⁰⁷Cd as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 6.  Relative yields (a) and cross section per equivalent quantum (b) of reactions ¹¹⁰Cd(γ, n)¹⁰⁹Cd and ¹¹¹Cd(γ, 2n)¹⁰⁹Cd as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 7.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) and simulated values using TALYS code (dashed lines)

Figure 8.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, n)¹¹⁵Cd as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangles) as well as simulated values using the CMPR (solid line) and TALYS code (dashed lines)

Figure 9.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, p)¹⁰⁵Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 10.  (color online) Cross section per equivalent quantum of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

The experimental yields of the reactions, Y_exp, were normalized to one electron of the accelerated beam incident on the bremsstrahlung target and calculated using the following formula:

where $ {S}_{p} $ is the full-energy-peak area; $ \varepsilon $ is the full-energy-peak detector efficiency; $ {I}_{\gamma } $ is the γ- emission probability; $ C\mathrm{_{abs}} $ is the correction for self-absorption of γ-rays in the sample; $ t\mathrm{_{real}} $ and $ t\mathrm{_{live}} $ are the real time and live time of the measurement, respectively; $ N $ is the number of atoms in the activation sample; $ {N}_{e} $ is the integral number of incident electrons; $ \lambda $ is the decay constant; $ t\mathrm{_{cool}} $ is the cooling time; and $ t\mathrm{_{irr}} $ is the irradiation time.

The experiment determined the yields Y_theor of the photonuclear reactions, which reflect the convolution of the photonuclear reaction cross section σ_i(E), and distribution density of the number of bremsstrahlung photons over the energy per electron of the accelerator W(E, E_γmax). The outcome of measuring the yield of isotope generation in all possible reactions on a natural mixture of isotopes is as follows:

where E_γmax is the kinetic energy of the electrons hitting the tungsten radiator, E is the energy of bremsstrahlung photons produced on the radiator, E_th is the threshold of the studied photonuclear reaction, η_i is the percentage of the studied isotope in the natural mixture, and the index i corresponds to the number of reactions contributing to the production of the studied isotope.

Figure 3 illustrates the distribution density of the number of bremsstrahlung photons W(E, E_γmax) per electron of the accelerator for accelerated electron energies from 10 to 23 MeV, determined using Geant4 for the bremsstrahlung target made of tungsten with a thickness of 3 mm.

Figure 3.  Distribution density of the number of bremsstrahlung photons at the energies of 10−23 MeV

The total and partial cross sections σ(E) of the photonuclear reactions on the cadmium and tellurium isotopes were estimated for monochromatic photons using the TALYS code [24] with standard parameters and CMPR [25]. The TALYS program examines all processes in the nucleus and transitions between the states. As a result, it is possible to calculate not only the total cross section of a photonuclear reaction but also the cross sections of reactions involving the production of certain states, particularly isomeric states. The standard (default) TALYS option uses the Simple Modified Lorentzian (SMLO) model for photon strength functions (PSFs). This model is used to calculate E1, M1, and upbend components, generally providing more accurate, temperature-dependent resonance shapes than those achieved with older models.

When compared with TALYS, the CMPR accurately considers the GDR isospin splitting, which is crucial for describing the proton decay channel. The basics of the GDR isospin splitting and some relevant CMPR results are presented in Appendix B. This Appendix also provides information on TALYS options as well as examples of comparison between the TALYS and CMPR results.

The yield measurement for a natural mixture of isotopes yields gives the amount of isotope produced in all potential reactions on the natural mixture. The primary problem of bremsstrahlung beam experiments is that the yield of photonuclear reaction depends on both the investigated cross section of the reaction σ_i(E) and the form of the bremsstrahlung spectrum W(E, E_γmax), which is often known with inadequate accuracy. The use of relative yields allows us to determine the dependency of the yield of photonuclear reactions on the maximal energy of bremsstrahlung under various experimental settings. The overall photon absorption cross section is not taken into account when calibrating the yield of one of the most likely reactions. The the most probable and well-studied ¹¹⁶Cd(γ, n)¹¹⁵Cd and ¹³⁰Te(γ, n)¹²⁹Te reactions were chosen as a primary reaction in case of cadmium and tellurium, respectively. In addition, there are no other channels (for example, (γ, 2n) reaction on heavier stable nuclei) for the product formation of ¹¹⁵Cd and ¹²⁹Te, as the nuclei ¹¹⁶Cd and ¹³⁰Te are the heaviest stable nuclei in the natural mixture of Cd and Te.

The theoretical values of the relative yields can be calculated using the following formula:

where η denotes the percentages of the ¹¹⁶Cd and ¹³⁰Te isotopes in the natural mixture of cadmium and tellurium isotopes, respectively. Owing to the assumption regarding the unchanged shape of the bremsstrahlung spectrum, the bremsstrahlung spectrum W(E, E_γmax) can be replaced by the photon production cross section σ(E, E_γmax) calculated using the Seltzer-Berger tables [39].

To represent the experimental photonuclear reaction data, the cross section per equivalent quantum σ_q, determined by the following expression, is used:

The cross section per equivalent quantum for a natural mixture of isotopes includes all possible channels of the final isotope production, where the percentage of initial nuclei is accounted for as follows:

The experimental points along the cross sections of the (γ, n) [22] and (γ, n) + (γ, pn) [16] reactions on the isotopes ^120,128,130Te were approximated by the Lorentz function, and the relative yields Y_rel and cross sections per equivalent quantum σ_q were calculated based on the least squares approximation. In Figs. 4−10, these points are indicated by open circles [22] and open rectangles [16], respectively.

Figure 4.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 11.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹²Cd(γ, p)¹¹¹Ag as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 12.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹³Cd(γ, p)¹¹²Ag as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 13.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁴Cd(γ, p)¹¹³Ag as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 14.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, p)¹¹⁵Ag as functions of bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 15.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹²⁰Te(γ, n)¹¹⁹Te as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [22] (open circles), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 16.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of the ¹²²Te(γ, n)¹²¹Te and ¹²³Te(γ, 2n)¹²¹Te reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 17.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe, and ¹²⁵Te(γ, 2n)^123mTe reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using TALYS code.

Figure 18.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using TALYS code.

Figure 19.  Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁸Te(γ, n)¹²⁷Te reaction as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [22] (open rectangles), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 20.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹³⁰Te(γ, n)¹²⁹Te as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [22] (open rectangles), and simulated values using the CMPR (solid line) and TALYS code (dashed lines).

Figure 21.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²³Te(γ, p)¹²²Sb and ¹²⁴Te(γ, np)¹²²Sb reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 22.  Ratio of the cross section per equivalent quantum $ \sigma_{q\mathrm{exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ for the ¹²³Te(γ, p)¹²²Sb reaction.

Figure 23.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 24.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹²⁸Te(γ, p)¹²⁷Sb as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 25.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹³⁰Te(γ, p)¹²⁹Sb as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 5.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁸Cd(γ, n)¹⁰⁷Cd as functions of the bremsstrahlung end-point energy from this study (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 6.  Relative yields (a) and cross section per equivalent quantum (b) of reactions ¹¹⁰Cd(γ, n)¹⁰⁹Cd and ¹¹¹Cd(γ, 2n)¹⁰⁹Cd as functions of the bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 7.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions as functions of bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangle), and simulated values using TALYS code (dashed lines).

Figure 8.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, n)¹¹⁵Cd as functions of bremsstrahlung end-point energy from this study (solid rectangles), literature data [3] (open rectangles), and simulated values using the CMPR (solid line) and TALYS code (dashed lines).

Figure 9.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, p)¹⁰⁵Ag as functions of bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

Figure 10.  (color online) Cross section per equivalent quantum of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as functions of the bremsstrahlung end-point energy from this study (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines).

The measured yields relative to the yield of the reaction ¹¹⁶Cd(γ, n)¹¹⁵Cd (in the case of ^natCd) and ¹³⁰Te(γ, n)¹²⁹Te (in the case of ^natTe) and cross sections per equivalent quantum for a natural mixture of isotopes are shown in Figs. 4−25 and Tables A1−A2 in Appendix A, along with theoretical computations using the TALYS and CMPR programs and previously published data.

The square root of the quadratic sum of all independent statistical and systematic uncertainties was used to determine the overall uncertainties in the results. The counting statistics from the observed number of counts under the photo-peak of each γ-line (2.5%−10.5%) were the primary contributors to the ensuing statistical uncertainty. Data accumulation for an optimal duration of measurements based on the half-life of the generated nuclides was used to estimate this. In addition, the systematic uncertainties were computed using the uncertainties in the following: number of target nuclei (~0.3%), irradiation and cooling time (~0.5%), current and electron beam energy (~2.5%), detector efficiency (~3%), half-life of reaction products (~2%), distance between the sample and detector (~2%), γ-ray abundance (~2%), flux estimation (~11.5%), and normalization of the experimental data to the yield of the ¹¹⁶Cd(γ, n)¹¹⁵Cd and ¹³⁰Te(γ, n)¹²⁹Te monitor reactions (0.5%−2%). The overall systematic uncertainty is approximately 12.58%. It is determined that the overall uncertainty ranges from approximately 12% to approximately 19%.

The measured yields relative to the yield of the reaction ¹¹⁶Cd(γ, n)¹¹⁵Cd (in the case of ^natCd) and ¹³⁰Te(γ, n)¹²⁹Te (in the case of ^natTe) and cross sections per equivalent quantum for a natural mixture of isotopes are shown in Figs. 4−25 and Tables A1−A2 in Appendix A, along with theoretical computations using the TALYS and CMPR programs and previously published data.

The square root of the quadratic sum of all independent statistical and systematic uncertainties was used to determine the overall uncertainties in the results. The counting statistics from the observed number of counts under the photo-peak of each γ-line (2.5%−10.5%) were the primary contributors to the ensuing statistical uncertainty. Data accumulation for an optimal duration of measurements based on the half-life of the generated nuclides was used to estimate this. In addition, the systematic uncertainties were computed using the uncertainties in the following: number of target nuclei (~0.3%), irradiation and cooling time (~0.5%), current and electron beam energy (~2.5%), detector efficiency (~3%), half-life of reaction products (~2%), distance between the sample and detector (~2%), γ-ray abundance (~2%), flux estimation (~11.5%), and normalization of the experimental data to the yield of the ¹¹⁶Cd(γ, n)¹¹⁵Cd and ¹³⁰Te(γ, n)¹²⁹Te monitor reactions (0.5%−2%). The overall systematic uncertainty is approximately 12.58%. It is determined that the overall uncertainty ranges from approximately 12% to approximately 19%.

The measured relative yields to the yield of the reaction ¹¹⁶Cd(γ,n)¹¹⁵Cd (in the case of ^natCd) and ¹³⁰Te(γ,n)¹²⁹Te (in the case of ^natTe) and cross sections per equivalent quantum for a natural mixture of isotopes are shown in Fig. 4-25 and Tables 1-2 in Appendix, along with theoretical computations using the TALYS and CMPR programs and previously published data.

The square root of the quadratic sum of all independent statistical and systematic uncertainties was used to determine the overall uncertainties in the results. The counting statistics from the observed number of counts under the photo-peak of each γ-line (2.5%~10.5%) were the primary contributors to the ensuing statistical uncertainty. Data accumulation for an optimal duration of measurements based on the half-life of the generated nuclides was used to estimate this. The systematic uncertainties, on the other hand, were computed using the uncertainties of the following: the number of target nuclei (~0.3%), the irradiation and cooling time (~0.5%), the current and electron beam energy (~2.5%), the detector efficiency (~3%), the half-life of the reaction products (~2%), the distance between the sample and detector (~2%), the γ-ray abundance (~2%), the flux estimation (~11.5%) and normalization of the experimental data to the ¹¹⁶Cd(γ,n)¹¹⁵Cd and ¹³⁰Te(γ,n)¹²⁹Te monitor reactions’ yield 0.5-2%. Roughly 12.58% is the overall systematic uncertainty. It is determined that the overall uncertainty ranges from about 12% to about 19%.

The measured yields relative to the yield of the reaction ¹¹⁶Cd(γ, n)¹¹⁵Cd (in the case of ^natCd) and ¹³⁰Te(γ, n)¹²⁹Te (in the case of ^natTe) and cross sections per equivalent quantum for a natural mixture of isotopes are shown in Figs. 4−25 and Tables A1−A2 in Appendix A, along with theoretical computations using the TALYS and CMPR programs and previously published data.

The square root of the quadratic sum of all independent statistical and systematic uncertainties was used to determine the overall uncertainties in the results. The counting statistics from the observed number of counts under the photo-peak of each γ-line (2.5%−10.5%) were the primary contributors to the ensuing statistical uncertainty. Data accumulation for an optimal duration of measurements based on the half-life of the generated nuclides was used to estimate this. In addition, the systematic uncertainties were computed using the uncertainties in the following: number of target nuclei (~0.3%), irradiation and cooling time (~0.5%), current and electron beam energy (~2.5%), detector efficiency (~3%), half-life of reaction products (~2%), distance between the sample and detector (~2%), γ-ray abundance (~2%), flux estimation (~11.5%), and normalization of the experimental data to the yield of the ¹¹⁶Cd(γ, n)¹¹⁵Cd and ¹³⁰Te(γ, n)¹²⁹Te monitor reactions (0.5%−2%). The overall systematic uncertainty is approximately 12.58%. It is determined that the overall uncertainty ranges from approximately 12% to approximately 19%.

Five cadmium isotopes are directly generated by ^natCd(γ, n) reactions when natural cadmium is irradiated with bremsstrahlung radiation with end-point energy of 10-23 MeV. In this study, the relative yields and cross section per equivalent quantum of the ^natCd(γ, n)^{105,107,109,111m,115g,115m}Cd reactions at the bremsstrahlung end-point energies of 10-23 MeV are determined and presented in Fig. 4-8. Besides, the tabulated results are given in Appendix 1.

Five cadmium isotopes are directly generated by ^natCd(γ, n) reactions when natural cadmium is irradiated with bremsstrahlung radiation with an end-point energy of 10−23 MeV. In this study, the relative yields and cross section per equivalent quantum of the ^natCd(γ, n)^{105,107,109,111m,115g,115m}Cd reactions at the bremsstrahlung end-point energies of 10−23 MeV were determined, and the results are presented in Figs. 4−8. In addition, the tabulated results are given in Appendix A.

Five cadmium isotopes are directly generated by ^natCd(γ, n) reactions when natural cadmium is irradiated with bremsstrahlung radiation with an end-point energy of 10−23 MeV. In this study, the relative yields and cross section per equivalent quantum of the ^natCd(γ, n)^{105,107,109,111m,115g,115m}Cd reactions at the bremsstrahlung end-point energies of 10−23 MeV were determined, and the results are presented in Figs. 4−8. In addition, the tabulated results are given in Appendix A.

Five cadmium isotopes are directly generated by ^natCd(γ, n) reactions when natural cadmium is irradiated with bremsstrahlung radiation with an end-point energy of 10−23 MeV. In this study, the relative yields and cross section per equivalent quantum of the ^natCd(γ, n)^{105,107,109,111m,115g,115m}Cd reactions at the bremsstrahlung end-point energies of 10−23 MeV were determined, and the results are presented in Figs. 4−8. In addition, the tabulated results are given in Appendix A.

No literature data are available for this reaction; hence, its measurements were compared only with the theoretical calculations. Figure 4 shows the experimentally obtained and simulated values of the relative yield as well as cross section per equivalent quantum of the reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd. In Fig. 4, it is clear that the cross section per equivalent quantum, calculated by the TALYS and CMPR codes, are almost the same, but they are higher than the currently presented results for the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd reaction.

At an energy of 12 MeV, the theoretical values for the two models are 4 times higher than the experimental values. When the energy is increased to 20 MeV, the ratio $ \sigma_{q\mathrm{exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ decreases and is equal to approximately 2.5. The apparent disparity between the theoretical and experimental values may stem from the fact that statistical models of photonuclear reactions, such as the CMPR and TALYS codes, overlook the unique structural characteristics of cadmium isotopes. Alternatively, the low experimental neutron yield in the reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd can be partly explained by the bypassed character of the nucleus ¹⁰⁶Cd.

No literature data are available for this reaction; hence, its measurements were compared only with the theoretical calculations. Figure 4 shows the experimentally obtained and simulated values of the relative yield as well as cross section per equivalent quantum of the reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd. In Fig. 4, it is clear that the cross section per equivalent quantum, calculated by the TALYS and CMPR codes, are almost the same, but they are higher than the currently presented results for the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd reaction.

At an energy of 12 MeV, the theoretical values for the two models are 4 times higher than the experimental values. When the energy is increased to 20 MeV, the ratio $ \sigma_{q\mathrm{exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ decreases and is equal to approximately 2.5. The apparent disparity between the theoretical and experimental values may stem from the fact that statistical models of photonuclear reactions, such as the CMPR and TALYS codes, overlook the unique structural characteristics of cadmium isotopes. Alternatively, the low experimental neutron yield in the reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd can be partly explained by the bypassed character of the nucleus ¹⁰⁶Cd.

For this reaction, no literature data was available; hence, its measurements were only compared with the theoretical calculations. Fig. 4 shows experimental obtained and simulated values relative yields as well as cross section per equivalent quantum of reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd. In Fig. 4, it is clear that the cross section per equivalent quantum calculated by the TALYS and CMPR codes are almost the same, but they are higher than the currently presented results for the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd reaction.

At an energy of 12 MeV, the theoretical values for the two models are 4 times higher than the experimental point, then with an increase in energy to 20 MeV, the ratio $ \sigma _{qexp}^{nat}/\sigma _{qtheory}^{nat} $ decreases and is equal to approximately 2.5. The apparent disparity between theory and experiment may stem from the fact that statistical models of photonuclear reactions, such as the CMPR and TALYS codes, overlook the unique structural characteristics of cadmium isotopes. Alternatively, the low experimental neutron yield in reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd can be partly explained by bypassed character of the nucleus ¹⁰⁶Cd.

No literature data are available for this reaction; hence, its measurements were compared only with the theoretical calculations. Figure 4 shows the experimentally obtained and simulated values of the relative yield as well as cross section per equivalent quantum of the reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd. In Fig. 4, it is clear that the cross section per equivalent quantum, calculated by the TALYS and CMPR codes, are almost the same, but they are higher than the currently presented results for the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd reaction.

At an energy of 12 MeV, the theoretical values for the two models are 4 times higher than the experimental values. When the energy is increased to 20 MeV, the ratio $ \sigma_{q\mathrm{exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ decreases and is equal to approximately 2.5. The apparent disparity between the theoretical and experimental values may stem from the fact that statistical models of photonuclear reactions, such as the CMPR and TALYS codes, overlook the unique structural characteristics of cadmium isotopes. Alternatively, the low experimental neutron yield in the reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd can be partly explained by the bypassed character of the nucleus ¹⁰⁶Cd.

Figure 5 shows that the current results follow the graphical shape but are lower than the theoretical values. The experimental results (γ, n) are two times lesser than the corresponding theoretical values. This discrepancy indicates the need for further research on photoneutron reactions on ^106,108Cd.

Figure 5 shows that the current results follow the graphical shape but are lower than the theoretical values. The experimental results (γ, n) are two times lesser than the corresponding theoretical values. This discrepancy indicates the need for further research on photoneutron reactions on ^106,108Cd.

Fig. 5 shows that the current results follow the graphical shape but are lower than the theoretical values. The experimental results (γ,n) are two times as less as its theoretical counterparts. This discrepancy indicates the need for further research in the study of photoneutron reactions on ^106,108Cd.

Figure 5 shows that the current results follow the graphical shape but are lower than the theoretical values. The experimental results (γ, n) are two times lesser than the corresponding theoretical values. This discrepancy indicates the need for further research on photoneutron reactions on ^106,108Cd.

Regarding the production of ¹⁰⁹Cd from the ^natCd(γ, Xn)¹⁰⁹Cd reactions, only one previous experimental data set in the GDR energy region based on the bremsstrahlung photons is available [3]; the values were found to be lower than the theoretical values obtained using the TALYS and CMPR codes, as shown in Fig. 6. The figure shows that the current results follow the graphical shape but are lower than the theoretical values; they are the closest to the values calculated using the TALYS code.

For the production of ¹⁰⁹Cd from the ^natCd(γ, Xn)¹⁰⁹Cd reactions, only one previous experimental data sets in the GDR energy region based on bremsstrahlung photons was available [3]; this was found to be lower than the theoretical values obtained using the TALYS and CMPR codes as shown in Fig. 6. The figure shows that the current results follow the graphical shape but are lower than the theoretical values; they are the closest to the values calculated using TALYS code.

Regarding the production of ¹⁰⁹Cd from the ^natCd(γ, Xn)¹⁰⁹Cd reactions, only one previous experimental data set in the GDR energy region based on the bremsstrahlung photons is available [3]; the values were found to be lower than the theoretical values obtained using the TALYS and CMPR codes, as shown in Fig. 6. The figure shows that the current results follow the graphical shape but are lower than the theoretical values; they are the closest to the values calculated using the TALYS code.

Regarding the production of ¹⁰⁹Cd from the ^natCd(γ, Xn)¹⁰⁹Cd reactions, only one previous experimental data set in the GDR energy region based on the bremsstrahlung photons is available [3]; the values were found to be lower than the theoretical values obtained using the TALYS and CMPR codes, as shown in Fig. 6. The figure shows that the current results follow the graphical shape but are lower than the theoretical values; they are the closest to the values calculated using the TALYS code.

The measured results for the ¹¹¹Cd(γ, γ`)<sup>111m</sup>Cd and <sup>112</sup>Cd(γ, n)<sup>111m</sup>Cd reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 7. For the production of <sup>111m</sup>Cd from the <sup>nat</sup>Cd target, only one previous experimental data set in the GDR energy region based on bremsstrahlung photons is available [3]. The value was found to be lower than the theoretical values obtained using the TALYS code, as shown in Fig. 7. The figure also shows that the theoretical values from both the TALYS and CMPR codes as well as literature data are in agreement with the data from this study. Based on Fig. 7, it can also be said that in the energy range up to 11 MeV, the <sup>111m</sup>Cd nucleus is formed by the <sup>111</sup>Cd(γ, γ`)^111mCd reaction, and the contributions of the ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions to the formation of ^111mCd are equal at 12 MeV, after which the ¹¹²Cd(γ, n)^111mCd reaction plays the dominant role.

The measured results for the ¹¹¹Cd(γ, γ`)<sup>111m</sup>Cd and <sup>112</sup>Cd(γ, n)<sup>111m</sup>Cd reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 7. For the production of <sup>111m</sup>Cd from the <sup>nat</sup>Cd target, only one previous experimental data set in the GDR energy region based on bremsstrahlung photons is available [3]. The value was found to be lower than the theoretical values obtained using the TALYS code, as shown in Fig. 7. The figure also shows that the theoretical values from both the TALYS and CMPR codes as well as literature data are in agreement with the data from this study. Based on Fig. 7, it can also be said that in the energy range up to 11 MeV, the <sup>111m</sup>Cd nucleus is formed by the <sup>111</sup>Cd(γ, γ`)^111mCd reaction, and the contributions of the ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions to the formation of ^111mCd are equal at 12 MeV, after which the ¹¹²Cd(γ, n)^111mCd reaction plays the dominant role.

The measured results for the ¹¹¹Cd(γ, γ`)<sup>111m</sup>Cd and <sup>112</sup>Cd(γ, n)<sup>111m</sup>Cd reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 7. For the production of <sup>111m</sup>Cd from the <sup>nat</sup>Cd target, only one previous experimental data set in the GDR energy region based on bremsstrahlung photons is available [3]. The value was found to be lower than the theoretical values obtained using the TALYS code, as shown in Fig. 7. The figure also shows that the theoretical values from both the TALYS and CMPR codes as well as literature data are in agreement with the data from this study. Based on Fig. 7, it can also be said that in the energy range up to 11 MeV, the <sup>111m</sup>Cd nucleus is formed by the <sup>111</sup>Cd(γ, γ`)^111mCd reaction, and the contributions of the ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions to the formation of ^111mCd are equal at 12 MeV, after which the ¹¹²Cd(γ, n)^111mCd reaction plays the dominant role.

The measured results for the ¹¹¹Cd(γ, γ`)<sup>111m</sup>Cd and <sup>112</sup>Cd(γ, n)<sup>111m</sup>Cd reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 7. For the production of <sup>111m</sup>Cd from the <sup>nat</sup>Cd target, only one previous experimental data set in the GDR energy region based on bremsstrahlung photons were available [3], this was found to be lower than the theoretical values obtained using the TALYS code as shown in Fig. 7. The figure also shows that the theoretical values from both the TALYS and CMPR codes as well as literature data are in agreement with the data from this study. Based on the Fig. 7, it can also be said that in the energy range up to 11 MeV, the <sup>111m</sup>Cd nucleus is formed due to the <sup>111</sup>Cd(γ, γ`)^111mCd reaction, the contributions of the ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions to the formation of ^111mCd are equal at 12 MeV, and then the ¹¹²Cd(γ, n)^111mCd reaction plays a dominant role.

The measured results for the ¹¹⁶Cd(γ, n)^115m,gCd reactions are compared with the theoretical values obtained using the TALYS and CMPR codes in Fig. 8. Only one value is available in literature for the ¹¹⁶Cd(γ, n)^115m,gCd reaction [3] at 23 MeV. As shown in Fig. 8, it is clear that the theoretical values from both the TALYS and CMPR codes as well as the literature value are in agreement with the data from this study.

The measured results for the ¹¹⁶Cd(γ, n)^115m,gCd reactions are compared with the theoretical values obtained using the TALYS and CMPR codes in Fig. 8. Only one value is available in literature for the ¹¹⁶Cd(γ, n)^115m,gCd reaction [3] at 23 MeV. As shown in Fig. 8, it is clear that the theoretical values from both the TALYS and CMPR codes as well as the literature value are in agreement with the data from this study.

The measured results for the ¹¹⁶Cd(γ, n)^115m,gCd reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 8. There is only one literature data for the ¹¹⁶Cd(γ, n)^115m,gCd reaction [3] in 23 MeV. As shown in Fig. 8, it is clear that the theoretical values from both the TALYS and CMPR codes as well as literature data are in agreement with the data from this study.

The measured results for the ¹¹⁶Cd(γ, n)^115m,gCd reactions are compared with the theoretical values obtained using the TALYS and CMPR codes in Fig. 8. Only one value is available in literature for the ¹¹⁶Cd(γ, n)^115m,gCd reaction [3] at 23 MeV. As shown in Fig. 8, it is clear that the theoretical values from both the TALYS and CMPR codes as well as the literature value are in agreement with the data from this study.

Five argentum isotopes are directly generated by ^natCd(γ, p) reactions when natural cadmium is irradiated with bremsstrahlung radiation with end-point energy of 10-23 MeV. In this study, the relative yields and cross section per equivalent quantum of the ^natCd(γ, p)^{105,111,112,113,115}Ag reactions at the bremsstrahlung end-point energies of 12-23 MeV are determined for the first time and presented in Fig. 9-14.

Five argentum isotopes are directly generated by the ^natCd(γ, p) reactions when natural cadmium is irradiated with bremsstrahlung radiation with the end-point energy of 10−23 MeV. The relative yields and cross section per equivalent quantum of the ^natCd(γ, p)^{105,111,112,113,115}Ag reactions at the bremsstrahlung end-point energies of 12−23 MeV were determined for the first time in this study, and the results are presented in Figs. 9−14.

Five argentum isotopes are directly generated by the ^natCd(γ, p) reactions when natural cadmium is irradiated with bremsstrahlung radiation with the end-point energy of 10−23 MeV. The relative yields and cross section per equivalent quantum of the ^natCd(γ, p)^{105,111,112,113,115}Ag reactions at the bremsstrahlung end-point energies of 12−23 MeV were determined for the first time in this study, and the results are presented in Figs. 9−14.

Five argentum isotopes are directly generated by the ^natCd(γ, p) reactions when natural cadmium is irradiated with bremsstrahlung radiation with the end-point energy of 10−23 MeV. The relative yields and cross section per equivalent quantum of the ^natCd(γ, p)^{105,111,112,113,115}Ag reactions at the bremsstrahlung end-point energies of 12−23 MeV were determined for the first time in this study, and the results are presented in Figs. 9−14.

These measurements were compared only with the theoretical values owing to unavailability of published data. In Fig. 9, the measured values are revealed to be higher than the calculated values. No theoretical calculation can describe the experimental data.

The ratio $ \sigma_{\mathrm{\mathit{q}exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ is approximately 10 for the two models. As discussed in Section A1, the proton Fermi surface is significantly higher than the neutron Fermi surface in the ¹⁰⁶Cd nucleus. Because of a reduction in the effective width of the Coulomb barrier, this must raise the proton penetrabilities and, consequently, the proton yield.

The proton yield on ¹⁰⁶Cd can also be boosted by the direct photoelectric effect, which is predominantly localized at the nucleus surface. Protons are expected to dominate in β⁺-radioactive nuclei and the nuclei bordering them. The structural (shell) unique features of the target nucleus have a significant effect on the direct photonuclear reactions. Cadmium isotopes exhibit the most significant single-particle dipole excitations during the 1g_9/2 → 1h_11/2 transitions. The decay of such excitations, which have a probability of approximately 40% in both the proton and neutron channels, leads to the emission of protons with the maximum possible energy, because the final-state nucleus {Z–1, N} arises in the ground state. The energy carried away by neutrons is 3 to 4 MeV smaller, because the final-state nucleus {Z, N–1} remains in an excited (hole) state. This significantly influences the relative output of protons and neutrons in proton-rich cadmium isotopes.

Figure 10 shows the relative yields of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as well as the sum of the values for the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions. The results in Fig. 10 show that the theoretical yields of the (γ, n) and (γ, p) reactions on ¹⁰⁶Cd nuclei differ significantly from their experimental counterparts, but their summed value agrees with the respective experimental value. This means that the original photoabsorption cross section calculated using the TALYS code is unlikely to differ significantly from the true value. The discrepancy in the cross section per equivalent quantum is owing to the redistribution of the cross section between the (γ, n) and (γ, p) reactions.

These measurements were compared only with the theoretical values owing to unavailability of published data. In Fig. 9, the measured values are revealed to be higher than the calculated values. No theoretical calculation can describe the experimental data.

The ratio $ \sigma_{\mathrm{\mathit{q}exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ is approximately 10 for the two models. As discussed in Section A1, the proton Fermi surface is significantly higher than the neutron Fermi surface in the ¹⁰⁶Cd nucleus. Because of a reduction in the effective width of the Coulomb barrier, this must raise the proton penetrabilities and, consequently, the proton yield.

The proton yield on ¹⁰⁶Cd can also be boosted by the direct photoelectric effect, which is predominantly localized at the nucleus surface. Protons are expected to dominate in β⁺-radioactive nuclei and the nuclei bordering them. The structural (shell) unique features of the target nucleus have a significant effect on the direct photonuclear reactions. Cadmium isotopes exhibit the most significant single-particle dipole excitations during the 1g_9/2 → 1h_11/2 transitions. The decay of such excitations, which have a probability of approximately 40% in both the proton and neutron channels, leads to the emission of protons with the maximum possible energy, because the final-state nucleus {Z–1, N} arises in the ground state. The energy carried away by neutrons is 3 to 4 MeV smaller, because the final-state nucleus {Z, N–1} remains in an excited (hole) state. This significantly influences the relative output of protons and neutrons in proton-rich cadmium isotopes.

Figure 10 shows the relative yields of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as well as the sum of the values for the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions. The results in Fig. 10 show that the theoretical yields of the (γ, n) and (γ, p) reactions on ¹⁰⁶Cd nuclei differ significantly from their experimental counterparts, but their summed value agrees with the respective experimental value. This means that the original photoabsorption cross section calculated using the TALYS code is unlikely to differ significantly from the true value. The discrepancy in the cross section per equivalent quantum is owing to the redistribution of the cross section between the (γ, n) and (γ, p) reactions.

These measurements were only compared with the theoretical values due to unavailability of published data. In Fig. 9, the measured values are revealed to be higher than the calculated values. No theoretical calculation can describe the experimental data.

The ratio $ \sigma _{qexp}^{nat}/\sigma _{qtheory}^{nat} $ is approximately 10 for the two models. As we discussed in Section A1 that, the proton Fermi surface is significantly higher than the neutron Fermi surface in the ¹⁰⁶Cd nucleus. As a result of a reduction in the effective width of the Coulomb barrier, this must raise the proton penetrabilities and, consequently, the proton yield.

Proton yield on ¹⁰⁶Cd can also be boosted by the direct photoelectric effect, which is predominantly localised at the nucleus’ surface. Protons are expected to dominate in β⁺-radioactive nuclei and nuclei bordering them. The target nucleus's structural (shell) unique features have a significant impact on direct photonuclear reactions. Cadmium isotopes exhibit the most significant single-particle dipole excitations during the 1g_9/2 → 1h_11/2 transitions. The decay of such excitations, which have a probability of about 40% in both the proton and neutron channels, leads to the emission of protons with the maximum possible energy, because the final-state nucleus {Z-1, N} arises in the ground state. The energy carried away by neutrons is 3 to 4 MeV smaller, because the final-state nucleus {Z, N-1} remains in an excited (hole) state. This significantly influences the relative output of protons and neutrons in proton-rich cadmium isotopes.

Fig. 10 shows the relative yields of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as well as sum of the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions. The results in Fig. 10 show that the theoretical yields of the (γ,n) and (γ,p) reactions on ¹⁰⁶Cd nuclei differ significantly from their experimental counterparts, but their summed value agrees with the respective experimental value. This means that the original photoabsorption cross section calculated using the TALYS code is unlikely to differ significantly from the true value. The discrepancy in cross sections per equivalent quantum is due to the redistribution of the cross section between the (γ,n) and (γ,p) reactions.

These measurements were compared only with the theoretical values owing to unavailability of published data. In Fig. 9, the measured values are revealed to be higher than the calculated values. No theoretical calculation can describe the experimental data.

The ratio $ \sigma_{\mathrm{\mathit{q}exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ is approximately 10 for the two models. As discussed in Section A1, the proton Fermi surface is significantly higher than the neutron Fermi surface in the ¹⁰⁶Cd nucleus. Because of a reduction in the effective width of the Coulomb barrier, this must raise the proton penetrabilities and, consequently, the proton yield.

The proton yield on ¹⁰⁶Cd can also be boosted by the direct photoelectric effect, which is predominantly localized at the nucleus surface. Protons are expected to dominate in β⁺-radioactive nuclei and the nuclei bordering them. The structural (shell) unique features of the target nucleus have a significant effect on the direct photonuclear reactions. Cadmium isotopes exhibit the most significant single-particle dipole excitations during the 1g_9/2 → 1h_11/2 transitions. The decay of such excitations, which have a probability of approximately 40% in both the proton and neutron channels, leads to the emission of protons with the maximum possible energy, because the final-state nucleus {Z–1, N} arises in the ground state. The energy carried away by neutrons is 3 to 4 MeV smaller, because the final-state nucleus {Z, N–1} remains in an excited (hole) state. This significantly influences the relative output of protons and neutrons in proton-rich cadmium isotopes.

Figure 10 shows the relative yields of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as well as the sum of the values for the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions. The results in Fig. 10 show that the theoretical yields of the (γ, n) and (γ, p) reactions on ¹⁰⁶Cd nuclei differ significantly from their experimental counterparts, but their summed value agrees with the respective experimental value. This means that the original photoabsorption cross section calculated using the TALYS code is unlikely to differ significantly from the true value. The discrepancy in the cross section per equivalent quantum is owing to the redistribution of the cross section between the (γ, n) and (γ, p) reactions.

For the ¹¹²Cd(γ, p)¹¹¹Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 11. In Fig. 11, it is shown that the currently measured and theoretical values based on the CMPR code are in good agreement, in terms of not only shape but also magnitude. TALYS predicts results that are approximately 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹²Cd(γ, p)¹¹¹Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 11. In Fig. 11, it is shown that the currently measured and theoretical values based on the CMPR code are in good agreement, in terms of not only shape but also magnitude. TALYS predicts results that are approximately 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹²Cd(γ, p)¹¹¹Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 11. In Fig. 11, it is shown that the currently measured and theoretical values based on the CMPR code are in good agreement, in terms of not only shape but also magnitude. TALYS predicts results that are about almost 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹²Cd(γ, p)¹¹¹Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 11. In Fig. 11, it is shown that the currently measured and theoretical values based on the CMPR code are in good agreement, in terms of not only shape but also magnitude. TALYS predicts results that are approximately 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹³Cd(γ, p)¹¹²Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 12. In Fig. 12, it is shown that the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. TALYS predicts results that are about almost 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹³Cd(γ, p)¹¹²Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 12. In Fig. 12, the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. TALYS predicts results that are approximately 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹³Cd(γ, p)¹¹²Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 12. In Fig. 12, the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. TALYS predicts results that are approximately 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹³Cd(γ, p)¹¹²Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 12. In Fig. 12, the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. TALYS predicts results that are approximately 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹⁴Cd(γ, p)¹¹³Ag reaction, only one previous experimental data set is available for 23 MeV [3]; this value was found to be lower than the theoretical values obtained using the CMPR code, as shown in Fig. 13. In Fig. 13, the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. The results predicted by TALYS are approximately 5 times lower than the CMPR values, and this difference increases rapidly with increasing energy.

As can be seen in Figs. 11−13, a discrepancy in the experimental data for the reactions ^natCd(γ, p)^111-113Ag is clearly observed, where our results are higher than the literature data [3]. The large difference between the results in [3] and those of this study for the reactions ^natCd(γ, p)^111-113Ag might have originated from the difference in the measurement duration of the irradiated targets.

For the ¹¹⁴Cd(γ, p)¹¹³Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 13. In Fig. 13, it is shown that the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. TALYS predicts results that are about almost 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

As can be seen in Fig.11-13, it is clear that a discrepancy in experimental data on the reactions ^natCd(γ, p)^111-113Ag is observed, our results are higher than literature data [3]. The large difference between the results of the work [3] and the present ones on the reactions ^natCd(γ, p)^111-113Ag might arise from the difference in the measuring duration of the irradiated targets.

For the ¹¹⁴Cd(γ, p)¹¹³Ag reaction, only one previous experimental data set is available for 23 MeV [3]; this value was found to be lower than the theoretical values obtained using the CMPR code, as shown in Fig. 13. In Fig. 13, the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. The results predicted by TALYS are approximately 5 times lower than the CMPR values, and this difference increases rapidly with increasing energy.

As can be seen in Figs. 11−13, a discrepancy in the experimental data for the reactions ^natCd(γ, p)^111-113Ag is clearly observed, where our results are higher than the literature data [3]. The large difference between the results in [3] and those of this study for the reactions ^natCd(γ, p)^111-113Ag might have originated from the difference in the measurement duration of the irradiated targets.

For the ¹¹⁴Cd(γ, p)¹¹³Ag reaction, only one previous experimental data set is available for 23 MeV [3]; this value was found to be lower than the theoretical values obtained using the CMPR code, as shown in Fig. 13. In Fig. 13, the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. The results predicted by TALYS are approximately 5 times lower than the CMPR values, and this difference increases rapidly with increasing energy.

As can be seen in Figs. 11−13, a discrepancy in the experimental data for the reactions ^natCd(γ, p)^111-113Ag is clearly observed, where our results are higher than the literature data [3]. The large difference between the results in [3] and those of this study for the reactions ^natCd(γ, p)^111-113Ag might have originated from the difference in the measurement duration of the irradiated targets.

The measurements from the reaction were only compared with the theoretical values due to unavailability of published data. In Fig. 14, it is shown that the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. TALYS predicts results approximately 16 times lower than CMPR.

The measurements from the reaction were compared with only the theoretical values owing to unavailability of published data. In Fig. 14, the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. The results predicted by TALYS are approximately 16 times lower than the CMPR results.

The measurements from the reaction were compared with only the theoretical values owing to unavailability of published data. In Fig. 14, the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. The results predicted by TALYS are approximately 16 times lower than the CMPR results.

The measurements from the reaction were compared with only the theoretical values owing to unavailability of published data. In Fig. 14, the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. The results predicted by TALYS are approximately 16 times lower than the CMPR results.

Nine tellurium isotopes are directly generated by the ^natTe(γ, n) reactions when natural tellurium is irradiated with bremsstrahlung radiation with an end-point energy of 10-23 MeV. In this study, the relative yields and cross sections per equivalent quantum of the ^natTe(γ, n)^{119g,119m,121g,121m,123m,125m,127,129g,129m}Te reactions at the bremsstrahlung end-point energies of 10−23 MeV were determined, and the results are presented in Figs. 15−20.

Nine tellurium isotopes are directly generated by the ^natTe(γ, n) reactions when natural tellurium is irradiated with bremsstrahlung radiation with an end-point energy of 10-23 MeV. In this study, the relative yields and cross sections per equivalent quantum of the ^natTe(γ, n)^{119g,119m,121g,121m,123m,125m,127,129g,129m}Te reactions at the bremsstrahlung end-point energies of 10−23 MeV were determined, and the results are presented in Figs. 15−20.

Nine tellurium isotopes are directly generated by ^natTe(γ, n) reactions when natural tellurium is irradiated with bremsstrahlung radiation with end-point energy of 10-23 MeV. In this study, the relative yields and cross sections per equivalent quantum of the ^natTe(γ, n)^{119g,119m,121g,121m,123m,125m,127,129g,129m}Te reactions at the bremsstrahlung end-point energies of 10-23 MeV are determined and presented in Fig. 15-20.

Nine tellurium isotopes are directly generated by the ^natTe(γ, n) reactions when natural tellurium is irradiated with bremsstrahlung radiation with an end-point energy of 10-23 MeV. In this study, the relative yields and cross sections per equivalent quantum of the ^natTe(γ, n)^{119g,119m,121g,121m,123m,125m,127,129g,129m}Te reactions at the bremsstrahlung end-point energies of 10−23 MeV were determined, and the results are presented in Figs. 15−20.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 15. There is only one value in literature for the ¹²⁰Te(γ, n)¹¹⁹Te reaction [22] in the energy range of the γ quantum (8.03−26.46 MeV). The theoretical values from both the TALYS and CMPR codes align with the literature data; however, our results are inferior to them, as shown in Fig. 15.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 15. There is only one value in literature for the ¹²⁰Te(γ, n)¹¹⁹Te reaction [22] in the energy range of the γ quantum (8.03−26.46 MeV). The theoretical values from both the TALYS and CMPR codes align with the literature data; however, our results are inferior to them, as shown in Fig. 15.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 15. There is only one literature data for the ¹²⁰Te(γ, n)¹¹⁹Te reaction [22] in the energy range of γ quantum 8.03-26.46 MeV. The theoretical values from both the TALYS and CMPR codes align with the literature data; yet, our results are inferior to them, as shown in Fig. 15.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 15. There is only one value in literature for the ¹²⁰Te(γ, n)¹¹⁹Te reaction [22] in the energy range of the γ quantum (8.03−26.46 MeV). The theoretical values from both the TALYS and CMPR codes align with the literature data; however, our results are inferior to them, as shown in Fig. 15.

The measured results for the ¹²²Te(γ,n)¹²¹Te and ¹²³Te(γ,2n)¹²¹Te reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 16. The measured values for the reaction are lower than the calculated values, as seen in Fig. 16.

The measured results for the ¹²²Te(γ, n)¹²¹Te and ¹²³Te(γ, 2n)¹²¹Te reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 16. The figure shows that the measured values for the reaction are lower than the calculated values.

The measured results for the ¹²²Te(γ, n)¹²¹Te and ¹²³Te(γ, 2n)¹²¹Te reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 16. The figure shows that the measured values for the reaction are lower than the calculated values.

The measured results for the ¹²²Te(γ, n)¹²¹Te and ¹²³Te(γ, 2n)¹²¹Te reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 16. The figure shows that the measured values for the reaction are lower than the calculated values.

The measured results for the ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe and ¹²⁵Te(γ, 2n)^123mTe reactions are compared with the theoretical values obtained with the TALYS code, as shown in Fig. 17. The measured values for the reaction are lower than the calculated values, as seen in Fig. 17.

The measured results for the ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe, and ¹²⁵Te(γ, 2n)^123mTe reactions are compared with the theoretical values obtained with the TALYS code in Fig. 17. The figure shows that the measured values for the reaction are lower than the calculated values.

The measured results for the ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe, and ¹²⁵Te(γ, 2n)^123mTe reactions are compared with the theoretical values obtained with the TALYS code in Fig. 17. The figure shows that the measured values for the reaction are lower than the calculated values.

The measured results for the ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe, and ¹²⁵Te(γ, 2n)^123mTe reactions are compared with the theoretical values obtained with the TALYS code in Fig. 17. The figure shows that the measured values for the reaction are lower than the calculated values.

The measured results for the ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions are compared with the theoretical values obtained with the TALYS code in Fig. 18. As can be seen in Fig. 18(a), the measured values for the reaction are higher than the calculated values. This may be because the nucleus ^125mTe emits a γ-ray with a low intensity (109.28 keV (0.28%)). However, with the exception of the data for 10−12 MeV, a good agreement is observed between the measured data and TALYS value in Fig. 18(b).

The measured results for the ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions are compared with the theoretical values obtained with the TALYS code in Fig. 18. As can be seen in Fig. 18(a), the measured values for the reaction are higher than the calculated values. This may be because the nucleus ^125mTe emits a γ-ray with a low intensity (109.28 keV (0.28%)). However, with the exception of the data for 10−12 MeV, a good agreement is observed between the measured data and TALYS value in Fig. 18(b).

The measured results for the ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions are compared with the theoretical values obtained with the TALYS code in Fig. 18. As can be seen in Fig. 18(a), the measured values for the reaction are higher than the calculated values. This may be because the nucleus ^125mTe emits a γ-ray with a low intensity (109.28 keV (0.28%)). However, with the exception of the data for 10−12 MeV, a good agreement is observed between the measured data and TALYS value in Fig. 18(b).

The measured results for the ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions are compared with the theoretical values obtained with the TALYS code, as shown in Fig. 18. As can be seen in Fig. 18a, the measured values for the reaction are higher than the calculated values. This may be due to the fact that the nucleus ^125mTe emits a γ-ray with low intensity (109.28 keV (0.28%)). However, with exception data in 10-12 MeV, there is a good agreement between measured data and TALYS value in Fig. 18b.

The measured results for the ¹²⁸Te(γ,n)¹²⁷Te reaction are compared with the theoretical values obtained with the TALYS, as shown in Fig. 19. The measured values for the reaction are lower than the calculated values, as seen in Fig. 19. There is a good agreement between literature data and theoretical calculations.

The measured results for the ¹²⁸Te(γ,n)¹²⁷Te reaction are compared with the theoretical values obtained with TALYS in Fig. 19. The figure shows that the measured values for the reaction are lower than the calculated values. There is a good agreement between the literature data and theoretical calculations.

The measured results for the ¹²⁸Te(γ,n)¹²⁷Te reaction are compared with the theoretical values obtained with TALYS in Fig. 19. The figure shows that the measured values for the reaction are lower than the calculated values. There is a good agreement between the literature data and theoretical calculations.

The measured results for the ¹²⁸Te(γ,n)¹²⁷Te reaction are compared with the theoretical values obtained with TALYS in Fig. 19. The figure shows that the measured values for the reaction are lower than the calculated values. There is a good agreement between the literature data and theoretical calculations.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 20. There is only one literature data for the ¹³⁰Te(γ, n)¹²⁹Te reaction [22] in the energy range of γ quantum 8.03-26.46 MeV. It is clear that the theoretical values from both the TALYS and CMPR codes are in agreement with the literature data, but our results are below them, as shown in Fig. 20.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 20. Only one value is available in literature for the ¹³⁰Te(γ, n)¹²⁹Te reaction [22] in the energy range of the γ quantum (8.03−26.46 MeV). It is clear that the theoretical values from both the TALYS and CMPR codes are in agreement with the literature data, but our results are lower, as shown in Fig. 20.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 20. Only one value is available in literature for the ¹³⁰Te(γ, n)¹²⁹Te reaction [22] in the energy range of the γ quantum (8.03−26.46 MeV). It is clear that the theoretical values from both the TALYS and CMPR codes are in agreement with the literature data, but our results are lower, as shown in Fig. 20.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 20. Only one value is available in literature for the ¹³⁰Te(γ, n)¹²⁹Te reaction [22] in the energy range of the γ quantum (8.03−26.46 MeV). It is clear that the theoretical values from both the TALYS and CMPR codes are in agreement with the literature data, but our results are lower, as shown in Fig. 20.

Four stibium (¹²²Sb, ¹²⁴Sb, ¹²⁷Sb, ¹²⁹Sb) radioisotopes were directly produced by the ^natTe(γ, p) reactions. The relative yields and cross section per equivalent quantum of the ^natTe(γ, p)^{122,124,127,129}Sb reactions at the bremsstrahlung end-point energies of 10−23 MeV were determined for the first time in this study and are presented in Figs. 21−25.

Four stibium (¹²²Sb, ¹²⁴Sb, ¹²⁷Sb, ¹²⁹Sb) radioisotopes were directly produced by the ^natTe(γ, p) reactions. The relative yields and cross section per equivalent quantum of the ^natTe(γ, p)^{122,124,127,129}Sb reactions at the bremsstrahlung end-point energies of 10−23 MeV were determined for the first time in this study and are presented in Figs. 21−25.

Four stibium (¹²²Sb, ¹²⁴Sb, ¹²⁷Sb, ¹²⁹Sb) radioisotopes were directly produced by the ^natTe(γ, p) reactions. The relative yields and cross section per equivalent quantum of the ^natTe(γ, p)^{122,124,127,129}Sb reactions at the bremsstrahlung end-point energies of 10−23 MeV were determined for the first time in this study and are presented in Figs. 21−25.

Four stibium (¹²²Sb, ¹²⁴Sb, ¹²⁷Sb, ¹²⁹Sb) radioisotopes were directly produced by ^natTe(γ, p) reactions. In this study, the relative yields and cross section per equivalent quantum of the ^natTe(γ, p)^{122,124,127,129}Sb reactions at the bremsstrahlung end-point energies of 10-23 MeV are determined for the first time and presented in Fig. 21-25.

Fig. 21 displays the measured data as well as the computed values. It is evident from the Fig. 21 that there is good agreement between the theoretical values on the basis of CMPR only for 22 and 23 MeV. The remaining experimental points are almost 100 times larger than theoretical calculations.

Since the threshold of the reaction ¹²⁴Te(γ, d)¹²²Sb is 15.33 MeV, then we can assume that up to 19 MeV (taking into account the Coulomb barrier) the nucleus ¹²²Sb is formed as a result of the reaction ¹²³Te(γ, p). Fig. 22 shows the ratios of the cross section per equivalent quantum $ \sigma _{qexp}^{nat}/\sigma _{qtheory}^{nat} $ for the (γ, p) reaction on ¹²³Te. As can be seen in Fig. 22, both models cannot describe the experimental points.

Figure 21 displays the measured data and computed values. It is evident from Fig. 21 that the theoretical values based on the CMPR show a good agreement only for 22 and 23 MeV. The remaining experimental points are almost 100 times larger than the theoretical calculations.

Because the threshold of the reaction ¹²⁴Te(γ, d)¹²²Sb is 15.33 MeV, we can assume that up to 19 MeV (considering the Coulomb barrier), the nucleus ¹²²Sb is formed as a result of the reaction ¹²³Te(γ, p). Figure 22 shows the ratios of the cross section per equivalent quantum $ \sigma_{q\mathrm{exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ for the (γ, p) reaction on ¹²³Te. As can be seen in Fig. 22, both models cannot describe the experimental points.

Figure 21 displays the measured data and computed values. It is evident from Fig. 21 that the theoretical values based on the CMPR show a good agreement only for 22 and 23 MeV. The remaining experimental points are almost 100 times larger than the theoretical calculations.

Because the threshold of the reaction ¹²⁴Te(γ, d)¹²²Sb is 15.33 MeV, we can assume that up to 19 MeV (considering the Coulomb barrier), the nucleus ¹²²Sb is formed as a result of the reaction ¹²³Te(γ, p). Figure 22 shows the ratios of the cross section per equivalent quantum $ \sigma_{q\mathrm{exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ for the (γ, p) reaction on ¹²³Te. As can be seen in Fig. 22, both models cannot describe the experimental points.

Figure 21 displays the measured data and computed values. It is evident from Fig. 21 that the theoretical values based on the CMPR show a good agreement only for 22 and 23 MeV. The remaining experimental points are almost 100 times larger than the theoretical calculations.

Because the threshold of the reaction ¹²⁴Te(γ, d)¹²²Sb is 15.33 MeV, we can assume that up to 19 MeV (considering the Coulomb barrier), the nucleus ¹²²Sb is formed as a result of the reaction ¹²³Te(γ, p). Figure 22 shows the ratios of the cross section per equivalent quantum $ \sigma_{q\mathrm{exp}}^{\mathrm{nat}}/\sigma_{q\mathrm{theory}}^{\mathrm{nat}} $ for the (γ, p) reaction on ¹²³Te. As can be seen in Fig. 22, both models cannot describe the experimental points.

The measured results for the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 23. A discrepancy between the theoretical calculations is clearly observed, and the experimental points are higher than the TALYS curve but lower than the CMPR curve with an exception at 19 MeV (this point is in good agreement with the TALYS calculation).

The measured results for the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 23. It is clear that there is a discrepancy between theoretical calculations, and the experimental points are higher than the TALYS curve, but lower than the CMPR curve with an exception 19 MeV (this point is in good agreement with the TALYS calculation).

The measured results for the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 23. A discrepancy between the theoretical calculations is clearly observed, and the experimental points are higher than the TALYS curve but lower than the CMPR curve with an exception at 19 MeV (this point is in good agreement with the TALYS calculation).

The measured results for the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 23. A discrepancy between the theoretical calculations is clearly observed, and the experimental points are higher than the TALYS curve but lower than the CMPR curve with an exception at 19 MeV (this point is in good agreement with the TALYS calculation).

The measured results for the ¹²⁸Te(γ, p)¹²⁷Sb reaction are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 24. It is evident from Fig. 24 that the theoretical values based on the CMPR and the measured values in this study agree well in terms of both form and magnitude.

The measured results for the ¹²⁸Te(γ, p)¹²⁷Sb reaction are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 24. It is evident from Fig. 24 that the theoretical values based on the CMPR and the measured values in this study agree well in terms of both form and magnitude.

The measured results for the ¹²⁸Te(γ,p)¹²⁷Sb reaction are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 24. It is evident from the Fig. 24 that there is good agreement between the theoretical values on the basis of CMPR and currently measured values in terms of both form and magnitude.

The measured results for the ¹²⁸Te(γ, p)¹²⁷Sb reaction are compared with the theoretical values obtained with the TALYS and CMPR codes in Fig. 24. It is evident from Fig. 24 that the theoretical values based on the CMPR and the measured values in this study agree well in terms of both form and magnitude.

Figure 25 displays the measured data and the computed values. A discrepancy between the theoretical calculations is clearly observed, and the experimental points are higher than the TALYS curve but lower than the CMPR curve. The experimentally obtained results lie closer to the theoretical curve obtained from the CMPR.

Figure 25 displays the measured data and the computed values. A discrepancy between the theoretical calculations is clearly observed, and the experimental points are higher than the TALYS curve but lower than the CMPR curve. The experimentally obtained results lie closer to the theoretical curve obtained from the CMPR.

Fig. 25 displays the measured data as well as the computed values. It is clear that there is a discrepancy between theoretical calculations, and the experimental points are higher than the TALYS curve, but lower than the CMPR curve. The experimentally obtained results lie closer to the theoretical curve according to the CMPR.

Figure 25 displays the measured data and the computed values. A discrepancy between the theoretical calculations is clearly observed, and the experimental points are higher than the TALYS curve but lower than the CMPR curve. The experimentally obtained results lie closer to the theoretical curve obtained from the CMPR.

The irradiation of the natural mixtures of Cd and Te allows us to study photonuclear reactions over a wide mass range of A=106−130. The cross section per equivalent quantum of the (γ, p) reaction in the case of monoisotopes σ_q calculated using CMPR and TALYS by applying Eq. (5) are contrasted against the experimental data in Fig. 26. The data in Fig. 26 show that the measured yields of the (γ, p) reactions on the isotopes ^{112,113,114,116}Cd and ^128,130Te agree within 30% with the results of the calculations based on the CMPR. The (γ, p) yields calculated using the TALYS code are underestimated with respect to the experimental data by one order of magnitude. The reason behind this difference is that the TALYS code disregards the special features of the decay of the T_> GDR component, where the decay through the proton channel to low-lying states of the final nucleus is forbidden by the isospin-selection rules. Thus, the T_> states decay through the proton channel with a higher probability. The cross section per equivalent quantum calculations for the reactions ¹¹⁴Cd(γ, p)¹¹³Ag and ¹²⁸Te(γ, p)¹²⁷Sb using the TALYS parameters, models of the nuclear level densities and γ-ray strength functions, and accounting for isospin splitting in the CMPR are given in Appendix B.

Figure 26.  (color online) Cross section per equivalent quantum of the (γ, p) reaction in the case of monoisotopes σ_q for the stable isotopes of cadmium (a) and tellurium (b).

The measured (γ, p) yields are a few percent of the (γ,n) yields for all nuclei, with the exception of the ¹⁰⁶Cd nucleus, for which the yield of the reaction ¹⁰⁶Cd(γ, p)¹⁰⁵Cd is commensurate with the yield of the reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd, but this contradicts the results of the theoretical calculations in [24, 25]. The situation is unclear for the ¹²³Te(γ, p)¹²²Sb reaction. In all experiments, the spectra show a line at 564 keV. However, theoretical calculations using TALYS and CMPR are several orders of magnitude smaller.

For a more thorough analysis of the obtained results, the ratios between the reaction yields (γ,p) and (γ,n) were calculated for the nuclei ¹⁰⁶Cd (¹⁰⁵Ag/¹⁰⁵Cd), ¹¹⁶Cd (¹¹⁵Ag/¹¹⁵Cd), ¹²⁸Te (¹²⁷Sb/¹²⁷Te), and ¹³⁰Te (¹²⁹Sb/¹²⁹Te). In addition, the ratios of the yields (γ, p)/(γ, n) were calculated for the nucleus ⁷⁴Se based on the experimental results in our previous study [40]. Figure 27(a) shows that the ratio between the reaction yields (γ, p) and (γ, n) depends on the electron energy of the accelerator. As shown in Fig. 27(a), the ratios of the yields (γ, p)/(γ, n) are almost equal to 1 for the bypassed nuclei ⁷⁴Se and ¹⁰⁶Cd. It can be seen that with the exception of the points for the nucleus ¹⁰⁶Cd, the experimental points are consistent with the calculated curves of the CMPR. In the case of ¹⁰⁶Cd (¹⁰⁵Ag/¹⁰⁵Cd), CMPR and TALYS cannot describe the experimental results. The reason for the observed discrepancy between theory and experiment may be explained by the fact that statistical models of photonuclear reactions do not consider the individual structural features of the Cd isotopes.

Figure 27.  (color online) Ratio of the reaction yields (γ, p)/(γ, n) as functions of: (a) the electron energy of the accelerator and (b) the proton-neutron ratio N/Z at the electron energy of 23 MeV of the accelerator.

Figure 27(b) shows the ratios of the yields (γ, p)/(γ, n) as functions of the proton-neutron ratio N/Z at the electron energy of 23 MeV of the accelerator. The literature data were calculated using the experimentally measured reaction cross sections (γ, p) and (γ, n) on the nuclei ⁹⁰Zr [41–42], ⁸⁹Y [42–43], ¹⁰³Rh [1, 44], ¹¹²Sn [45–46], and ¹⁶⁰Gd [47]. With the exception of the points at N/Z = 1.176 (⁷⁴Se) and 1.208 (¹⁰⁶Cd), the experimental points are consistent with the curve calculated using the CMPR. The ratio of the yields (γ, p)/(γ, n) decreases with increasing proton-neutron ratio N/Z.

The irradiation of the natural mixtures of Cd and Te allows us to study photonuclear reactions over a wide mass range of A=106−130. The cross section per equivalent quantum of the (γ, p) reaction in the case of monoisotopes σ_q calculated using CMPR and TALYS by applying Eq. (5) are contrasted against the experimental data in Fig. 26. The data in Fig. 26 show that the measured yields of the (γ, p) reactions on the isotopes ^{112,113,114,116}Cd and ^128,130Te agree within 30% with the results of the calculations based on the CMPR. The (γ, p) yields calculated using the TALYS code are underestimated with respect to the experimental data by one order of magnitude. The reason behind this difference is that the TALYS code disregards the special features of the decay of the T_> GDR component, where the decay through the proton channel to low-lying states of the final nucleus is forbidden by the isospin-selection rules. Thus, the T_> states decay through the proton channel with a higher probability. The cross section per equivalent quantum calculations for the reactions ¹¹⁴Cd(γ, p)¹¹³Ag and ¹²⁸Te(γ, p)¹²⁷Sb using the TALYS parameters, models of the nuclear level densities and γ-ray strength functions, and accounting for isospin splitting in the CMPR are given in Appendix B.

Figure 26.  (color online) Cross section per equivalent quantum of the (γ, p) reaction in the case of monoisotopes σ_q for the stable isotopes of cadmium (a) and tellurium (b).

The measured (γ, p) yields are a few percent of the (γ,n) yields for all nuclei, with the exception of the ¹⁰⁶Cd nucleus, for which the yield of the reaction ¹⁰⁶Cd(γ, p)¹⁰⁵Cd is commensurate with the yield of the reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd, but this contradicts the results of the theoretical calculations in [24, 25]. The situation is unclear for the ¹²³Te(γ, p)¹²²Sb reaction. In all experiments, the spectra show a line at 564 keV. However, theoretical calculations using TALYS and CMPR are several orders of magnitude smaller.

For a more thorough analysis of the obtained results, the ratios between the reaction yields (γ,p) and (γ,n) were calculated for the nuclei ¹⁰⁶Cd (¹⁰⁵Ag/¹⁰⁵Cd), ¹¹⁶Cd (¹¹⁵Ag/¹¹⁵Cd), ¹²⁸Te (¹²⁷Sb/¹²⁷Te), and ¹³⁰Te (¹²⁹Sb/¹²⁹Te). In addition, the ratios of the yields (γ, p)/(γ, n) were calculated for the nucleus ⁷⁴Se based on the experimental results in our previous study [40]. Figure 27(a) shows that the ratio between the reaction yields (γ, p) and (γ, n) depends on the electron energy of the accelerator. As shown in Fig. 27(a), the ratios of the yields (γ, p)/(γ, n) are almost equal to 1 for the bypassed nuclei ⁷⁴Se and ¹⁰⁶Cd. It can be seen that with the exception of the points for the nucleus ¹⁰⁶Cd, the experimental points are consistent with the calculated curves of the CMPR. In the case of ¹⁰⁶Cd (¹⁰⁵Ag/¹⁰⁵Cd), CMPR and TALYS cannot describe the experimental results. The reason for the observed discrepancy between theory and experiment may be explained by the fact that statistical models of photonuclear reactions do not consider the individual structural features of the Cd isotopes.

Figure 27.  (color online) Ratio of the reaction yields (γ, p)/(γ, n) as functions of: (a) the electron energy of the accelerator and (b) the proton-neutron ratio N/Z at the electron energy of 23 MeV of the accelerator.

Figure 27(b) shows the ratios of the yields (γ, p)/(γ, n) as functions of the proton-neutron ratio N/Z at the electron energy of 23 MeV of the accelerator. The literature data were calculated using the experimentally measured reaction cross sections (γ, p) and (γ, n) on the nuclei ⁹⁰Zr [41–42], ⁸⁹Y [42–43], ¹⁰³Rh [1, 44], ¹¹²Sn [45–46], and ¹⁶⁰Gd [47]. With the exception of the points at N/Z = 1.176 (⁷⁴Se) and 1.208 (¹⁰⁶Cd), the experimental points are consistent with the curve calculated using the CMPR. The ratio of the yields (γ, p)/(γ, n) decreases with increasing proton-neutron ratio N/Z.

Since we are irradiating natural mixtures of Cd and Te, this will give us the opportunity to study photonuclear reactions over a wide mass range with A=106-130. The cross section per equivalent quantum of the (γ,p) reaction in a case of monoisotopes σ_q calculated on the basis of the CMPR and TALYS by equation (5) are contrasted against experimental data in Fig. 26. The data in Fig. 26 shows that the measured yields of the (γ,p) reactions on the isotopes ^{112,113,114,116}Cd and ^128,130Te agree within 30% with the results of the calculations based on the CMPR. The (γ,p) yields calculated on the basis of the TALYS code are underestimated with respect to experimental data by one order of magnitude. The reason behind this difference is that the TALYS code disregards special features of the decay of the T_> GDR component, whose decay through the proton channel to low-lying states of the final nucleus is forbidden by isospin-selection rules. As a result, T_> states decay through the proton channel with a higher probability. The cross section per equivalent quantum calculations for the reactions ¹¹⁴Cd(γ,p)¹¹³Ag and ¹²⁸Te(γ,p)¹²⁷Sb using TALYS parameters on the basis of the models of the nuclear level densities and γ-ray strength functions and accounting of isospin splitting in CMPR are given in Appendix 2.