Monopole effects and high-spin levels in neutron-rich 132Te

  • The neutron-rich nuclei near doubly magic 132Sn have attracted considerable interest in both nuclear physics and nuclear astrophysics. For the particle-hole nuclei in this region, the low-lying and high core excitations have been well described by shell model calculations using the extended pairing plus multipole-multipole force model. However, there is a significant difference between experiment and theory in the high-spin level 17+ of 132Te. We intend to illustrate this difference through monopole interactions. For this purpose, the monopole corrections between π(ν)0g7/2, ν1d5/2 and π(ν)0h11/2 are investigated in 132134Te, 131133Sb, and 130Sn. Some theoretical levels are connected to the (17+) state of 132Te with the monopole correction (Mc) of Mc(νd5/2,νh11/2) and the quadruple-quadruple force between the proton and neutron, i.e., levels 3(8) in 130Sn, level 14 in 132Te, and level 23/2 in 131Sb. Their observations at lower energies can confirm the datum of level (17+) in 132Te with an illustration of monopole effects and quadruple-quadruple force.
      PCAS:
    • 21.30.Fe(Forces in hadronic systems and effective interactions)
  • The analysis of neutron-rich isotopes near the doubly magic nucleus 132Sn can provide fascinating findings related to nuclear physics and nuclear astrophysics. The abundance peak appears at A130, which is formed through the rapid neutron capture process [1, 2]. The properties of doubly magic 132Sn have been explored and confirmed in both experiments and theories [38]. In this nuclei region, tellurium isotopes have attracted experimental and theoretical research interest [5, 913]. For example, the g-factor of 134Te in the 4+ state was measured, which provides direct insight into the single particle structure [9]. The state (17+) of 132Te was observed to be 6.166 MeV using the reaction 9Be(238U, f ) with a beam energy of 6.2 MeV/u at GANIL [14]. A significant energy difference exists in this state between experiments and shell-model calculations, which should conceal unknown information about the nuclear structure.

    In theory, the extended pairing plus multipole-multipole force and monopole correction terms model (EPQQM) provides a suitable method to describe both the low-lying states and core excitations [1518]. For example, the ordering and energies of the low-lying isomers in 129Cd are predicted and determined by using the implemented phase-imaging ion-cyclotron-resonance method [18, 19]. The 16+ level in 128Cd is predicted as a spin-trap isomer feeding the known 16+ of 128In through β decay [20]. In addition to monopole interactions, it is necessary to consider the cross-shell excitations to study the properties of these neutron-rich nuclei in this region. For example, identifying the isomer state of level 19/2+ at 1942 keV in 133Ba requires the cross-shell orbits lying above the energy gap N=82. As reported in Ref. [21], the interactions without core excitations cannot provide the B(E1) value for the transition from Jπ=19/2+ to Jπ=19/2.

    This model has an advantage for studying monopole effects by employing monopole correction (Mc) terms. For example, in the southwest quadrant (Z50,N82) of 132Sn, the level spectra and the energy gap across N=82 can be modified by monopole correction between neutron orbit h11/2 and f7/2 [15]. In the northeast quadrant (Z50,N82), five monopole terms are used to describe core excitations and high-spin levels, and the states 2 and 9 in 136,138Te are predicted as a spin-trap structure coupled by the neutron intruder orbit i13/2 [22]. Different effects of tensor forces are also discussed together with the monopole-driven shell evolutions [23], as well as other ones in the nucleon-nucleon interaction [2427]. For the particle-hole nuclei in the northwest region of 132Sn, a suitable interaction has been found, and the spectra of Sb and Te isotopes are well described as single-orbital couplings and cross-shell excitations [18, 28]. The transition probabilities in these nuclei are also calculated and reproduced well through comparisons with the known data.

    In this study, we investigate high-spin levels and monopole effects in particle-hole nuclei near 132Sn by employing the interaction in Ref. [18]. The shell-model code NUSHELLX@MSU is used for the calculations [29].

    In this work, we use the Hamiltonian in the proton-neutron (pn) representation [18]:

    H=Hsp+HP0+HP2+HQQ+HOO+HHH+Hmc=α,iεiacα,icα,i12J=0,2iigJ,iiMPJM,iiPJM,ii12iiχ2,iib4M:Q2M,iiQ2M,ii:12iiχ3,iib6M:O3M,iiO3M,ii:12iiχ4,iib8M:H4M,iiH4M,ii:+ac,iikmc(ia,ic)JMAJM(ia,ic)AJM(ia,ic).

    (1)

    Equation (1) includes the single-particle Hamiltonian (Hsp); the J=0 and J=2 pairings (P0P0 and P2P2); the quadrupole-quadrupole (QQ), octupole-octupole (OO), and hexadecapole-hexadecapole (HH) terms; and the monopole corrections (Hmc). In the pn-representation, PJM,ii and AJM(ia,ic) are the pair operators, while Q2M,ii, O3M,ii, and H4M,ii are the quadrupole, octupole, and hexadecapole operators, respectively, in which i (i) is an index for protons (neutrons). The parameters gJ,ii, χ2,ii, χ3,ii, χ4,ii, and kmc(ia,ic) are the corresponding force strengths, and b is the harmonic-oscillator range parameter.

    The model space includes five orbits (0g7/2,1d5/2,1d3/2,2s1/2,0h11/2) for both protons and neutrons. Two extra neutron orbits above the N=82 shell, i.e., (1f7/2 and 2p3/2), are added to allow neutron cross-shell excitations. We keep the same parameters of single-particle energies and the two-body force strengths used in Ref. [18]. The monopole interactions were found to be crucial for describing nuclear properties, which are entirely responsible for global saturation properties and single-particle behavior. The neutron-rich nuclei near 132Sn can be divided into four quadrants by the crossing of Z=50 and N=82. According to nuclei studied previously [15, 22, 30], the monopole corrections are necessary for the hole (particle) nuclei in the southwest (northeast) quadrant of 132Sn.

    In southwest quadrant (Z50,N82), the ground state inversion in 129Cd can be well described by the monopole correction between proton orbit 0g9/2 and neutron orbit 0h11/2 with a strength of –0.40 MeV [17], and it was verified using the recently implemented phase-imaging ion-cyclotron-resonance method [19]. Recently, the ground-state inversions from N=81 to N=79 were explained for the first time by monopole correction between neutron orbits h11/2 and d3/2. Furthermore, this monopole correction has been found in different isotonic chains of N=79,80,81, as all being hole nuclei near 132Sn.

    In the northeast quadrant (Z50,N82), five monopole terms are used to describe core excitations and high-spin levels [22]. For particle-pole nuclei in the northwest quadrant of 132Sn (Z50,N82), the protons and neutrons occupy the same major shell. The properties of particle-hole nuclei can be well described without additional monopole correlations [28]. Such a situation is confirmed by the electromagnetic transitions of Sb and Te isotopes in the northwest quadrant of 132Sn [28, 31], which is a strict test for shell model calculations. However, in level 17+ of 132Te, the large difference between experiment and theory motivates us to investigate monopole interactions in the particle-hole nuclei region near 132Sn.

    In this part, high-spin levels are investigated with the monopole effects and quadruple-quadruple force in 132134Te, 131133Sb, and 130Sn. The monopole correction alone cannot solve the puzzle of level 17+; it should be combined with quadrupole correction. As shown in Table 1, there are four different types of level 17+ under 10 MeV according to the EPQQM model, i.e., Nos. 1 to 4. The possibility of neutron core excitation (config.1 in Table 1) at 8.189 MeV can be excluded to explain the high-spin level 17+ of 132Te [28]. The given experimental data of 134Te and 133Sb have been reproduced very well as core excitations with a common neutron configuration of νh111/2f7/2 (Fig. 1). If we modify the monopole term of Mc(νh111/2,νf7/2) to explain the level 17+ of 132Te, the 17 states of neutron core excitations would catastrophically depart from their corresponding data.

    Figure 1

    Figure 1.  (color online) Neutron core excitations in 134Te and 133Sb nuclei. Corresponding data are from Ref. [32].

    Table 1

    Table 1.  17+ states in 132Te with main configurations. The data are from Ref. [14].
    132TeEx(MeV)Config.
    JπTh.Exp.No.P(\%)
    (17+)8.1896.1661. πg27/2νh311/2f7/288
    8.7792. πg7/2h11/2νg17/2h111/276
    9.1253. πg7/2h11/2νd15/2h111/272
    9.3144. πh211/2νh211/293
    DownLoad: CSV
    Show Table

    After excluding neutron core excitation, we focus on the level at 8.779 MeV coupled by config.2 πg7/2h11/2νg17/2h111/2. This level can be affected by these monopole terms from this configuration, i.e., Mc(πg7/2,πh11/2), Mc(νg7/2,νh11/2), and Mc(πg7/2,νh11/2). The level at 8.779 MeV is abandoned, since the biggest difference is only 0.227 MeV in level 3 of 132Sb (Fig. 2). For the 17+ level at 9.314 MeV, it has a new monopole term of Mc(πh11/2νh11/2). This monopole term has almost no effects in levels 17+ coupled by config.1, 2, and 3. (κ=0.10.9 MeV), while the level 17+ at 9.314 MeV drops to 8.3 MeV (Fig. 3). The level at 9.134 MeV is excluded too, because all 17+ levels are increased sharply when the strength is κ>0.9 MeV. For the last one coupled by config.3, the suitable monopole term Mc(νd5/2,νh11/2) is turned up from this configuration. Its monopole effects are investigated in the states of 132Te from 0+ to 17+ by adding Mc(νd5/2,νh11/2) = –2.6 MeV. As shown in Fig. 4, the level 17+ is reduced to 6.311 MeV, but the values of the 5 and 7 levels become far from the corresponding data.

    Figure 2

    Figure 2.  (color online) Levels produced by particular configurations in 134Te, 133Te, 132Sb, 131Sb, and 130Sn nuclei, in comparison with given data [32].

    Figure 3

    Figure 3.  (color online) Monopole effects of Mc(πh11/2νh11/2) in level 17+ of 132Te.

    Figure 4

    Figure 4.  (color online) Monopole effects of Mc(νd5/2,νh11/2) in 132Te. Data marked with stars are from Ref. [32].

    As shown above, the monopole interaction alone cannot solve the present puzzle, and we focus on the quadrupole-quadrupole force between the proton and neutron (QQπ,ν).

    As shown in Fig. 5, the value of theQQπ,ν force equals the quadruple-quadruple force strength divided by [1/A(132Sn)]5/3. The level 17+ coupled by configuration πg7/2h11/2νh111/2d15/2 is reduced by 2.121 MeV when the QQ force changes from 300 to –450. The lowest value is 7.107 MeV, which occurs when QQπν = –350. It seems the QQπ,ν force provides a new method to explain the large difference in level 17+. As shown in Fig. 6, the datum (17+) is reproduced very well with QQπν = –350 and Mc(νd5/2,νh11/2)=0.8 MeV. Furthermore, the values of 5 and 7 levels are close to data (5) and (7). The levels 13 and 14 drop by approximately 1 MeV with QQπ,ν correction (Qc). The levels 3 and 14 are sensitive to the monopole effects of Mc(νd5/2,νh11/2). These levels are connected with datum 17+ by the QQπ,ν force and monopole effects of Mc(νd5/2,νh11/2). If they could be observed experimentally, this would be evidence confirming the datum (17+).

    Figure 5

    Figure 5.  (color online) Effects of the quadruple-quadruple force between the proton and neutron in level 17+ of 132Te.

    Figure 6

    Figure 6.  (color online) QQπ,ν force and monopole effects of Mc(νd5/2,νh11/2) in 132Te. Data marked with stars are from Refs. [14, 32].

    For determining the QQπ,ν correction and monopole term Mc(νd5/2,νh11/2), an alternative of lack data in 132Te is to study the QQπ,ν correction and monopole effects in other nuclei nearby. The monopole effects of Mc(νd5/2,νh11/2) also exist in 130Sn and 131Sb. In 130Sn, the configuration νh111/2d15/2 produces levels from 3 to 8. With the Mc(νd5/2,νh11/2), the configuration percentages have almost no change in levels 3, 7, and 8, while the percentage of level 5 (6) drops from 57% (49%) to 52% (39%). Level 3 is the first state of Jπ=3, and its energy decreases by 1.01 MeV when Mc is added. Here, the QQπ,ν force has no effect on one-shell closed nuclei. If this state could be observed near 2.199 MeV, this would be evidence for considering monopole correction in particle-hole nuclei near 132Sn. The same applies to level 8 as the first state of Jπ=8.

    In 131Sb, levels from 1/2 to 21/2 have a main configuration of πg7/2νh111/2. As shown in Fig. 7(b), the QQπ,ν correction has obvious effects on levels 1/2, 3/2, 5/2, 21/2, and 23/2, while monopole correction Mc has almost no effects except in the case of level 23/2. The lowest energy level of Jπ=23/2 drops to 2.570 MeV with Qc and Mc. We are very interested in whether the high-spin state 23/2 can be observed experimentally. This 23/2 level can be used to determine the necessity of QQπ,ν correction in the particle-hole nuclei region and finally explain the large difference in level (17+) of 132Te.

    Figure 7

    Figure 7.  (color online) QQπ,ν force and monopole effects of Mc(νd5/2,νh11/2) in 130Sn and 131Sb. Data marked with stars are from Ref. [32].

    The monopole effects and high-spin levels in 132134Te, 131133Sb, and 130Sn are investigated. The datum 6.166 MeV of level 17+ in 132Te is excluded from configurations πg7/2h11/2νg17/2h111/2 or πh211/2νh211/2. The present work suggests the datum (17+) coupled by configuration πg7/2h11/2νd15/2h111/2. Several levels are connected with state (17+) by monopole effects of Mc(νd5/2,νh11/2) and the quadruple-quadruple force between the proton and neutron, i.e., 3 (8) in 130Sn, 14 in 132Te, and 23/2 in 131Sb. If these states could be observed at lower energies, the lower state (17+) of 132Te would be explained with quadruple-quadruple correction between the proton and neutron and the increasing strength of the monopole interaction between neutron orbits d5/2 and h11/2.

    [1] G. Lorusso, S. Nishimura, Z. Y. Xu et al., Phys. Rev. Lett. 114, 192501 (2015) doi: 10.1103/PhysRevLett.114.192501
    [2] M. E. Burbidge, G. R. Burbidge, W. A. Fowler et al., Rev. Mod. Phys. 29, 547 (1957) doi: 10.1103/RevModPhys.29.547
    [3] K. L. Jones, A. S. Adekola, D. W. Bardayan et al., Nature 465, 454 (2010) doi: 10.1038/nature09048
    [4] K. L. Jones, F. M. Nunes, A. S. Adekola et al., Physical Review C 84, 034601 (2011) doi: 10.1103/PhysRevC.84.034601
    [5] B. A. Brown, N. J. Stone, J. R. Stone et al., Phys. Rev. C 71, 044317 (2005) doi: 10.1103/PhysRevC.71.044317
    [6] M. Mumpower, R. Surman, G. McLaughlin et al., Prog. Part. Nucl. Phys. 86, 86 (2016) doi: 10.1016/j.ppnp.2015.09.001
    [7] O. Sorlin and M. G. Porquet, Prog. Part. Nucl. Phys. 61, 602 (2008) doi: 10.1016/j.ppnp.2008.05.001
    [8] C. Gorges, L. V. Rodrguez, D. L. Balabanski et al., Phys. Rev. Lett. 122, 192502 (2019) doi: 10.1103/PhysRevLett.122.192502
    [9] C. Goodin, N. J. Stone, A. V. Ramayya et al., Phys. Rev. C 78, 044331 (2008a) doi: 10.1103/PhysRevC.78.044331
    [10] D. C. Radford, C. Baktash, J. R. Beene et al., Phys. Rev. C 88, 222501 (2002) doi: 10.1103/PhysRevLett.88.222501
    [11] K. Sieja, G. Martinez-Pinedo, L. Coquard et al., Phys. Rev. C 80, 054311 (2009) doi: 10.1103/PhysRevC.80.054311
    [12] S. Sarkar and M. S. Sarkar, Phys. Rev. C 64, 014312 (2001) doi: 10.1103/PhysRevC.64.014312
    [13] C. J. Barton, M. A. Caprio, D. Shapira et al., Phys. Lett. B 551, 269 (2003) doi: 10.1016/S0370-2693(02)03066-6
    [14] S. Biswas, R. Palit, A. Navin et al., Phys. Rev. C 93, 034324 (2016) doi: 10.1103/PhysRevC.93.034324
    [15] H. K. Wang, Y. Sun, H. Jin et al., Phys. Rev. C 88, 054310 (2013) doi: 10.1103/PhysRevC.88.054310
    [16] H. K. Wang, K. Kaneko, and Y. Sun, Phys. Rev. C 89, 064311 (2014) doi: 10.1103/PhysRevC.89.064311
    [17] H. K. Wang, K. Kaneko, and Y. Sun, Phys. Rev. C 91, 021303 (2015) doi: 10.1103/PhysRevC.91.021303
    [18] H. K. Wang, K. Kaneko, Y. Sun et al., Phys. Rev. C 95, 011304 (2017a) doi: 10.1103/PhysRevC.95.011304
    [19] V. Manea, J. Karthein, D. Atanasov et al., Phys. Rev. Lett. 124, 092502 (2020) doi: 10.1103/PhysRevLett.124.092502
    [20] H. K. Wang, Z. H. Li, Y. B. Wang et al., Phys. Lett. B 833, 137337 (2022a) doi: 10.1016/j.physletb.2022.137337
    [21] L. Kaya, A. Vogt, P. Reiter et al., Phys. Rev. C 100, 024323 (2019) doi: 10.1103/PhysRevC.100.024323
    [22] H. K. Wang, G. X. Li, B. Jian et al., Phys. Rev. C 106, 054313 (2022) doi: 10.1103/PhysRevC.106.054313
    [23] R. F. Takaharu Otsuka, Toshio Suzuki, H. Grawe et al., Phys. Rev. Lett. 95, 232502 (2005) doi: 10.1103/PhysRevLett.95.232502
    [24] N. Smirnova, B. Bally, K. Heyde et al., Phys. Lett. B 686, 109 (2010) doi: 10.1016/j.physletb.2010.02.051
    [25] T. Otsuka, T. Suzuki, M. Honma et al., Phys. Rev. Lett. 104, 012501 (2010) doi: 10.1103/PhysRevLett.104.012501
    [26] N. A. Smirnova, K. Heyde, B. Bally et al., Phys. Rev. C 86, 034314 (2012) doi: 10.1103/PhysRevC.86.034314
    [27] Y. Tsunoda, T. Otsuka, N. Shimizu et al., Phys. Rev. C 89, 031301(R) (2014) doi: 10.1103/PhysRevC.89.031301
    [28] H. K. Wang, S. K. Ghorui, Z. Q. Chen et al., Phys. Rev. C 102, 054316 (2020) doi: 10.1103/PhysRevC.102.054316
    [29] B. A. Brown and W. D. M. Rae, Nucl. Data Sheets 120, 115 (2014) doi: 10.1016/j.nds.2014.07.022
    [30] H. K. Wang, S. K. Ghorui, K. Kaneko et al., Phys. Rev. C 96, 054313 (2017b) doi: 10.1103/PhysRevC.96.054313
    [31] H. K. Wang, Z. Q. Chen, H. Jin et al., Phys. Rev. C 104, 014301 (2021) doi: 10.1103/PhysRevC.104.014301
    [32] N. N. D. Center, Data extracted using the NNDC On-line Data Service from the ENSDF database with nucleus (cutoff dates) of \begin{document}$^{132}$\end{document}
    Te(10-Feb-2005), \begin{document}$^{133}$\end{document}
    Te(31-Oct-2010), \begin{document}$^{134}$\end{document}
    Te(31-Jul-2004), \begin{document}$^{133}$\end{document}
    Sb(31-Oct-2010), \begin{document}$^{132}$\end{document}
    Sb(10-Feb-2005) http://www.nndc.bnl.gov.
  • [1] G. Lorusso, S. Nishimura, Z. Y. Xu et al., Phys. Rev. Lett. 114, 192501 (2015) doi: 10.1103/PhysRevLett.114.192501
    [2] M. E. Burbidge, G. R. Burbidge, W. A. Fowler et al., Rev. Mod. Phys. 29, 547 (1957) doi: 10.1103/RevModPhys.29.547
    [3] K. L. Jones, A. S. Adekola, D. W. Bardayan et al., Nature 465, 454 (2010) doi: 10.1038/nature09048
    [4] K. L. Jones, F. M. Nunes, A. S. Adekola et al., Physical Review C 84, 034601 (2011) doi: 10.1103/PhysRevC.84.034601
    [5] B. A. Brown, N. J. Stone, J. R. Stone et al., Phys. Rev. C 71, 044317 (2005) doi: 10.1103/PhysRevC.71.044317
    [6] M. Mumpower, R. Surman, G. McLaughlin et al., Prog. Part. Nucl. Phys. 86, 86 (2016) doi: 10.1016/j.ppnp.2015.09.001
    [7] O. Sorlin and M. G. Porquet, Prog. Part. Nucl. Phys. 61, 602 (2008) doi: 10.1016/j.ppnp.2008.05.001
    [8] C. Gorges, L. V. Rodrguez, D. L. Balabanski et al., Phys. Rev. Lett. 122, 192502 (2019) doi: 10.1103/PhysRevLett.122.192502
    [9] C. Goodin, N. J. Stone, A. V. Ramayya et al., Phys. Rev. C 78, 044331 (2008a) doi: 10.1103/PhysRevC.78.044331
    [10] D. C. Radford, C. Baktash, J. R. Beene et al., Phys. Rev. C 88, 222501 (2002) doi: 10.1103/PhysRevLett.88.222501
    [11] K. Sieja, G. Martinez-Pinedo, L. Coquard et al., Phys. Rev. C 80, 054311 (2009) doi: 10.1103/PhysRevC.80.054311
    [12] S. Sarkar and M. S. Sarkar, Phys. Rev. C 64, 014312 (2001) doi: 10.1103/PhysRevC.64.014312
    [13] C. J. Barton, M. A. Caprio, D. Shapira et al., Phys. Lett. B 551, 269 (2003) doi: 10.1016/S0370-2693(02)03066-6
    [14] S. Biswas, R. Palit, A. Navin et al., Phys. Rev. C 93, 034324 (2016) doi: 10.1103/PhysRevC.93.034324
    [15] H. K. Wang, Y. Sun, H. Jin et al., Phys. Rev. C 88, 054310 (2013) doi: 10.1103/PhysRevC.88.054310
    [16] H. K. Wang, K. Kaneko, and Y. Sun, Phys. Rev. C 89, 064311 (2014) doi: 10.1103/PhysRevC.89.064311
    [17] H. K. Wang, K. Kaneko, and Y. Sun, Phys. Rev. C 91, 021303 (2015) doi: 10.1103/PhysRevC.91.021303
    [18] H. K. Wang, K. Kaneko, Y. Sun et al., Phys. Rev. C 95, 011304 (2017a) doi: 10.1103/PhysRevC.95.011304
    [19] V. Manea, J. Karthein, D. Atanasov et al., Phys. Rev. Lett. 124, 092502 (2020) doi: 10.1103/PhysRevLett.124.092502
    [20] H. K. Wang, Z. H. Li, Y. B. Wang et al., Phys. Lett. B 833, 137337 (2022a) doi: 10.1016/j.physletb.2022.137337
    [21] L. Kaya, A. Vogt, P. Reiter et al., Phys. Rev. C 100, 024323 (2019) doi: 10.1103/PhysRevC.100.024323
    [22] H. K. Wang, G. X. Li, B. Jian et al., Phys. Rev. C 106, 054313 (2022) doi: 10.1103/PhysRevC.106.054313
    [23] R. F. Takaharu Otsuka, Toshio Suzuki, H. Grawe et al., Phys. Rev. Lett. 95, 232502 (2005) doi: 10.1103/PhysRevLett.95.232502
    [24] N. Smirnova, B. Bally, K. Heyde et al., Phys. Lett. B 686, 109 (2010) doi: 10.1016/j.physletb.2010.02.051
    [25] T. Otsuka, T. Suzuki, M. Honma et al., Phys. Rev. Lett. 104, 012501 (2010) doi: 10.1103/PhysRevLett.104.012501
    [26] N. A. Smirnova, K. Heyde, B. Bally et al., Phys. Rev. C 86, 034314 (2012) doi: 10.1103/PhysRevC.86.034314
    [27] Y. Tsunoda, T. Otsuka, N. Shimizu et al., Phys. Rev. C 89, 031301(R) (2014) doi: 10.1103/PhysRevC.89.031301
    [28] H. K. Wang, S. K. Ghorui, Z. Q. Chen et al., Phys. Rev. C 102, 054316 (2020) doi: 10.1103/PhysRevC.102.054316
    [29] B. A. Brown and W. D. M. Rae, Nucl. Data Sheets 120, 115 (2014) doi: 10.1016/j.nds.2014.07.022
    [30] H. K. Wang, S. K. Ghorui, K. Kaneko et al., Phys. Rev. C 96, 054313 (2017b) doi: 10.1103/PhysRevC.96.054313
    [31] H. K. Wang, Z. Q. Chen, H. Jin et al., Phys. Rev. C 104, 014301 (2021) doi: 10.1103/PhysRevC.104.014301
    [32] N. N. D. Center, Data extracted using the NNDC On-line Data Service from the ENSDF database with nucleus (cutoff dates) of \begin{document}$^{132}$\end{document}
    Te(10-Feb-2005), \begin{document}$^{133}$\end{document}
    Te(31-Oct-2010), \begin{document}$^{134}$\end{document}
    Te(31-Jul-2004), \begin{document}$^{133}$\end{document}
    Sb(31-Oct-2010), \begin{document}$^{132}$\end{document}
    Sb(10-Feb-2005) http://www.nndc.bnl.gov.
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Han-Kui Wang, Amir Jalili, G. X. Li and Y. B. Wang. The monopole effects and high-spin levels in neutron-rich 132Te[J]. Chinese Physics C. doi: 10.1088/1674-1137/accdc6
Han-Kui Wang, Amir Jalili, G. X. Li and Y. B. Wang. The monopole effects and high-spin levels in neutron-rich 132Te[J]. Chinese Physics C.  doi: 10.1088/1674-1137/accdc6 shu
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Monopole effects and high-spin levels in neutron-rich 132Te

  • 1. Department of Physics, Zhejiang SCI-TECH University, Hangzhou 310018, China
  • 2. China Institute of Atomic Energy, Beijing 102413, China
  • 3. School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

Abstract: The neutron-rich nuclei near doubly magic 132Sn have attracted considerable interest in both nuclear physics and nuclear astrophysics. For the particle-hole nuclei in this region, the low-lying and high core excitations have been well described by shell model calculations using the extended pairing plus multipole-multipole force model. However, there is a significant difference between experiment and theory in the high-spin level 17+ of 132Te. We intend to illustrate this difference through monopole interactions. For this purpose, the monopole corrections between π(ν)0g7/2, ν1d5/2 and π(ν)0h11/2 are investigated in 132134Te, 131133Sb, and 130Sn. Some theoretical levels are connected to the (17+) state of 132Te with the monopole correction (Mc) of Mc(νd5/2,νh11/2) and the quadruple-quadruple force between the proton and neutron, i.e., levels 3(8) in 130Sn, level 14 in 132Te, and level 23/2 in 131Sb. Their observations at lower energies can confirm the datum of level (17+) in 132Te with an illustration of monopole effects and quadruple-quadruple force.

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    I.   INTRODUCTION
    • The analysis of neutron-rich isotopes near the doubly magic nucleus 132Sn can provide fascinating findings related to nuclear physics and nuclear astrophysics. The abundance peak appears at A130, which is formed through the rapid neutron capture process [1, 2]. The properties of doubly magic 132Sn have been explored and confirmed in both experiments and theories [38]. In this nuclei region, tellurium isotopes have attracted experimental and theoretical research interest [5, 913]. For example, the g-factor of 134Te in the 4+ state was measured, which provides direct insight into the single particle structure [9]. The state (17+) of 132Te was observed to be 6.166 MeV using the reaction 9Be(238U, f ) with a beam energy of 6.2 MeV/u at GANIL [14]. A significant energy difference exists in this state between experiments and shell-model calculations, which should conceal unknown information about the nuclear structure.

      In theory, the extended pairing plus multipole-multipole force and monopole correction terms model (EPQQM) provides a suitable method to describe both the low-lying states and core excitations [1518]. For example, the ordering and energies of the low-lying isomers in 129Cd are predicted and determined by using the implemented phase-imaging ion-cyclotron-resonance method [18, 19]. The 16+ level in 128Cd is predicted as a spin-trap isomer feeding the known 16+ of 128In through β decay [20]. In addition to monopole interactions, it is necessary to consider the cross-shell excitations to study the properties of these neutron-rich nuclei in this region. For example, identifying the isomer state of level 19/2+ at 1942 keV in 133Ba requires the cross-shell orbits lying above the energy gap N=82. As reported in Ref. [21], the interactions without core excitations cannot provide the B(E1) value for the transition from Jπ=19/2+ to Jπ=19/2.

      This model has an advantage for studying monopole effects by employing monopole correction (Mc) terms. For example, in the southwest quadrant (Z50,N82) of 132Sn, the level spectra and the energy gap across N=82 can be modified by monopole correction between neutron orbit h11/2 and f7/2 [15]. In the northeast quadrant (Z50,N82), five monopole terms are used to describe core excitations and high-spin levels, and the states 2 and 9 in 136,138Te are predicted as a spin-trap structure coupled by the neutron intruder orbit i13/2 [22]. Different effects of tensor forces are also discussed together with the monopole-driven shell evolutions [23], as well as other ones in the nucleon-nucleon interaction [2427]. For the particle-hole nuclei in the northwest region of 132Sn, a suitable interaction has been found, and the spectra of Sb and Te isotopes are well described as single-orbital couplings and cross-shell excitations [18, 28]. The transition probabilities in these nuclei are also calculated and reproduced well through comparisons with the known data.

      In this study, we investigate high-spin levels and monopole effects in particle-hole nuclei near 132Sn by employing the interaction in Ref. [18]. The shell-model code NUSHELLX@MSU is used for the calculations [29].

    II.   HAMILTONIAN AND MONOPOLE EFFECTS
    • In this work, we use the Hamiltonian in the proton-neutron (pn) representation [18]:

      H=Hsp+HP0+HP2+HQQ+HOO+HHH+Hmc=α,iεiacα,icα,i12J=0,2iigJ,iiMPJM,iiPJM,ii12iiχ2,iib4M:Q2M,iiQ2M,ii:12iiχ3,iib6M:O3M,iiO3M,ii:12iiχ4,iib8M:H4M,iiH4M,ii:+ac,iikmc(ia,ic)JMAJM(ia,ic)AJM(ia,ic).

      (1)

      Equation (1) includes the single-particle Hamiltonian (Hsp); the J=0 and J=2 pairings (P0P0 and P2P2); the quadrupole-quadrupole (QQ), octupole-octupole (OO), and hexadecapole-hexadecapole (HH) terms; and the monopole corrections (Hmc). In the pn-representation, PJM,ii and AJM(ia,ic) are the pair operators, while Q2M,ii, O3M,ii, and H4M,ii are the quadrupole, octupole, and hexadecapole operators, respectively, in which i (i) is an index for protons (neutrons). The parameters gJ,ii, χ2,ii, χ3,ii, χ4,ii, and kmc(ia,ic) are the corresponding force strengths, and b is the harmonic-oscillator range parameter.

      The model space includes five orbits (0g7/2,1d5/2,1d3/2,2s1/2,0h11/2) for both protons and neutrons. Two extra neutron orbits above the N=82 shell, i.e., (1f7/2 and 2p3/2), are added to allow neutron cross-shell excitations. We keep the same parameters of single-particle energies and the two-body force strengths used in Ref. [18]. The monopole interactions were found to be crucial for describing nuclear properties, which are entirely responsible for global saturation properties and single-particle behavior. The neutron-rich nuclei near 132Sn can be divided into four quadrants by the crossing of Z=50 and N=82. According to nuclei studied previously [15, 22, 30], the monopole corrections are necessary for the hole (particle) nuclei in the southwest (northeast) quadrant of 132Sn.

      In southwest quadrant (Z50,N82), the ground state inversion in 129Cd can be well described by the monopole correction between proton orbit 0g9/2 and neutron orbit 0h11/2 with a strength of –0.40 MeV [17], and it was verified using the recently implemented phase-imaging ion-cyclotron-resonance method [19]. Recently, the ground-state inversions from N=81 to N=79 were explained for the first time by monopole correction between neutron orbits h11/2 and d3/2. Furthermore, this monopole correction has been found in different isotonic chains of N=79,80,81, as all being hole nuclei near 132Sn.

      In the northeast quadrant (Z50,N82), five monopole terms are used to describe core excitations and high-spin levels [22]. For particle-pole nuclei in the northwest quadrant of 132Sn (Z50,N82), the protons and neutrons occupy the same major shell. The properties of particle-hole nuclei can be well described without additional monopole correlations [28]. Such a situation is confirmed by the electromagnetic transitions of Sb and Te isotopes in the northwest quadrant of 132Sn [28, 31], which is a strict test for shell model calculations. However, in level 17+ of 132Te, the large difference between experiment and theory motivates us to investigate monopole interactions in the particle-hole nuclei region near 132Sn.

    III.   HIGH-SPIN LEVELS
    • In this part, high-spin levels are investigated with the monopole effects and quadruple-quadruple force in 132134Te, 131133Sb, and 130Sn. The monopole correction alone cannot solve the puzzle of level 17+; it should be combined with quadrupole correction. As shown in Table 1, there are four different types of level 17+ under 10 MeV according to the EPQQM model, i.e., Nos. 1 to 4. The possibility of neutron core excitation (config.1 in Table 1) at 8.189 MeV can be excluded to explain the high-spin level 17+ of 132Te [28]. The given experimental data of 134Te and 133Sb have been reproduced very well as core excitations with a common neutron configuration of νh111/2f7/2 (Fig. 1). If we modify the monopole term of Mc(νh111/2,νf7/2) to explain the level 17+ of 132Te, the 17 states of neutron core excitations would catastrophically depart from their corresponding data.

      Figure 1.  (color online) Neutron core excitations in 134Te and 133Sb nuclei. Corresponding data are from Ref. [32].

      132TeEx(MeV)Config.
      JπTh.Exp.No.P(\%)
      (17+)8.1896.1661. πg27/2νh311/2f7/288
      8.7792. πg7/2h11/2νg17/2h111/276
      9.1253. πg7/2h11/2νd15/2h111/272
      9.3144. πh211/2νh211/293

      Table 1.  17+ states in 132Te with main configurations. The data are from Ref. [14].

      After excluding neutron core excitation, we focus on the level at 8.779 MeV coupled by config.2 πg7/2h11/2νg17/2h111/2. This level can be affected by these monopole terms from this configuration, i.e., Mc(πg7/2,πh11/2), Mc(νg7/2,νh11/2), and Mc(πg7/2,νh11/2). The level at 8.779 MeV is abandoned, since the biggest difference is only 0.227 MeV in level 3 of 132Sb (Fig. 2). For the 17+ level at 9.314 MeV, it has a new monopole term of Mc(πh11/2νh11/2). This monopole term has almost no effects in levels 17+ coupled by config.1, 2, and 3. (κ=0.10.9 MeV), while the level 17+ at 9.314 MeV drops to 8.3 MeV (Fig. 3). The level at 9.134 MeV is excluded too, because all 17+ levels are increased sharply when the strength is κ>0.9 MeV. For the last one coupled by config.3, the suitable monopole term Mc(νd5/2,νh11/2) is turned up from this configuration. Its monopole effects are investigated in the states of 132Te from 0+ to 17+ by adding Mc(νd5/2,νh11/2) = –2.6 MeV. As shown in Fig. 4, the level 17+ is reduced to 6.311 MeV, but the values of the 5 and 7 levels become far from the corresponding data.

      Figure 2.  (color online) Levels produced by particular configurations in 134Te, 133Te, 132Sb, 131Sb, and 130Sn nuclei, in comparison with given data [32].

      Figure 3.  (color online) Monopole effects of Mc(πh11/2νh11/2) in level 17+ of 132Te.

      Figure 4.  (color online) Monopole effects of Mc(νd5/2,νh11/2) in 132Te. Data marked with stars are from Ref. [32].

      As shown above, the monopole interaction alone cannot solve the present puzzle, and we focus on the quadrupole-quadrupole force between the proton and neutron (QQπ,ν).

      As shown in Fig. 5, the value of theQQπ,ν force equals the quadruple-quadruple force strength divided by [1/A(132Sn)]5/3. The level 17+ coupled by configuration πg7/2h11/2νh111/2d15/2 is reduced by 2.121 MeV when the QQ force changes from 300 to –450. The lowest value is 7.107 MeV, which occurs when QQπν = –350. It seems the QQπ,ν force provides a new method to explain the large difference in level 17+. As shown in Fig. 6, the datum (17+) is reproduced very well with QQπν = –350 and Mc(νd5/2,νh11/2)=0.8 MeV. Furthermore, the values of 5 and 7 levels are close to data (5) and (7). The levels 13 and 14 drop by approximately 1 MeV with QQπ,ν correction (Qc). The levels 3 and 14 are sensitive to the monopole effects of Mc(νd5/2,νh11/2). These levels are connected with datum 17+ by the QQπ,ν force and monopole effects of Mc(νd5/2,νh11/2). If they could be observed experimentally, this would be evidence confirming the datum (17+).

      Figure 5.  (color online) Effects of the quadruple-quadruple force between the proton and neutron in level 17+ of 132Te.

      Figure 6.  (color online) QQπ,ν force and monopole effects of Mc(νd5/2,νh11/2) in 132Te. Data marked with stars are from Refs. [14, 32].

      For determining the QQπ,ν correction and monopole term Mc(νd5/2,νh11/2), an alternative of lack data in 132Te is to study the QQπ,ν correction and monopole effects in other nuclei nearby. The monopole effects of Mc(νd5/2,νh11/2) also exist in 130Sn and 131Sb. In 130Sn, the configuration νh111/2d15/2 produces levels from 3 to 8. With the Mc(νd5/2,νh11/2), the configuration percentages have almost no change in levels 3, 7, and 8, while the percentage of level 5 (6) drops from 57% (49%) to 52% (39%). Level 3 is the first state of Jπ=3, and its energy decreases by 1.01 MeV when Mc is added. Here, the QQπ,ν force has no effect on one-shell closed nuclei. If this state could be observed near 2.199 MeV, this would be evidence for considering monopole correction in particle-hole nuclei near 132Sn. The same applies to level 8 as the first state of Jπ=8.

      In 131Sb, levels from 1/2 to 21/2 have a main configuration of πg7/2νh111/2. As shown in Fig. 7(b), the QQπ,ν correction has obvious effects on levels 1/2, 3/2, 5/2, 21/2, and 23/2, while monopole correction Mc has almost no effects except in the case of level 23/2. The lowest energy level of Jπ=23/2 drops to 2.570 MeV with Qc and Mc. We are very interested in whether the high-spin state 23/2 can be observed experimentally. This 23/2 level can be used to determine the necessity of QQπ,ν correction in the particle-hole nuclei region and finally explain the large difference in level (17+) of 132Te.

      Figure 7.  (color online) QQπ,ν force and monopole effects of Mc(νd5/2,νh11/2) in 130Sn and 131Sb. Data marked with stars are from Ref. [32].

    IV.   CONCLUSION
    • The monopole effects and high-spin levels in 132134Te, 131133Sb, and 130Sn are investigated. The datum 6.166 MeV of level 17+ in 132Te is excluded from configurations πg7/2h11/2νg17/2h111/2 or πh211/2νh211/2. The present work suggests the datum (17+) coupled by configuration πg7/2h11/2νd15/2h111/2. Several levels are connected with state (17+) by monopole effects of Mc(νd5/2,νh11/2) and the quadruple-quadruple force between the proton and neutron, i.e., 3 (8) in 130Sn, 14 in 132Te, and 23/2 in 131Sb. If these states could be observed at lower energies, the lower state (17+) of 132Te would be explained with quadruple-quadruple correction between the proton and neutron and the increasing strength of the monopole interaction between neutron orbits d5/2 and h11/2.

Reference (32)

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