Observation of a new isomer in ¹⁸⁵Au

In the lead region (Z = 82) near the neutron mid-shell (N = 104), the shape coexistence of spherical, oblate, and prolate shapes is well established. A striking example of shape coexistence is ¹⁸⁶Pb, where a triplet of low-lying $ 0^+ $ states has been found [1, 2]. In odd-A ¹⁸⁷Pb, three bands with different shapes have also been reported [3, 4]. In addition, different shapes have been observed in ^188,189Po and ^{185,188,189,190}Pb [5−10].

Another interesting phenomenon in this region is the presence of high-K isomers. They are present in well-deformed nuclei and even in transitional nuclei with mass near 190 [11, 12]. High-K isomers arise from the breaking of one or more nucleon pairs to form multi-quasiparticle (multi-qp) configurations. The K-hindrance and other properties of these states depend strongly on the proton and neutron states involved [13]. In ¹⁷⁸Hf, besides the remarkable 31-year $ K^{\pi} $ = $ 16^{+} $ four-quasineutron isomer [14], a two-quasineutron $K ^{\pi} $ = $ 8^{-} $ isomer arises from the coupling between nucleons in high-j orbitals ($ \nu 9/2^+[624] \otimes \nu 7/2^-[514] $). Similar two-quasineutron isomers have been observed systematically in even-mass N = 106 isotones from ¹⁷⁴Er to ¹⁸⁸Pb [11, 15].

Furthermore, in the N = 106 odd-mass isotones from ¹⁷⁵Tm to ¹⁸⁷Tl (except the ¹⁸³Ir) [16−21], 3-qp high-K isomers, originating from the coupling between the odd proton and abovementioned $K ^{\pi} $ = $ 8^{-} $ isomer in even-mass cores, have been identified.

The $ N = 106 $ nucleus, ¹⁸⁵Au, was previously studied in decay and in-beam γ-ray spectroscopy [22, 23]. A ground-state quadrupole deformation of $ \beta_2 $ = 0.24 was determined in a laser spectroscopy experiment [24].

In this paper, we report on the discovery of a new isomeric state in ¹⁸⁵Au at an excitation energy of 1504.2(4) keV, with a half-life of $ T_{1/2} = 630(80) $ ns, decaying to the (17/2⁻) level previously assigned to the $ \pi1h_{11/2} $ band [22]. The possible spin-parities of this isomer are tentatively assigned based on Weisskopf estimates. The possible configuration of this isomer is discussed within the framework of configuration-constrained potential energy surface (cc-PES) calculations [25].

The experiment was conducted at Argonne National Laboratory (ANL), and this study extends prior results reported in earlier experiments from the same experimental program, which included ¹⁸⁷Pb, ¹⁸⁸Bi, ¹⁸⁸Po, ¹⁸³Hg, and ¹⁸⁷Tl [3, 6, 21, 26]. In the present study, the ¹⁸⁵Au nucleus was produced in the ⁵⁰Cr + ¹⁴²Nd → ¹⁹²Po^* → ¹⁸⁵Au + 3pα fusion-evaporation reaction. The ⁵⁰Cr ions were accelerated to an energy of 255 MeV with a typical intensity of 7 pnA by the superconducting linear accelerator at ANL. The target material, enriched to 99.8% in ¹⁴²NdF₃, had a thickness of 700 μg/cm². To minimize target heating, four target sectors were mounted on a rotating wheel, and the beam was wobbled horizontally by ±2.5 mm across the target using a magnetic steerer.

Evaporation residues (EVRs) were separated from the primary beam by the Argonne Gas-Filled Analyzer (AGFA) [27], which was filled with 0.65 mbar of helium gas. The flight time of EVRs in the AGFA separator was estimated to be several hundred nanoseconds (approximately 500 ns flight time for v = 0.02c EVRs). The energy loss and arrival time of the EVRs were measured by a parallel grid avalanche counter (PGAC). The EVRs were then implanted into a double-sided silicon strip detector (DSSD) located at the focal plane, which recorded the deposition energy of the recoil and subsequent charged particle decay.

The present study was conducted with the delayed γ correlation method, using the DSSD and X-array detector in the focal plane. The X-array detector setup consisted of four Clover HPGe detectors and was used to detect X rays and γ rays emitted from the EVRs [28]. The typical energy resolution for the X-array was approximately 4 keV (FWHM) for γ rays of approximately 300 keV.

The delayed γ-ray spectrum recorded by the X-array detectors within 2 µs after implantation in the DSSD, with the background in the time window of 2−4 µs subtracted, is shown in Fig. 1. Most of the prominent γ-ray peaks are from known isomers produced in other reaction channels, including the strong γ ray from microsecond isomers in ¹⁸⁷Tl and ^187,188Pb.

Figure 1.  (color online) Main panel: γ-ray energy spectrum recorded by the X-array within a 2 μs window after EVR implantation in the DSSD. A background spectrum taken from the 2−4 μs after EVR implantation is subtracted. The three γ-rays highlighted in red were experimentally established as a cascade in ¹⁸⁵Au [22]. Inset: Expanded view of prominent γ-ray peaks from 260 to 400 keV.

The 212-, 462-, and 527-keV γ rays shown in Fig. 1 were initially reported in the in-beam experiment by Larabee et al. [22] as a prompt 527-462-212 keV transition cascade. Considering that the transport time through AGFA is more than hundreds of nanoseconds, these transitions are considerably delayed, indicating the existence of an isomer de-exciting via this prompt cascade.

A previously unobserved 294.8(3)-keV transition was identified in the γ-gated spectra of 527-, 462-, and 212-keV γ transitions, as shown in Fig. 2(a)−(c). The spectrum gated on the 295-keV transition and summed spectrum gated on the four transitions are shown in Fig. 2(d) and (e), respectively. This 295-keV γ ray is attributed to the deexcitation of the new isomer in ¹⁸⁵Au.

Figure 2.  (color online) γ-ray energy spectrum gated on the 527-, 462-, 212-, and 295-keV transitions (a)−(d) and the sum of these spectra (e).

The time distribution of $ \Delta T $(EVR-γ (212 keV and 527 keV)) is shown in Fig. 3. Based on a least-squares fit of this time distribution, with an exponential function plus a constant background, the half-life of the isomer was determined to be 630(80) ns.

Figure 3.  (color online) Time distribution of the summed 212 and 527 keV γ rays after EVR implantation, with a background subtraction made by gating on nearby Compton background. The data are fitted with an exponential function with a constant background.

Figure 4 illustrates the proposed decay scheme of the isomer along with a partial level scheme of ¹⁸⁵Au, and it shows that the new 1504.2(4)-keV isomer decays to the 1209.4(3)-keV (17/2⁻) level. The spin and parity assignments for established levels were adopted from previous studies [22, 23], while the corresponding energy values were derived from the latest ENDF Library evaluations of ¹⁸⁵Au [29].

Figure 4.  (color online) Partial level scheme of ¹⁸⁵Au: spin and parity are taken from Refs. [22, 23]. For the new isomer, possible spin-parities are given based on Weisskopf estimates, and states are labeled with their energies in keV.

No decay to other low-lying levels from this isomer was observed after a thorough analysis of the singles and coincidence spectra. We attempted to perform an intensity balance analysis of the 295-527-462-212 keV γ-ray cascade in the recoil-delayed γ-ray spectrum Fig. 1. However, as shown in the inset of Fig. 1, there is only a slight indication of a peak at 295 keV; hence, no definitive conclusions can be drawn on its multipolarity.

The Weisskopf single-particle transition probabilities for possible multipolarities (E1, M1, E2, M2, and E3) of the 295-keV γ-ray, corrected for internal conversion, are presented in Table 1. The E3 and higher multipolarities can be excluded based on the recommended upper limits [32]. The possible multipolarities constrain the spin of the 1504 keV isomer, decaying to (17/2⁻), to a range from 13/2 to 21/2. The Weisskopf hindrance factors (Fw, which is the reciprocal of transition probability) of the E1, M1, and E2 multipolarities are large, indicating significant hindrance.

Multipolarity assumed	Weisskopf half-life estimates (s)	Transition probability (W.u)
E1	8.13(3)$ \times 10^{-15} $	1.3(2)$ \times 10^{-4} $ a
M1	8.59(3)$ \times 10^{-13} $	1.4(2)$ \times 10^{-6} $
E2	4.06(2)$ \times 10^{-9} $	6.5(8)$ \times 10^{-3} $
M2	4.29(2)$ \times 10^{-7} $	6.9(9)$ \times 10^{-1} $
E3	3.08(2)$ \times 10^{-3} $	4.9(7)$ \times 10^{3} $
a The transition probability of K-allowed E1 transitions is multiplied by $ 10^4 $, as suggested in Refs. [30, 31].

Table 1.  Weisskopf estimates of single-particle transition probabilities for different multipolarities of the 295-keV γ ray.

To assign the possible configuration to this new isomer in ¹⁸⁵Au, we performed cc-PES calculations [25] based on the non-axial deformed Woods-Saxon (WS) potential [33] with universal parameters [34]. The total energy is composed of a macroscopic part with the standard liquid-drop energy [35]. To avoid possible pairing collapse in multi-qp states, the approximate particle-number conservation uses the Lipkin-Nogami (LN) method [36]. For a multi-qp state, the microscopic energy incorporates the contribution from the unpaired particles that occupy the single-particle orbits associated with the given configuration. The blocking effects from the unpaired nucleons are considered by removing the singly occupied orbitals from the LN calculation. The cc-PES calculations were performed in the lattice of deformation space $ (\beta_2, \beta_4, \gamma) $. The resultant PESs can self-consistently provide information on the deformation, excitation energy, and pairing interaction properties of multi-qp states. The calculations successfully reproduced the experimental results for the 3-qp configurations in N = 106 odd-A isotones, with excitation energy deviations ranging between 1 and 174 keV (¹⁸¹Re 21/2⁻ isomeric state [19] and ¹⁷⁵Tm 23/2 ⁺ isomeric state [16]). Details of the calculations will be presented in a forthcoming paper [37].

In previous experimental studies, the ground-state band (C) was proposed to originate from the strongly mixed $ \pi3/2^-[532] $ and $ \pi1/2^-[541] $ configuration [38, 39], while Band (B) was assigned to an $ h_{11/2} $ single-quasiproton configuration [22]. PES calculations for all possible low-lying proton configurations near the Fermi surface were also performed, and the results for the $ 3/2^-[532] $ and $ 1/2^-[550] $ configurations are shown in Fig. 5. The results for the $ 3/2^-[532] $ configuration reproduce the $ \beta_2 = 0.24 $ ground-state deformation from the laser spectroscopy measurements [40]. Band (B) corresponds to the $ 1/2^-[550] $ orbital, as shown in Fig. 5 (right). Notably, the PES calculations show remarkable triaxial deformations for the two low-lying configurations, similar to those observed in calculations for neighboring ^183,187Au [41, 42].

Figure 5.  PES of low-lying proton states in ¹⁸⁵Au: (left) $ h_{9/2} $ground-state band and (right) $ h_{11/2} $ band. In calculations using cc-PES calculations, the minima are indicated by black circles and labeled with their deformation parameters.

The calculated excitation energies and deformations for possible 3-qp configurations in ^185mAu are presented in Table 2. These high-K states are all predicted to lie close to the measured excitation energy of 1504 keV. However, it should be mentioned that the residual interactions between unpaired nucleons are not accounted for in the present calculations. These residual interactions can lead to energy shifts of up to a few hundred keV, depending on the relative orientation of intrinsic spins of the nucleons involved [43−45]. Therefore, in the context of the excitation energy and decay patterns, we are unable to make a firm assignment for the configuration of the observed isomer from the calculated 3-qp configurations. The calculated results incorporating the neutron configuration $ \nu 9/2^+[624] \otimes \nu 7/2^-[514] $ are consistent with systematics of 3-qp configurations in odd-mass nuclei with N = 106. However, further experimental data are required to unambiguously assign the spin-parity and configuration of the 1504 keV isomer.

$ K^{\pi} $	Configuration	Energy/keV	$ \beta_2 $	$ \beta_4 $	γ
17/2−	$ \pi 1/2^- [541] \otimes \nu 9/2^- [505] \otimes \nu7/2^- [503] $	1041	0.153	-0.010	22.907
21/2+	$ \pi 11/2^- [505] \otimes \nu 9/2^- [624] \otimes \nu1/2^- [521] $	1289	0.168	-0.041	-25.477
17/2+	$ \pi 1/2^- [541] \otimes \nu 9/2^+ [624] \otimes \nu7/2^- [514] $	1444	0.230	-0.033	1.036
19/2+	$ \pi 3/2^- [532] \otimes \nu 9/2^+ [624] \otimes \nu7/2^- [514] $	1458	0.246	-0.031	1.144
17/2+	$ \pi 1/2^- [541] \otimes \nu 9/2^+ [624] \otimes \nu7/2^- [503] $	1582	0.165	-0.037	25.680
17/2+	$ \pi 1/2^- [541] \otimes \nu 9/2^- [505] \otimes \nu7/2^+ [633] $	1632	0.159	-0.024	24.605
17/2+	$ \pi 1/2^- [530] \otimes \nu 9/2^+ [624] \otimes \nu7/2^- [514] $	1633	0.252	-0.030	0.210
13/2+	$ \pi 3/2^- [532] \otimes \nu 9/2^+ [624] \otimes \nu1/2^- [521] $	1652	0.223	-0.038	20.593
15/2+	$ \pi 1/2^- [541] \otimes \nu 7/2^+ [633] \otimes \nu7/2^- [503] $	1667	0.169	-0.032	25.437
19/2−	$ \pi 3/2^- [532] \otimes \nu 9/2^+ [624] \otimes \nu7/2^+ [633] $	1733	0.227	-0.037	-14.634
21/2−	$ \pi 5/2^+ [402] \otimes \nu 9/2^+ [624] \otimes \nu7/2^- [514] $	1757	0.266	-0.028	0.299
17/2−	$ \pi 1/2^- [550] \otimes \nu 9/2^+ [624] \otimes \nu7/2^+ [633] $	1778	0.153	-0.026	-26.763
19/2+	$ \pi 3/2^- [532] \otimes \nu 9/2^+ [624] \otimes \nu7/2^- [503] $	1875	0.200	-0.044	-26.624
15/2−	$ \pi 1/2^- [541] \otimes \nu 7/2^- [503] \otimes \nu7/2^- [514] $	1969	0.214	-0.031	21.749

Table 2.  Possible 3-qp configurations for the isomeric states in ¹⁸⁵Au. Excitation energies and deformation parameters were calculated using cc-PES calculations.

A new isomer at 1504 keV in ¹⁸⁵Au was identified through its deexcitation to a previously known level, by a 295-keV transition coinciding with the known 212-462-527 keV cascade. Possible multipolarities of E1, M1, E2, and M2 have been proposed for this transition in comparison with predictions from Weisskopf estimates. By using the cc-PES calculations, which describe the systematics of known three-quasiparticle isomers in odd-mass N = 106 isotones well [37], possible spin-parity and configuration candidates for the new isomer at 1504 keV in ¹⁸⁵Au were provided.

We thank the Target Labor team of GSI for preparing the targets for the experiment.