De-excitation of the strongly coupled band in 177 Au and implications for core intruder conﬁgurations in the light Hg isotopes

Excited states in the proton-unbound nuclide 177 Au were populated in the 92 Mo( 88 Sr, p 2 n ) reaction and identiﬁed using the Jurogam-II and GREAT spectrometers in conjunction with the RITU gas-ﬁlled separator at the University of Jyväskylä Accelerator Laboratory. A strongly coupled band and its decay path to the 11 / 2 − α -decaying isomer have been identiﬁed using recoil-decay tagging. Comparisons with cranked Hartree-Fock-Bogoliubov (HFB) calculations based on Skyrme energy functionals suggest that the band has a prolate deformation and is based upon coupling the odd 1 h 11 / 2 proton hole to the excited 0 + 2 conﬁguration in the 178 Hg core. Although these conﬁgurations might be expected to follow the parabolic trend of core Hg(0 + 2 ) states as a function of neutron number, the electromagnetic decay paths from the strongly coupled band in 177 Au are markedly different from those observed in the heavier isotopes above the midshell. This indicates that a signiﬁcant change in the structure of the underlying A + 1 Hg core occurs below the neutron midshell.

Excited states in the proton-unbound nuclide 177 Au were populated in the 92 Mo( 88 Sr, p2n) reaction and identified using the Jurogam-II and GREAT spectrometers in conjunction with the RITU gas-filled separator at the University of Jyväskylä Accelerator Laboratory.A strongly coupled band and its decay path to the 11/2 − α-decaying isomer have been identified using recoil-decay tagging.Comparisons with cranked Hartree-Fock-Bogoliubov (HFB) calculations based on Skyrme energy functionals suggest that the band has a prolate deformation and is based upon coupling the odd 1h 11/2 proton hole to the excited 0 + 2 configuration in the 178 Hg core.Although these configurations might be expected to follow the parabolic trend of core Hg(0 + 2 ) states as a function of neutron number, the electromagnetic decay paths from the strongly coupled band in 177 Au are markedly different from those observed in the heavier isotopes above the midshell.This indicates that a significant change in the structure of the underlying A+1 Hg core occurs below the neutron midshell.DOI: 10.1103/PhysRevC.95.061302 The complexities of the atomic nucleus as a many-body system arise from the interplay between single-particle and collective degrees of freedom.This is particularly apparent in heavy nuclei near closed shells where near degenerate spherical and deformed intrinsic configurations can coexist at low-excitation energies.This shape coexistence arises from the opposing tendencies of shell structure and residual interactions that promote sphericity and deformation, respectively, and is especially sensitive to the arrangement of nucleons at the Fermi surface.
Shape coexistence in nuclei near the Z = 82 closed shell was first apparent from the unexpected isotope shifts between 185 Hg and 187 Hg measured using optical hyperfine spectroscopy [1].Subsequent in-beam and decay experiments revealed excited 0 + states in the even-mass 180 N 190 Hg isotopes, which were interpreted in terms of weakly deformed ground states and strongly deformed intruder configurations based on proton-pair excitations across the Z = 82 shell gap [2].This interpretation has been confirmed experimentally in recent Coulomb excitation measurements using accelerated radioactive ion beams [3].
The excited 0 + state energies in the Hg isotopes exhibit a well-established parabolic dependence on neutron number with a minimum at N = 102 near the neutron midshell between N = 82 and N = 126.However, recent mean-field calculations suggest that the smooth parabolic behavior of the excited 0 + states in the Hg isotopes may hide differences in the shape of the underlying potentials whence these states have their origin [4].Indeed, these calculations predict that the relative excitation energies of the oblate and prolate minima could be exchanged in the highly neutron-deficient Hg isotopes.Both proton-particle and proton-hole configurations are observed in odd-Au isotopes.Proton holes couple to even-even Hg cores, while proton particles couple to even-even Pt cores, resulting in distinct groups of states [5].Therefore, one method for revealing subtle structural differences in the Hg isotopes is to identify excited states in their odd-mass Au isotones where the odd proton hole couples to the Hg core configurations.The analogous excited hole states in the Au isotopes that couple to Hg cores have been observed in 185 Au 106 and 187 Au 108 [6,7] but not in others.
In this work, we report the detailed characterization of a strongly coupled band with K = = 11/2 (13/2) in the proton-unbound nucleus 177 Au, which exhibits low rotational alignment relative to the underlying 178 Hg core.These results are interpreted in terms of mean-field calculations and the implications for the structure of the highly neutron-deficient Hg cores are discussed.The strongly coupled band was first observed in a prior experiment by Kondev et al. [8,9].Reference [8] showed singles γ -ray spectra tagged by the two low-lying α-decaying states in 177 Au while level schemes, energies, and intensities were presented in Ref. [9].In the present work, we present γ -ray coincidence spectra, which augment the known level scheme.Newly identified transitions feeding low-spin states and comparison of the strongly coupled band with the intruder bands in 176 Pt and 178 Hg lead us to propose alternative spin assignments for the strongly coupled band.The absence of strongly coupled bands with similar decay paths to the low-spin states in the heavier odd-mass Au isotopes indicates a significant difference in the nature of the deformed even-Hg core structure between A = 178 and 184.We note that there is another well-developed strongly coupled band in 181 Au 102 [10] originating from the same configuration.However, the excitation energy of this band cannot be established firmly due to the proximity of 181 Au to the neutron midshell, which presumably places the K = = 11/2 band head very close to the 11/2 − isomeric state.
The experiment was performed at the University of Jyväskylä Accelerator Laboratory.A beam of 88 Sr 10+ ions with an energy of 399 MeV and average intensity of approximately 2 particle nA was delivered by the K = 130 MeV cyclotron and impinged on a target inducing fusion-evaporation reactions.Self-supporting metallic targets with a thickness of 0.6 mg/cm 2 were prepared from isotopically enriched material of 92 Mo (98% enrichment).The total irradiation time was approximately 230 h.Fusion evaporation residues were separated from the the scattered primary beam and fission products according to their different magnetic rigidities by the gas-filled recoil separator RITU [11].After separation, the evaporation residues passed through the multiwire proportional counter (MWPC) and were implanted into the double-sided silicon strip detectors (DSSD) of the focal-plane spectrometer GREAT [12].Recoiling evaporation residues were distinguished from the scattered beam and subsequent radioactive decays by energy loss in the MWPC and, in conjunction with the DSSD, time-of-flight information.γ rays emitted promptly at the target position were detected by the JUROGAM-II array, consisting of 24 clover-and 15 EUROGAM-type Compton suppressed spectrometers.The time-stamped stream of data was acquired from each detector independently using the total data readout digital data acquisition system [13].Data were sorted offline and analysed using the GRAIN [14] and RADWARE [15] software analysis packages.
1/2 = 1.18 s [17]), make 177 Au suitable for recoil-decay tagging.In this technique, γ rays detected at the target position are identified through spatial and temporal correlations with recoil implantations at the separator focal plane and their subsequent characteristic radioactive decays [19,20].
Figure 1(a) shows the energy spectrum of γ rays associated with the decay of the 11/2 − isomer, which were identified recoil-decay correlations with the corresponding α particles.The spectrum is dominated by the de-excitations of the known 1i 13/2 cascade.Two γ -ray transitions at 228 and 203 keV were identified as feeding the 11/2 − isomer.The spectra of the γ rays in coincidence with these transitions are shown in Figs.1(b) and 1(c).Spectra show monotonic sequences of M1/E2 and E2 in-band transitions together with several linking transitions.The γ -ray coincidence analysis revealed that these transitions form a strongly coupled band that is placed unambiguously in the energy level scheme; see Fig. 2. Hereafter, the excitation energies of all states are quoted relative to the 11/2 − α decaying isomer.The strongly coupled band decays exclusively to the 11/2 − isomer via two intermediate states at 521 and 525 keV.The 521-and 525-keV γ rays depopulating these states have similar energies to the 2 + 1 → 0 + 1 transition in 178 Hg (558 keV) [21] and are likely to be configurations formed by coupling 1h 11/2 proton holes to the weakly oblate 178 Hg core.The multipolarity of the 521-keV γ ray was determined using directional correlations from oriented states [22] and is consistent with a I = 1 transition [R DCO = 0.6(1)] leading to possible spin assignments of 9/2 or 13/2 for the initial state.The level energies associated with the 1h 11/2 ⊗ A+1 Hg configurations in odd-Au isotopes are established from the line of stability to beyond the proton drip line and vary smoothly as a function of neutron number [23][24][25].These systematic trends favor the 13/2 − assignment for the 521-keV level.The 525-keV level is fed by 727-and 871-keV γ rays and has a similar feeding pattern to that observed in the heavier odd-mass Au isotopes where γ rays depopulating the 17/2 − and 19/2 − states feed the 15/2 − state strongly.This similarity favours a 15/2 − spin-parity assignment for the 525-keV state.
Based on the K x-ray intensity balance, a conversion coefficient for the 228-keV transition of 0.58 (23) was deduced, which compares well with the BRICC estimates for a pure M1 transition of 0.588(9) [26].Within the experimental uncertainty an E2 admixture cannot be excluded.Moreover, the subsequent intensity balance between the transitions feeding the (13/2 − ) state with the 521-keV transition that depopulates it implies that there is no significant E0 component in the latter transition.The absence of a strong E0 component suggests that the 521-keV transition is not a J → J transition, which further supports the (13/2 − ) assignment for the 521-keV level.The nature of the other decay paths from the strongly coupled band and the absence of other γ -ray transitions feeding the 11/2 − isomer directly constrains the lowest observed level in the strongly coupled band to be either 11/2 − or 13/2 − .It was not possible to constrain the multipolarities of other transitions in the same way.Although a tentative 11/2 − assignment is proposed for the band head of the strongly coupled band in Fig. 2, a 13/2 − assignment would not materially affect the conclusions drawn below.
The γ -ray energies of the strongly coupled band in 177 Au are plotted as a function of the initial state angular momentum, assuming that the 749-keV level is the 11/2 − band head, alongside the prolate bands of its neighboring isotones 178 Hg [21,27] and 176 Pt [28] in Fig. 3(a).The curves for the 177 Au band are almost identical to those of the prolate bands in the even-mass isotones 178 Hg and 176 Pt.The strongly coupled band in 177 Au band is assigned to be a configuration formed by the coupling of the 1h 11/2 proton hole to the unobserved well-deformed excited 0 + state in the 178 Hg core.The moments of inertia extracted for this configuration and the small signature splitting are consistent with a well-deformed axial prolate shape.
The 1h −1 11/2 ⊗ 178 Hg(0 + 2 ) configuration in 177 Au is markedly different from analogous configurations in the heavier Au isotopes whose energies as a function of the neutron number should lie on a similar parabola to that established for the 0 + 2 states in the Hg core [2].The structures of 1h −1 11/2 ⊗ A+1 Hg(0 + 2 ) configurations have been studied in 185 Au and 187 Au [6,7] by conversion-electron-γ -ray coincidence measurements [29].In these isotopes, the deformed 11/2 − and 13/2 − states decay predominantly to the near-spherical 11/2 − member of the 1h 11/2 ⊗ A+1 Hg(0 + 1 ) proton-hole configuration.It should be noted that the J → J decay paths in these nuclei have strong electric monopole (E0) components [6,7].This is not the case in 177 Au, where the decay proceeds through pairs of levels with spin (13/2 − ) and (15/2 − ) and not directly to the near spherical 11/2 − level; see Fig. 2.This indicates that there is no strong electromagnetic coupling between the strongly coupled band and the weakly deformed states and that the 0 + 2 state in the corresponding Hg core has a different structure in 177 Au.We note that a strongly coupled band has been reported in 181 Au [10]; however, without removal of transitions assigned to this band and changes to the spin assignments, it does not match the characteristics of the band discussed herein.
These results have been interpreted in terms of cranked Hartree-Fock-Bogoliubov (HFB) calculations based on a Skyrme energy functional.A microscopic description of rotational bands is obtained by introducing a so-called cranking constraint on the collective angular momentum.This approach has been applied successfully to study superdeformed bands in the A ≈ 190 region [30].The creation of a quasiparticle is treated self-consistently, which means that the polarization of the even-even vacuum on which the quasiparticle is created is fully taken into account [31].The conditions of the calculation are the same as for the recent systematic study of the even-even nuclei in the neutron-deficient lead region using the SLy6 parametrization [4].The use of alternative Skyrme functionals does not affect the results.
It should be noted that the assumptions of the cranked HFB approach do not allow for a precise assignment of angular momentum to a calculated level, especially at the bottom of a band.Indeed, there is no unique procedure to link the constraint on the collective rotation to the total angular momentum in the case of an odd nucleus where the quasiparticle also contributes to the spin.The relation that we have chosen is J (J + 1) = Ĵx 2 + K 2 , where Ĵx is the mean value of the constrained component of the angular momentum and K is the expectation value of angular momentum of the blocked quasiparticle along the symmetry axis of the nucleus in the nonrotating configuration.However, similar to the other existing recipes, this relation is not well defined for Ĵx → 0. Also, with increasing Ĵx the deformation becomes slightly triaxial such that this recipe can also only be approximate at large spin.
The deformation energy curves of the Hg isotopes obtained with the SLy6 parametrisation have been published in Ref. [4].These calculations predict the excitation energies of the oblate, nearly spherical, and prolate minima to be close in 178 Hg.Cranked HFB calculations of states for the three different minima lead to very different spin dependences of the γ -ray energies.For 178 Hg, only states in the prolate well lead to an agreement with experiment.The calculated states in this band are predicted to have an intrinsic electric cartesian quadrupole moment Q 0 ∼ 8.1 eb.The results obtained for the prolate minimum are plotted in Fig. 3(b).For 177 Au, we find two prolate bands with similar deformation, one based on a K π = 9/2 − level and the other on a K π = 11/2 − , both originating from the spherical 1h 11/2 shell.The band built on the K π = 9/2 − is predicted to have a lower excitation energy in our calculations.However, previous studies have shown that the relative placement of single-particle levels predicted by mean-field models does not always reproduce the relative position of band heads in odd-mass nuclei [32].A small rearrangement of single-particle states at sphericity would change the order of levels in the second prolate minimum and bring the K π = 11/2 − member of 1h 11/2 shell closer to the Fermi level.The calculated angular-momentum dependence of γ -ray energies for both prolate assignments in 177 Au resembles that of 178 Hg; see Fig. 3(b).
The similarity of the spin dependence of γ -ray energies in 178 Hg and 177 Au is a necessary condition to consider that one has a strongly coupled band in the Au isotope.It is not evident how to check in a fully self-consistent calculation that the angular momentum of 177 Au is generated by the rotation of a 178 Hg core, with the quasiparticle remaining unaffected.In order to get an impression of how the total angular momentum decouples into collective rotation and the intrinsic spin of the quasiparticle, we have analyzed three mean-field configurations, the noncranked band head of the K π = 9/2 − band and two of its cranked states at J π = 15/2 − and 27/2 − , by projecting them on good angular momentum and particle number using the method presented in Refs.[33,34].The two higher-spin states are slightly triaxial with triaxiality angles of γ = 2.5 • and 8.5 • , respectively.In all three cases, the K π = 9/2 − component dominates the decomposition of the wave function, from 99% at zero rotation to 55% at J ≈ 15/2, and still 30% at J ≈ 27/2, with no other component exceeding 10%.Although these calculations have to be treated with caution since there is no one-to-one correspondence between cranked mean-field states and the particle-rotor model, this is a strong indication that the cranked HFB wave function is dominated by the K π = 9/2 − quasiparticle.
In summary, a strongly coupled band in 177 Au and its decay paths to the 11/2 − α-decaying isomer have been observed.This configuration has a very low degree of rotational alignment relative to the prolate 178 Hg and 176 Pt core configurations.The results have been interpreted with cranked HFB calculations based upon a Skyrme energy functional.These calculations predict three coexisting structures for the 178 Hg core.Using the cranking model, we have shown that only states in the moderately deformed prolate well have moments of inertia with a dependence on energy similar to the data.In particular, quasiparticle excitations based on single-particle states originating from the 1h 11/2 spherical subshell and with K = 9/2 or 11/2 reproduce the data for 177 Au rather well.The rotational alignment of excited states based upon these configurations is very similar to those calculated for the cores.We interpret the strongly coupled band in 177 Au to be based on a configuration coupling a negative parity high-K proton hole with the unobserved 0 + 2 state in 178 Hg, which corresponds to a predicted low-lying prolate minimum.Although this configuration might be expected to follow the parabolic trend established for the excited 0 + 2 states in the core, its electromagnetic decay paths to the 11/2 − isomeric state are markedly different from those observed from the lowest deformed 11/2 − states in the 185 Au and 187 Au isotopes.On this basis, we conclude that a significant change in the structure of the underlying A+1 Hg core has occurred between 186 Hg (N = 106) and 178 Hg (N = 98).At present, attempting to give further interpretation for such an unexpected insight to the structure of the even Hg 0 + 2 core configurations seems premature.More detailed studies of 181-187 Au are clearly mandated.

FIG. 1 .
FIG.1.γ -ray spectra measured with the JUROGAM-II spectrometer.Spectra showing γ rays correlated with ion implantations followed by the characteristic α decay the 11/2 − isomer in177 Au (E α = 6124 keV) within the same DSSD pixel of the GREAT spectrometer.The recoil-α correlation time was limited to 3 s.(a) γ -ray singles spectrum, while panels (b) and (c) show γ rays in coincidence with 228-and 203-keV transitions.γ rays assigned to the strongly coupled band in177 Au are labeled by their transition energies.Inband transitions are highlighted with an asterisk.

FIG. 3 .
FIG. 3. (a) γ -ray energies as a function of initial state angular momentum for E2 transitions in the 177 Au strongly coupled band, 178 Hg and 176 Pt intruder bands.The inset gives the rotational alignment calculated as shift of the 177 Au curve relatively to 178 Hg.(b) Theoretical calculations of γ -ray energies as a function of initial state angular momentum for E2 transitions for the prolate 178 Hg band and for the 177 Au strongly coupled band based on 1h 11/2 , K = 9/2 and K = 11/2 configurations.
Level scheme of the states associated with 1h 11/2 proton-hole configuration in177Au deduced in the present work compared with the analogous spherical and deformed configurations in the heavier isotope 187 Au.Level excitation energies are stated relative to the 11/2 − state.The decay paths from the deformed structures to their respective 11/2 − states are different in the two isotopes.