Population of a low-spin positive-parity band from high-spin intruder states in 177Au

The extremely neutron-deﬁcient isotopes 177 , 179 Au were studied by means of in-beam γ -ray spectroscopy. Speciﬁc tagging techniques, α -decay tagging 177 and isomer tagging 179 were used for these studies. Feeding of positive-parity, nearly spherical states, which are associated with 2 d and 3 2 proton-hole conﬁgurations, from the 1 i 13 / 2 proton-intruder conﬁguration was observed in 177 Au. Such a decay path has no precedent in odd-Au isotopes and it is explained by the effect of mixing of wave functions of the initial state.

In this Letter we present results on in-beam γ -ray spectroscopic studies of 177,179 Au, with various tagging techniques [1,2].
Previously, both isotopes were studied by means of in-beam γray spectroscopy using the Gammasphere spectrometer coupled to the Fragment Mass Analyser (FMA) at Argonne National Laboratory. In 179 Au [3], four rotational bands associated with 1h 9/2 , 2 f 7/2 , and 1i 13/2 proton-intruder configurations were observed. Transitions connecting these structures to the ground state were not observed. In 177 Au, only the yrast 1i 13/2 band together with its decay pattern was reported in the original publication [4]. Later, a data evaluation was published [5], which also contained a rotational band based on the 9/2 − state, probably associated with the 1h 9/2 proton-intruder configuration. However, no relevant spectra documenting this band were ever reported in any refereed journal. The Au isotopes play a unique role in our understanding of shape coexistence in that strongly-deformed structures intrude to become the ground state at mid shell ( 183 Au) and to exhibit a classic "parabolic" trend in excitation energy. The isotopes 177,179 Au play a key role in that they establish the "left-hand side" of the parabola of intruder states. As we show in the present study, a clear picture now emerges regarding which states are intruder structures. Further, there is the subtle feature of changing spins of intruder bands, namely that decoupling effects result in changing spin order in each intruder band. This is established as occurring in a systematic manner in the positive-parity ("1i 13/2 ") band for the first time.
A major step in understanding the structure of 179 Au, and of odd-mass Au isotopes in general, was the discovery of a 326 ns isomer, with spin-parity 3/2 − [6]. The discovery required a combined analysis of data acquired at the University of Jyväskylä and at the CERN-ISOLDE facility, with application of various techniques such as high-statistics γ -ray spectroscopy, α-decay spectroscopy, αelectron summing effects, including GEANT4 simulations of atomic relaxation processes, and mass measurements. The 326 ns isomer in 179 Au de-excites by either a strong 62.4-27.1 keV cascade or via a weak 89.5 keV cross-over transition to the ground state. The decay pattern suggested a positive-parity, proton-hole configuration to be the ground state. The in-source laser spectroscopy experiment, performed recently at ISOLDE has assigned ground state spin-parities for both 177,179 Au unambiguously as 1/2 + [7], confirming the previous conclusion. Measured magnetic moments suggest mixed 3s 1/2 ⊕ 2d 3/2 proton-hole configurations for these ground states, in agreement with findings reported in [6]. The band head of structures reported in [3] was proposed to de-excite to the 326 ns isomer. Connecting transitions were not observed, due to their low energy and thus strong internal conversion. However, the data provided indirect evidence for them, see a detailed discussion in [6].
The data presented here prove that intruder configurations in 179 Au, identified in the study [3], decay exclusively via the 326 ns isomer. A new level scheme for 177 Au is constructed, which significantly differs from that reported in [4]. A major difference between the decay of the 1i 13/2 band in 177 Au and 179 Au is observed. The head of this band also feeds positive-parity structures, which is unprecedented in odd-mass Au isotopes. The 177 Au isotope is a unique case, with mixing of coexisting strongly and weakly deformed configurations, caused by their proximity. This mixing opens the decay path, which is otherwise suppressed.
Two separate experiments were performed at the Accelerator Laboratory of the University of Jyvaskylä. First, the 177 Au nuclei were produced via the 92 Mo( 88 Sr,p2n) 177 Au fusion-evaporation reaction. The bombarding energy of the 88 Sr 10+ beam was 399 MeV with an average intensity of approximately 2 particle nA. For production of 179 Au, the 82 Kr( 100 Ru,p2n) 179 Au reaction was used. The energy of the 82 Kr 15+ beam was 352 MeV with an average intensity of approximately 5 particle nA. In both experiments, selfsupporting metallic targets of isotopically enriched materials were used. Heavy-ion beams were delivered to the target chamber by the K = 130 MeV cyclotron.
Prompt γ radiation following reactions in the target was detected by the JUROGAM-II array, which consists of 24 clover-and 15 single-crystal EUROGAM-type Compton-suppressed germanium detectors. Reaction products were separated in-flight from the primary beam by the RITU gas-filled separator [8] according to their magnetic rigidities. At the focal plane of the separator, nuclei were implanted into double-sided silicon strip detectors (DSSD) of the detection system GREAT [9]. Prior to the implantation, nuclei passed through the multiwire proportional counter (MWPC), which provides discrimination of recoiling evaporation residues from the scattered primary beam particles (using energy losses in the gas and time-of-flight measured between the MWPC and the DSSD) and radioactive decays. The data were analyzed using GRAIN [10] and RADWARE [11] software. Isomeric transitions were detected at the focal plane of the separator with a planar double-sided germanium strip detector and three Clover-germanium detectors.
Partial level schemes of both 177,179 Au, constructed in the present work are presented in Fig. 1 and are discussed in detail and explained in the following text.
The relatively long half life of 179 Au (t 1/2 = 7.1(3) s [12]) and high implantation rate into the DSSD prevented the use of the recoil-decay tagging technique for this isotope. Fortunately, the high production rate of the 326 ns isomer [6], which decays via low-energy electric-dipole (E1) transitions that can be detected with high efficiency, offers an excellent option for application of the recoil-isomer tagging technique. In the data analysis process, the recoil implantations that were followed by detection of the aforementioned isomeric γ rays within the time window up to 1 μs, were selected. Prompt γ rays, observed in the target position array, that preceded such implantations, were sorted into a γ -γ matrix. Fig. 2a gives a projection of the matrix with the gate on the 353.8 keV transition, which is a known de-excitation of the 25/2 + member of the yrast 1i 13/2 band [3]. Except for other known inband transitions of the yrast band, the unresolved 144.7-145.3 keV doublet together with the 220.3, 241.9, 349.9, and 370.5 keV transitions are evident. Energies of components of the doublet were determined using the "running" gate technique [13]. The 220.3 and 241.9 keV transitions are known de-excitations of the 11/2 − and 13/2 − members of the 2 f 7/2 and 1h 9/2 proton-intruder configurations. The 144.7, and 145.3 keV transitions, as correctly assigned in the previous in-beam study [3], are de-excitations of the 13/2 + state of the yrast band feeding nearly degenerate 11/2 − and 13/2 − states, see the level scheme in Fig. 1. In the study [3], the 349.9 and 370.5 keV transitions were assigned as de-excitations of 13/2 + and 9/2 + members of the 1i 13/2 proton-intruder configuration feeding a floating state without spin assignment. Still the authors of the study [3] discuss the option that these γ rays arise from a single initial state in the text.
Since the 349.9 and 370.5 keV transitions are observed in the spectrum tagged with the decay of the 326 ns isomer, they feed states associated with intruder structures above the isomer. In the previous study, no γ -ray detectors were employed at the focal plane of the FMA and thus this conclusion could not be made. The energy difference of the 349.9 and 370.5 keV transitions exactly matches the energy difference of known 9/2 − , and 7/2 − band heads of 1h 9/2 , and 2 f 7/2 intruder configurations. This suggests that both transitions have a common initial state and feed these band heads, see the level scheme in Fig. 1. Fig. 2b depicts a projection of the γ -γ matrix tagged with the decay of the 326 ns isomer, with the gate on the 370.5 keV transition. The spectrum shows only known in-band transitions of the 1i 13/2 yrast band. Therefore, the initial state of the 370.5 keV transition is a member of this configuration. An alternative assignment with, e.g., 1h 9/2 , or the 2 f 7/2 intruders, would require an observation of corresponding rotational bands in coincidence with the 370.5 keV transition. This is not observed in the data and therefore the initial state is interpreted as the 9/2 + member of the 1i 13/2 proton-intruder configuration. The 9/2 + state is produced by the anti-aligned coupling of the 1i 13/2 proton with the firstexcited 2 + state in the 178 Pt core. Several such anti-aligned states are known in odd-mass Au isotopes, see [13][14][15] and references therein, although all of them are associated with the 1h 9/2 , or the 2 f 7/2 intruder configuration. The 15.1 keV transition with presumably electric-quadrupole (E2) character, connecting the 13/2 + with the 9/2 + state was not observed due to strong internal conversion. Au isotopes deduced in the present work. Note that transitions between 3/2 + and 1/2 + states, and between 7/2 − and 9/2 − states were not observed due to the strong internal conversion and low detection efficiency. Rotational bands associated with the 1i 13/2 proton-intruder configuration are known up to spin 57/2h in 177 Au, and 53/2h in 179 Au. So-far unobserved positive-parity states that are expected according to known systematics of odd-mass Au isotopes, associated with 3s 1/2 ⊕ 2d 3/2 proton-hole configuration (ground state), are indicated with dashed lines. The blue insert gives possible decays of 9/2 − , 7/2 − and 5/2 − states of the 1h 9/2 and 2 f 7/2 proton-intruder configurations in 179 Au. These transitions are not known. However there is indirect evidence for them from the present data and from the α decay of 183 Tl [6].
States associated with the 3s 1/2 ⊕ 2d 3/2 proton-hole configuration were studied in heavier odd-mass Au isotopes and welldeveloped systematics were established [14][15][16]. The first excited state above the 1/2 + ground state is the 3/2 + state, which was observed in 179 Au at 27.1 keV [6]. According to known systematics, a spin-parity of the next excited state is 5/2 + . This state, which is expected at approximately 270 keV in 179 Au, could be fed by the E2 de-excitation of the 9/2 + state of the 1i 13/2 configuration. Such a decay branch would not proceed through the 326 ns isomeric state and therefore cannot be observed in the spectrum presented in Fig. 2a. To identify this decay path, prompt γ rays preceding all recoil implantations, i.e., without requiring the isomeric decay to be detected, were analyzed. To suppress contaminations from isotopes produced via different evaporation channels of the reaction, the data were sorted into a triple-γ coincidence cube. This results in significantly reduced statistics, compared with double coincidences, but the influence of contaminations in a double gate is negligible and thus cleaner spectra can be projected. Fig. 2c gives a projection of the cube with gates on the 262.1, and 353.8 keV transitions. A signature of the direct decay path into the ground state would be observation of two parallel transitions that differ by 27.1 keV, and of the E2 de-excitation of the 9/2 + state. Parallel transitions would be decays of the 5/2 + to the 1/2 + ground state, and to the 3/2 + 27.1 keV first-excited state. No such transitions appear in the spectrum depicted in Fig. 2c.
The isotope 177 Au has two α-decaying states with well separated energies of emitted α particles (E α = 6.12 MeV and t 1/2 = 1.18 s for the ground state and E α = 6.16 MeV and t 1/2 = 1.46 s for the isomeric state [4]). In contrast to the 179 Au data, influence of randomly correlated events was found to be negligible and the recoildecay tagging technique could be applied. The prompt γ -ray data were sorted into two separate γ -γ matrices, tagged with the two different α decays.
The isomer that emits 6.12 MeV α particles is assigned as the 11/2 − state of the 1h 11/2 proton-hole configuration. This assignment is supported by the recent observation of a pattern of transitions feeding this state [17] and comparison with well established systematics [13][14][15]. The excitation energy of 189(16) keV was determined by the α-γ decay spectroscopy of 181 Tl [18]. Note that the 1h 11/2 proton-hole configuration is not involved in the decay of intruder configurations in 179 Au, because known systematics [14] suggests that the intruder band-head is located below the 1h 11/2 .  Fig. 3a gives the spectrum of γ rays tagged with the 11/2 − isomeric state α decay and in coincidence with the 257.5 keV transition of the known yrast band, which is associated with the 1i 13/2 proton-intruder coinfiguration, see previous in-beam γ -ray study [4]. In addition to the yrast band transitions the 241.2, 289.9, and 319.7 keV transitions are observed. The 241.2 keV transition is the known magnetic-dipole (M1) de-excitation of the 9/2 − band head of the 1h 9/2 intruder configuration to the 11/2 − of the 1h 11/2 proton-hole configuration [18]. Fig. 3b gives a spectrum of γ rays tagged with the 11/2 − isomeric state α decay and in coincidence with the 319.7 keV transition, which shows only the 241.2 keV transition together with the yrast band members. Therefore, the initial state of the 319.7 keV transition is interpreted as the 9/2 + member of the 1i 13/2 protonintruder configuration, on the basis of the same arguments as were used for the 370.5 keV transition in 179 Au, see the above discussion.
In the data evaluation for 177 Au [5], the 290.3 keV transition was reported. It was interpreted as the first in-band transition of the 1h 9/2 band. The observed coincidence between the 290.3 keV and transitions of the 1i 13/2 band, which was reported already in the original publication [4], was explained by an unobserved E1 feeding from the 13/2 + state of the yrast band. Presently, the 289.9 keV transition is interpreted as a feeding of the 7/2 − band head of the so-far unknown 2 f 7/2 band from the 9/2 + state. This interpretation is based on the analogy with the decay pattern of the 9/2 + state in 179 Au, see the level scheme in Fig. 1. However, E1 decays of the 13/2 + , analogous to 144.7, and 145.3 keV transitions in 179 Au, can exist. There is a weak peak at 261.2 keV observed in coincidence with the 257.5 keV transition, see Fig. 3a. The rotational band associated with the 2 f 7/2 configuration is not known, but according to known systematics of 1h 9/2 and 2 f 7/2 bands [3,19,20], 11/2 − and 13/2 − members are expected to be nearly degenerate. Therefore, the 261.2 keV γ ray is interpreted as the 11/2 − to 7/2 − transition of the 2 f 7/2 band. The 289.9 keV peak is probably an unresolved doublet. In this case it is not possible to apply the "running" gate technique, since there are no characteris- tic coincidences for both transitions. However, this does not affect the understanding of the nuclear structure of 177 Au. The E1 transitions feeding the 11/2 − and the 13/2 − state were not observed because of their low energy and thus low detection efficiency of the JUROGAM-II array.
Transition probabilities for possible decays of 13/2 + states of the yrast bands were investigated for both isotopes. In the present work, fast collective E2 transitions feeding 9/2 + band heads are proposed as dominant de-excitation paths, see the discussion above. In the 179 Au isotope, branching ratios of 31.6% for the 144.7 keV, 22.6% for the 145.3 keV, and 45.8% for un-observed the 15.1 keV transition, were determined. The branching ratio for the un-observed transition was deduced as the sum of intensities of the 370.5, and 349.9 keV γ rays in the 353.8 keV coincidence gate, see Fig. 2a. The reduced transition probability of 100 -300 W.u. is assumed for the 13/2 + to 9/2 + transition. This assumption is based on the known reduced transition probability of 200(120) W.u. [21] of the 9/2 − to 5/2 − de-excitation in 185 Au. Using the above branching ratios, this yields the reduced transition probabilities of (1 -5)×10 −5 W.u. for both E1 transitions de-exciting the 13/2 + state in 179 Au. The information on the E1 transition strengths is scanty in odd-mass Au isotopes. In 189 Au, the 7/2 − state of the 1h 11/2 proton-hole configuration feeds two 5/2 + states of the mixed 3s 1/2 ⊕ 2d 3/2 proton-hole configuration via E1 transitions. These de-excitations have reduced transition probabilities of 3.0 +15 −7 ×10 −5 W.u. and 2.1 +11 −5 ×10 −5 W.u., respectively [22]. Strengths of E1 transitions connecting two states with proton-intruder character are not known in odd-mass Au isotopes. In 175,179 Au, isomeric E1 transitions with the intruder-to-hole nature were observed, however their reduced transition probabilities were measured to be 10 −6 -10 −8 W.u. [6,23]. Therefore, the above values, estimated for transitions in 179 Au, corroborate the interpretation with the intruder character of both of its initial and final states. Adopting these values of reduced transition probabilities for the 177 Au isotope suggests that 5 -10% of de-excitation of 13/2 + state should proceed via unobserved E1 transitions, feeding the 11/2 − and 13/2 − states of intruder bands. This is in agreement with the observation of the weak 261.2 keV transition in coincidence with the 257.5 keV transition, see Fig. 3a. Fig. 4a gives the spectrum of γ rays tagged with the groundstate α decay and in prompt coincidence with the 257.5 keV transition which, as already noted, is a member of the 1i 13/2 band. In addition to the yrast band members, 264.5, 290.2, and 452.6 keV transitions are observed. Fig. 4b,c give spectra of γ rays tagged with the ground-state α decay and in prompt coincidence with the The unambiguous 1/2 + ground-state spin-parity assignment [7] provides another supporting argument for an unobserved transition in the de-excitation path of the 13/2 + state of the yrast band. This path contains only two transitions in a cascade, since the 290.2, and 264.5 keV transitions are parallel, see the level scheme in Fig. 1. The 13/2 + state cannot de-excite into the 1/2 + ground state via only two transitions, since it would require a large multipolarity, and thus a slow transition rate, for at least one of them. This is clearly not the case with the present data, since all transitions were observed at the target position, and in prompt coincidences.
The 177 Au isotope is a unique case where the proton-intruder 1i 13/2 yrast cascade splits at the bottom, feeding both the ground and the isomeric state (via the 1h 9/2 intruder state). This is not the case with the 179 Au isotope, see the discussion above and the level scheme in Fig. 1. The de-excitation probabilities of the bottom of the 1i 13/2 intruder band were determined to be 69(13)% for the feeding the ground state, and 31(6)% for the feeding the αdecaying isomeric state, using the "inverse" tagging technique. The gate was set on the 160.2 keV transition detected at the target position, and the spectrum of corresponding α-particle energies was plotted. The intensities of 6.12 and 6.16 MeV peaks in the α spectrum (not shown here) gave corresponding de-excitation probabilities (after correction for known α-decay branching ratios, taken from [18]). Weak de-exctitation paths through 13/2 − and 11/2 − states were neglected. Assuming the same reduced transition probabilities for E1 de-excitations as those estimated in 179 Au, the B(E2) = 1 -20 W.u. is expected for the 9/2 + to 5/2 + transition. This is comparable with the reduced transition probability of 14(7) W.u. for the 5/2 + to 1/2 + E2 transition in 193 Au [24], which is the nearest odd-mass Au isotope, where the strength of the E2 transition connecting positive-parity, proton-hole states is known. The same transition in the stable 197 Au isotope has a reduced transition probability of 14.4(17) W.u. [25]. This suggests an unhindered character for the 9/2 + to 5/2 + transition in 177 Au. Measurements of lifetimes of excited states of both 177,179 Au isotopes, that would yield absolute values of reduced transition probabilities, are therefore highly demand to elucidate the details.
The different de-excitation pattern observed in 177 Au is explained by a configuration mixing. According to the systematics of the positive-parity bands in odd-mass Au isotopes, the 9/2 + state of the ground state band can be expected at a similar energy as in 187,189 Au, i.e., between 700 and 760 keV [13][14][15]. Therefore, there are two 9/2 + states expected to be located close to each other in 177 Au. One is the anti-aligned state of the 1i 13/2 configuration, see the discussion above and one is the 9/2 + member of the groundstate band. Because these configurations are probably located close to each other, a strong mixing is expected. It is an intruder component in the wave function of both states that opens a decay path of the 13/2 + member of the 1i 13/2 configuration towards the ground state. Estimated unhindered nature of the E2 transition, see discussion above, corroborates such interpretation. Such a situation is not known not occur in any other odd-mass Au isotope, and therefore decays into proton-hole states were not observed. In 179 Au, the effect is weaker, since both 9/2 + states are more separated in the energy. However, the non-observation of the 9/2 + to 5/2 + decay in 179 Au can be explained by the parabolic pattern of the excitation energy of intruder configurations [6]. The energy of the 9/2 + to 5/2 + transition in 179 Au can be expected to be approximately 215 keV. Since the E2 transition strength depends on the γ -ray energy in the fifth power, branching ratio of only approximately 2% for the feeding of the ground-state configuration can be expected. Such a weak transition cannot be observed in present experiment due to limited statistics.
The extensive systematics for intruder structures in odd-mass Au isotopes were established by means of in-beam γ -ray spectroscopy [3,19,20,[26][27][28][29], and β-decay spectroscopy [13,14]. The states associated with the 1i 13/2 band were observed to de-excite exclusively to states of the same configuration or into the 1h 9/2 configuration via parity-changing E1 transitions. De-excitations into positive-parity states associated with the proton-hole configurations are strongly hindered due to the intruder-state-to-holestate character of such transitions, or might be suppressed by the energy factor, as it is in 179 Au. Another examples of such hindrance is the observation of retarded M1 hole-state-to-intruderstate transitions with reduced transition probabilities of approximately 5 × 10 −5 W.u. in 185,187,189 Au [14], or the E3 isomerism in odd-Tl isotopes, see [18], and references therein.
The present work provides a key advance in understanding spin order associated with intruder bands. Thus, the 1i 13/2 band exhibits the appearance of a spin-(j−2) state below the spin-j state, similar to the 1h 9/2 and 2 f 7/2 bands. Establishing this is critical for the organization of the decays of high-spin states. In this mass region, high-spin in-beam studies play a major role because it is very difficult to populate low-spin states: the standard approach via β decay is limited by competing α-decay channels.
At the next level of study, the present work paves the road to adding the high level of detail expected in 181,183 Au by comparison with 185,187 Au. We note in particular that the strongly-coupled band observed in 177 Au, reported earlier [17], indicates that there are structural changes occurring in the Au isotopes which point to multiple shape coexistence, even lying beyond such structures established in 187 Au. Recent measurement [30] of lifetimes of excited states of the rotational band associated with the intruder 0 + configuration in 178 Hg corroborates such interpretation.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.