Emergence of an island of extreme nuclear isomerism at high excitation near $^{208}$Pb

Metastable states with T$_{1/2}$ = 8(2) ms in $^{205}$Bi and T$_{1/2}$ = 0.22(2) ms in $^{204}$Pb, with $\approx $ 8 MeV excitation energy and angular momentum $\ge $ 22 $\hbar $, have been established. These represent, by up to two orders of magnitude, the longest-lived nuclear states above an excitation energy of 7 MeV, ever identified in the nuclear chart. Additionally, the half-life of the 10.17 MeV state in $^{206}$Bi has been determined to be 0.027(2) ms, the next highest value in this highly excited regime. These observations indicate the emergence of an island of extreme nuclear isomerism arising from core-excited configurations at high excitation in the vicinity of the doubly closed-shell nucleus $^{208}$Pb. These results are expected to provide discriminating tests of the effective interactions used in current large-scale shell-model calculations.

Metastable states in atomic nuclei, also referred to as isomers, represent the manifestation of the associated wave functions being pure and quite distinct from those of other levels in their vicinity. Consequently, transition rates for decay of these states are orders of magnitude lower than those of nearby levels. The exploration of a variety of nuclear isomers, whose decay may be hindered by the required large change in angular momentum, or in its projection on the symmetry axis of a deformed nucleus, or in its shape, or a considerable difference in the configurations of initial and final levels, leads to crucial insights which further the understanding of the strongly-interacting, nuclear many-body system. Specifically, isomeric properties play a major role in refining effective interactions for shell-model calculations of near-spherical nuclei. Detailed descriptions are available in recent reviews [1][2][3][4].
In some instances, the degree of hindrance of the decay may be quite extreme, leading to isomeric half-lives which are larger by many orders of magnitude in comparison to those of other similar states. Some examples of such extreme nuclear isomerism are the: (a) "spin isomer" in 180 Ta (Z=73) with T 1/2 > 7.1 x 10 15 y [5], (b) "K isomer" in 178 Hf (Z=72) with T 1/2 = 31(1) y [6], (c) "shape isomer" in 242 Am (Z=95) with T 1/2 = 14(1) ms [7]. All of these isomers lie at relatively low (< 2.5 MeV) excitation energy. In the region around the doubly closed-shell nucleus 208 Pb, a notable isomer at relatively low excitation is the α-decaying 2.93-MeV state with T 1/2 = 45.1(6) s in 212 Po [8]. With an increase in excitation energy, a trend of decreasing half-lives is evident. In lighter nuclei, with fewer valence nucleons and lower level density, in some instances, longer-lived states may result, such as the 45.9(6)-s level at 6.958 MeV, with total angular momentum (henceforth, referred to as spin), I = 12 , in 52 Fe (Z=26) [9], and the β-decaying (21 + ), 0.40(4)-s state at 6.67 MeV in 94 Ag [10]. The longest-lived isomers at very high excitation (> 7 MeV), known prior to this work, are the 8.533-MeV state in 212 Fr (Z=87) with T 1/2 = 23.6(21) µs [11], and the 8.095-MeV level in 213 Fr with T 1/2 = 3.1(2) µs [12]. In fact, the isomer in 212 Fr had been characterized as an "outstanding example" of a spin trap in near-spherical nuclei, and given its long half-life and high excitation energy, had been termed as an "extreme isomer" [2]. It had also been recognized then that "more extreme isomers might exist in heavy nuclei" [2].
It should be noted though that no specific predictions were made. The isomers reported in the present work have been discovered two decades later, despite the large body of recent work on isomers in the A = 200-215 region by several groups worldwide [13]. The presence of such long-lived states in the >7-8 MeV excitation range, which decay by γ-ray emission, is noteworthy.
Surveys of isomers across the nuclear chart [13,14] reveal that many long-lived states at high excitation are known to exist in heavy nuclei, which lie near the line of β-stability.
As a result, these isomers are difficult to access experimentally, since compound nuclear fusion-evaporation reactions, which can populate levels at the highest excitation, favor the production of isotopes deficient in neutrons. Inelastic excitation and multi-nucleon transfer reactions, on the other hand, can be used to access nuclei near the line of stability or even on the neutron-rich side. However, the cross sections and highest spin attainable are limited in comparison with fusion-evaporation products. With the sensitivity provided by large γ-ray detector arrays, and pulsed beams from accelerators with a range of timing options, exploring isomers at high excitation near the line of β-stability becomes feasible.
An impressive example is the recent study of the heaviest known doubly closed-shell nucleus 208 Pb (Z=82, N =126), wherein states up to spin 30 and excitation energy, E x = 16.4 MeV, have been established [15]. The focus of the present work is the region near 208 Pb, where the availability of numerous orbitals with high values of intrinsic angular momentum, e.g., h 11/2 proton (π) and i 13/2 neutron (ν) holes, and πh 9/2 , πi 13/2 and νg 9/2 particles, leads to conditions conducive for the realization of long-lived states at very high excitation. Recent work, including that of this collaboration [16][17][18], has revealed the presence of several states with half-lives up to hundreds of microseconds at intermediate excitation, but the 23.6(21)µs isomer in 212 Fr at 8.533 MeV was thus far the longest-lived state above 7 MeV [11].
The present work describes newly identified metastable states in 205 Bi (Z = 83) and 204 Pb whose half-lives are about two orders of magnitude larger than other isomers in a similar excitation range. Additionally, the half-life of the 10.17-MeV state in 206 Bi, which was previously reported to be > 2 µs [19], has been measured and found to be slightly longer than that of the 212 Fr isomer. These newly-identified metastable states have a different character as compared to the so-called "spin isomers" in the Rn-Fr-Ra region, as will be described below.
The work described in this letter involves the population of highly-excited levels in isotopes of Pb, Bi and other elements through multi-nucleon transfer reactions with heavy, highly-energetic projectiles: (a) 1450-MeV 209 Bi and (b) 1430-MeV 207 Pb beams, incident on a 50 mg/cm 2 Au target. The Gammasphere detector array [20], which at the time consisted of 100 Compton-suppressed high-purity germanium detectors, was used to record coincident γ rays emitted within ≈1 µs of each other. Details regarding the experiment and data analysis are presented elsewhere [21]. In previous reports on 205 Bi and 204 Pb, levels up to 6.7 MeV and 8.1 MeV, respectively, had been identified utilizing α particles as projectiles incident on 205 Tl and 204 Hg targets [22,23]. These experiments were focused on the decays of short-lived levels, and a number of transitions up to I ≈ 20 were placed in the respective level schemes. The focus of the present work was on identifying metastable states and establishing their half-lives and decay paths.
Pulsed beams from the ATLAS accelerator at Argonne National Laboratory were used in different beam-sweeping intervals: successive bursts separated by ≈ 825 ns up to 8 s, enabled a search for and identification of isomers with half-lives in the microseconds, milliseconds and seconds time ranges. The data were collected in "beam-off" periods of 800 µs, 3 ms, 3 s and 8 s, i.e., the pulsed beam was deflected away from the target for these durations. The coincidence window was ≈ 1 µs. When beam pulses were separated by 825 ns, three-or higher-fold coincidence data were collected. For larger time periods, during the "beam-off" periods of 800 µs and above, two-and higher-fold data were recorded. The data were sorted offline into histograms of two, three and four dimensions involving energy and time parameters, and subsequently analyzed using the RADWARE and TSCAN suite of programs [24,25]. Some examples of the histograms used for the data analysis are listed here: (a) two-, three-and four-dimensional symmetric, γ-energy histograms for establishing the excited level structures; (b) time-gated, triple-γ energy coincidence histograms to establish long half-lives; (c) energy-energy-time difference histograms for determining half-lives T 1/2 < 1 µs; (d) prompt-delayed, two-and three-dimensional γ-energy histograms for identifying coincidence events across isomeric states with T 1/2 < 1 µs; (e) angle-sorted, γ-energy, asymmetric matrices to determine transition multipolarities using the method of directional angular correlations from oriented states (DCO) [26]. The so-called "prompt" and "delayed" coincidence events corresponded to the detection of at least three γ rays within ±40 ns and 50-650 ns of the trigger, respectively, when the beam pulses were separated by 825 ns.
A total of thirty new γ rays have been placed in the level schemes of 204 Pb and 205 Bi from the present work. However, only the transitions crucial for establishing the spin and parity quantum numbers of the isomeric levels are discussed. A paper describing the detailed level schemes for 204 Pb and 205 Bi deduced from this work is being prepared [27]. The newly established γ rays, along with previously reported ones, are displayed in Fig. 1. The γ-ray spectra illustrated in Figs. 1 and 2 represent three-fold delayed coincidence events. In To determine the half-life of the 10.17-MeV level in 206 Bi, previously reported to be > 2 µs [19], the time distribution of the summed coincidence counts of the most intense γ rays in the cascade between the 10.17 and 1.045 MeV levels was inspected in the 800-µs beam-off data, leading to a half-life of 0.027(2) ms, as indicated in Fig. 3(c). A comparison of the above half-lives with those of other isomeric levels above an excitation energy of 7 MeV [14], and with T 1/2 > 1 µs, across the nuclear chart is displayed in Fig. 4, where it is evident that the data points for 204 Pb and 205 Bi are outliers compared to those previously identified.
The excitation energy and spin-parity quantum numbers for the newly-identified isomer in 204 Pb were established as E x = 8349 keV and I π = (22 + ). The 481-keV γ ray in 204 Pb ( Fig. 1) is not observed in the so-called "prompt" data, which are recorded within a few tens of nanoseconds of the beam being incident on the target, but is clearly visible in the data collected during the "beam-off" periods. Therefore, it is attributed to the direct deexcitation of the 8349-keV isomer. The 481-and 2520-keV γ rays, which are newly identified in the present work, are found to be in cascade, with the latter directly feeding the previously established 16 + , 5348-keV level with a proposed ν(i −2 13/2 , f −1 5/2 , p −1 3/2 ) configuration in 204 Pb [23].
The 2520-keV transition most likely has E3 character based on a calculation following the prescription in previous work [28][29][30][31], described below, leading to an I π = (19 − ) assignment for the E x = 7868-keV initial level. The expected transition energy for the E3 excitation built on the four-nucleon-hole, 16 + state can be estimated as follows. The unperturbed energy of the E3 excitation in 208 Pb would be 2615 keV. On account of the coupling to configurations involving multiple nucleons, energy shifts would result from the two i 13/2 neutrons and the two low-j neutrons. The final energy can be expressed as the sum of energy shifts corresponding to the individual constituents of such a configuration, which, in this case, turns out to be 2483 keV, in fair agreement with the experimentally observed 2520-keV value, thus validating its E3 assignment. To determine the multipolarity of the 481-keV transition feeding the level deexcited by the 2520-keV γ ray, intensity balance considerations have been used, for which a detailed procedure may be found in our earlier work [16][17][18]: either E3 or M 1 character is inferred, due to the similarity of the theoretical total conversion coefficients (0.111 and 0.119, respectively), from BRICC [32]. Based on typical transition rates expected for γ rays with different multipolarities, M 1 character appears unlikely. An a background of about 1 count. The resultant peak may or may not be discernible in the spectra, therefore the upper limit of 150 keV. Of course, it is quite possible that the actual energy or energies of the transitions deexciting the isomer is significantly lower, which is why x < 150 keV represents an upper limit only. We have performed additional calculations towards a more sophisticated estimate which will be described in our future paper [27]. In view of the measured half-life and the corresponding inferred transition rates for different multipolarities, and based on the results of shell-model calculations performed (described below), a (51/2 − ) spin-parity assignment appears quite probable for the isomer implying a decay through low-energy (< 150 keV) E3 and/or M 2 transitions.
Prior to this work, metastable states reported in this region beyond E x = 7 MeV, with the highest half-lives, were in the Rn-Fr-Ra isotopes [1,2,11,12]. The ones identified in Tl-Pb-Bi isotopes prior to this work were primarily at lower excitation [28][29][30][31]33], except the states at very high excitation in 208 Pb [15]. The primary differences in the nature of the above the 9/2 + ground state, with these levels resulting from the occupation of the j 15/2 and g 9/2 orbitals, respectively, therefore the half-life of the 15/2 − level is only 1.36 (30) ns [34].
It is possible that long-lived states at high excitation may also be realized in Po (Z = 84) and At (Z = 85) isotopes with N < 126, and neutron-rich ones with Z < 82, which would become accessible with rare-isotope beams.
It may be noted that the isomers in the Rn-Fr-Ra region were populated through fusionevaporation reactions, as compared to multi-nucleon transfer reactions in the present work.
In the latter case, quality spectroscopic data at high excitation are relatively more difficult to obtain, therefore long-lived isomers in this energy range in the Tl-Pb-Bi region around the line of stability remained undiscovered until now. It is noteworthy that the isomers in the Tl-Pb-Bi region involve either hole-hole or particle-hole excitations, and in the Rn-Fr-Ra case particle-particle configurations, comprising nucleons in high-j orbitals.
To aid in the understanding of the experimental data, shell-model calculations have been performed for 204 Pb and 205 Bi using the KHH7B effective interaction in the model space Z = 58-114 and N = 100-164 around doubly-magic 208 Pb using the OXBASH code [35]. The model space includes the proton orbitals 1d 5/2 , 0h 11/2 , 1d 3/2 and 2s 1/2 below Z = 82, and the 0h 9/2 , 1f 7/2 , and 0i 13/2 ones above, and the neutron orbitals 0i 13/2 , 2p 3/2 , 1f 5/2 , and 2p 1/2 below N = 126 and the 1g 9/2 , 0i 11/2 , and 0j 15/2 ones above it. For the KHH7B effective interaction, the cross-shell two-body matrix elements (TBMEs) are taken from the G-matrix potential (H7B) [36], while the proton-neutron hole-hole and particle-particle TBMEs are from the Kuo-Herling interaction [37], with modifications included later [38]. with a νi −4 13/2 configuration is also expected to lie in this vicinity. It is quite unlikely that any of these states are candidates for the isomer at 8349 keV since, in that case, the 481-keV deexciting transition (Fig. 1) would be of dipole character and would be inconsistent with the 0.22(2) ms half-life. The calculations indicate that states with spin > 20 can arise in either of two ways viz., the π(h −1 11/2 , h 9/2 ) ⊗ ν(i −2 13/2 ) and the π(h −1 11/2 , h 9/2 ) ⊗ ν(f −1 5/2 , p −1 1/2 , i −2 13/2 ) configurations. While both these configurations can lead to the 22 + level calculated to be at 8085 keV, the amplitude for the 4-quasiparticle state is found to be 14.2%, while for the one with six quasiparticles it is 56.1%. Though the excitation energies are reasonably reproduced in most cases, the shell-model calculations do not give a good account of the measured transition probabilities.
In 205 Bi, levels with spin-parity quantum numbers 43/2 − , 45/2 + , 45/2 − , 47/2 + , 47/2 − and 51/2 − are calculated to lie in the region between 6.5-7.7 MeV. It is quite unlikely that the isomer at an excitation energy of 7913+x keV has I ≤ 47/2 since, in that case, relatively fast E2 or M 2 transitions of several hundred keV would deexcite to levels with spin up to 43/2 , inconsistent with the measured 8-ms half-life. While the shell-model calculations indicate that multiple 51/2 − states are possible, only one of these, with the πi 13/2 ⊗ ν(f −1 5/2 , i −3 13/2 ) configuration, is low enough in energy to be consistent with the experimental value. Four other 51/2 − states, all involving the νg 9/2 orbital, are possible but are calculated to lie above 9 MeV, and are therefore unlikely to be candidates for the isomeric configuration.
Further, all other levels such as the 53/2 + state with the πi 13/2 ⊗ ν(i −4 13/2 ) configuration are also unlikely since they lie above 9 MeV. Therefore, based on the expectation from the shell-model calculations, the only candidate for the isomer would be the 51/2 − state with the πi 13/2 ⊗ ν(f −1 5/2 , i −3 13/2 ) configuration. In the previous work on 206 Bi [19], configuration assignments for the isomers with I π = (28 − ) and (31 + ), and half-lives of 155 ns and 0.027 ms, respectively, had not been proposed. The (28 − ) isomer likely results from the πi 13/2 ⊗ ν[i −3 13/2 , (p −1 1/2 , g 9/2 )] 43/2− configuration, with the (26 + ) state to which it decays having a πh 9/2 ⊗ ν[i −3 13/2 , (p −1 1/2 , g 9/2 )] 43/2− one. Thus, the isomerism would be associated with the πi 13/2 → πh 9/2 transition with a strength With focused experiments to identify more such instances, using multi-nucleon transfer reactions with highly-energetic, heavy-ion beams and suitably long pulsing periods, coupled with the sensitive detection of γ rays using large detector arrays, which are being planned by this collaboration, similar long-lived states are expected to be found in neighboring nuclei, thus redefining one extreme of isomerism.    Rn-Fr-Ra region, respectively. The evidently different nature of these two types of isomers is discussed in the text.