# Emergence of an island of extreme nuclear isomerism at high excitation near
208Pb

S.G. Wahid  University of Massachusetts Lowell, USA School of Physical
Sciences, UM-DAE Centre for Excellence in Basic Sciences, University of
Mumbai, Mumbai 400098, India  S.K. Tandel<EMAIL_ADDRESS>;
<EMAIL_ADDRESS>School of Physical Sciences, UM-DAE Centre for Excellence
in Basic Sciences, University of Mumbai, Mumbai 400098, India  Department of
Physics, University of Massachusetts Lowell, Lowell, Massachusetts 01854, USA
Saket Suman  School of Physical Sciences, UM-DAE Centre for Excellence in
Basic Sciences, University of Mumbai, Mumbai 400098, India  P.C. Srivastava
Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667,
India  Anil Kumar  Department of Physics, Indian Institute of Technology
Roorkee, Roorkee 247667, India  P. Chowdhury  Department of Physics,
University of Massachusetts Lowell, Lowell, Massachusetts 01854, USA  F.G.
Kondev  Argonne National Laboratory, Argonne, Illinois 60439, USA  R.V.F.
Janssens  Department of Physics and Astronomy, University of North Carolina at
Chapel Hill, Chapel Hill, North Carolina 27599, USA  Triangle Universities
Nuclear Laboratory, Duke University, Durham, North Carolina 27708, USA  M.P.
Carpenter  Argonne National Laboratory, Argonne, Illinois 60439, USA  T.
Lauritsen  Argonne National Laboratory, Argonne, Illinois 60439, USA  D.
Seweryniak  Argonne National Laboratory, Argonne, Illinois 60439, USA  S. Zhu
Argonne National Laboratory, Argonne, Illinois 60439, USA

###### Abstract

Metastable states with T1/2 = 8(2) ms in 205Bi and T1/2 = 0.22(2) ms in 204Pb,
with $\approx$ 8 MeV excitation energy and angular momentum $\geq$ 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 206Bi 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 208Pb.
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 Dracoulis2016 ; Walker1999 ; Kondev2015 ; Walker2020 . 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 180Ta ($Z$=73) with T1/2 $>$
7.1 x 1015 y Hult2006 , (b) “K isomer” in 178Hf ($Z$=72) with T1/2 = 31(1) y
Helmer1973 , (c) “shape isomer” in 242Am ($Z$=95) with T1/2 = 14(1) ms
Polikanov1962 . All of these isomers lie at relatively low ($<$ 2.5 MeV)
excitation energy. In the region around the doubly closed-shell nucleus 208Pb,
a notable isomer at relatively low excitation is the $\alpha$-decaying
2.93-MeV state with T1/2 = 45.1(6) s in 212Po Perlman1962 . 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 $\hbar$, in 52Fe ($Z$=26) Geesaman1975 , and the $\beta$-decaying (21+),
0.40(4)-s state at 6.67 MeV in 94Ag LaCommara . The longest-lived isomers at
very high excitation ($>$ 7 MeV), known prior to this work, are the 8.533-MeV
state in 212Fr ($Z$=87) with T1/2 = 23.6(21) $\mu$s Byrne1990 , and the
8.095-MeV level in 213Fr with T1/2 = 3.1(2) $\mu$s Byrne1989 . In fact, the
isomer in 212Fr 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” Walker1999 . It had
also been recognized then that “more extreme isomers might exist in heavy
nuclei” Walker1999 . 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 Kondev2021 . The presence of such
long-lived states in the $>$7-8 MeV excitation range, which decay by
$\gamma$-ray emission, is noteworthy.

Surveys of isomers across the nuclear chart Kondev2021 ; Jain2015  reveal that
many long-lived states at high excitation are known to exist in heavy nuclei,
which lie near the line of $\beta$-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
$\gamma$-ray detector arrays, and pulsed beams from accelerators with a range
of timing options, exploring isomers at high excitation near the line of
$\beta$-stability becomes feasible. An impressive example is the recent study
of the heaviest known doubly closed-shell nucleus 208Pb ($Z$=82, $N$=126),
wherein states up to spin 30 $\hbar$ and excitation energy, Ex = 16.4 MeV,
have been established Broda2017 . The focus of the present work is the region
near 208Pb, where the availability of numerous orbitals with high values of
intrinsic angular momentum, e.g., h11/2 proton ($\pi$) and i13/2 neutron
($\nu$) holes, and $\pi$h9/2, $\pi$i13/2 and $\nu$g9/2 particles, leads to
conditions conducive for the realization of long-lived states at very high
excitation. Recent work, including that of this collaboration Wahid2020 ;
Roy2019 ; Bothe2022 , has revealed the presence of several states with half-
lives up to hundreds of microseconds at intermediate excitation, but the
23.6(21)-$\mu$s isomer in 212Fr at 8.533 MeV was thus far the longest-lived
state above 7 MeV Byrne1990 . The present work describes newly identified
metastable states in 205Bi (Z = 83) and 204Pb 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 206Bi, which was
previously reported to be $>$ 2 $\mu$s Cieplicka2012 , has been measured and
found to be slightly longer than that of the 212Fr 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 209Bi and (b)
1430-MeV 207Pb beams, incident on a 50 mg/cm2 Au target. The Gammasphere
detector array LeeJanssens , which at the time consisted of 100 Compton-
suppressed high-purity germanium detectors, was used to record coincident
$\gamma$ rays emitted within $\approx$1 $\mu$s of each other. Details
regarding the experiment and data analysis are presented elsewhere Tandel2015
. In previous reports on 205Bi and 204Pb, levels up to 6.7 MeV and 8.1 MeV,
respectively, had been identified utilizing $\alpha$ particles as projectiles
incident on 205Tl and 204Hg targets Byrne1989_2 ; Linden1978 . These
experiments were focused on the decays of short-lived levels, and a number of
transitions up to I $\approx$ 20 $\hbar$ 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
$\approx$ 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 $\mu$s, 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 $\approx$ 1 $\mu$s. 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 $\mu$s 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
Radford1995 ; Jin1992 . Some examples of the histograms used for the data
analysis are listed here: (a) two-, three- and four-dimensional symmetric,
$\gamma$-energy histograms for establishing the excited level structures; (b)
time-gated, triple-$\gamma$ energy coincidence histograms to establish long
half-lives; (c) energy-energy-time difference histograms for determining half-
lives T1/2 $<$ 1 $\mu$s; (d) prompt-delayed, two- and three-dimensional
$\gamma$-energy histograms for identifying coincidence events across isomeric
states with T1/2 $<$ 1 $\mu$s; (e) angle-sorted, $\gamma$-energy, asymmetric
matrices to determine transition multipolarities using the method of
directional angular correlations from oriented states (DCO) Krane73 . The so-
called “prompt” and “delayed” coincidence events corresponded to the detection
of at least three $\gamma$ rays within $\pm$40 ns and 50-650 ns of the
trigger, respectively, when the beam pulses were separated by 825 ns.

A total of thirty new $\gamma$ rays have been placed in the level schemes of
204Pb and 205Bi 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 204Pb and
205Bi deduced from this work is being prepared Wahid2022 . The newly
established $\gamma$ rays, along with previously reported ones, are displayed
in Fig. 1. The $\gamma$-ray spectra illustrated in Figs. 1 and 2 represent
three-fold delayed coincidence events. In Figs. 1(a) and 1(b), the summed
coincidence spectra obtained with two simultaneous gates on all combinations
of pairs of transitions in the previously known cascades in: (a) 204Pb:
1006-325-618-167-1046-316-433 keV spanning I = 9 to 19 $\hbar$, and (b) 205Bi:
881-286-697-641-600-516 keV spanning I = 9/2 to 31/2 $\hbar$, are presented.
The quality of the data with fewer gating transitions, specifically the three
decay branches from the isomer in 204Pb, are displayed in Fig. 2.

The level scheme of 204Pb has been extended up to a new long-lived isomer at
Ex = 8349 keV, the half-life of which has been determined to be 0.22(2) ms
[Fig. 3(a)], by inspecting the time distribution of the summed coincidence
counts in the previously known 1006-325-618-167-1046-316-433 keV cascade
spanning I = 9-19 $\hbar$ Linden1978 , when the beam was incident on the
target for 200 $\mu$s, and data were collected during a 800-$\mu$s beam-off
period. In the case of 205Bi, an inspection of the 800-$\mu$s and 3-ms beam-
off data indicated that the half-life of the isomer was greater than these
periods. Therefore, data from the next higher available pulsing period (3-s
beam-off) were scrutinized. The time distribution of the summed coincidence
counts in the previously known 641-600-516-keV cascade [Fig. 1(b)] spanning a
spin range 25/2 to 31/2 $\hbar$ Byrne1989  indicate a half-life of 8(2) ms for
the metastable state in 205Bi [Fig. 3(b)]. To determine the half-life of the
10.17-MeV level in 206Bi, previously reported to be $>$ 2 $\mu$s Cieplicka2012
, the time distribution of the summed coincidence counts of the most intense
$\gamma$ rays in the cascade between the 10.17 and 1.045 MeV levels was
inspected in the 800-$\mu$s 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 Jain2015 , and
with T1/2 $>$ 1 $\mu$s, across the nuclear chart is displayed in Fig. 4, where
it is evident that the data points for 204Pb and 205Bi are outliers compared
to those previously identified.

The excitation energy and spin-parity quantum numbers for the newly-identified
isomer in 204Pb were established as Ex = 8349 keV and Iπ = (22+). The 481-keV
$\gamma$ ray in 204Pb (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 $\gamma$ 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 $\nu(i^{-2}_{13/2},f^{-1}_{5/2},p^{-1}_{3/2})$ configuration in 204Pb
Linden1978 . The 2520-keV transition most likely has $E3$ character based on a
calculation following the prescription in previous work Wrzesinski2003 ;
Broda2011 ; Szpak2011 ; Wrzesinski2015 , described below, leading to an Iπ =
(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 208Pb would be 2615 keV. On account of the coupling to
configurations involving multiple nucleons, energy shifts would result from
the two i13/2 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 $\gamma$ ray,
intensity balance considerations have been used, for which a detailed
procedure may be found in our earlier work Wahid2020 ; Roy2019 ; Bothe2022 :
either $E$3 or $M$1 character is inferred, due to the similarity of the
theoretical total conversion coefficients (0.111 and 0.119, respectively),
from BRICC Kibedi2008 . Based on typical transition rates expected for
$\gamma$ rays with different multipolarities, $M$1 character appears unlikely.
An $E$3 character for the 481-keV transition would imply spin-parity quantum
numbers (22+) for the isomeric level. This would be consistent with similar
isomeric transitions in 212,213Fr, 206Bi Byrne1990 ; Byrne1989 ; Cieplicka2012
, and many other nuclei in the vicinity of 208Pb. It may be noted that there
are no long-lived isomers in this region which decay via $M$1 transitions.

In 205Bi, it was only possible to constrain the spin-parity of the isomer
based on various experimental and theoretical considerations, but a firm
assignment, comparable to the 204Pb case, was not possible. All $\gamma$ rays
assigned to 205Bi [Fig. 1(b)] are visible in the “prompt” data ruling out the
possibility that any of these directly deexcite the isomer. The 8-ms isomer,
therefore, most likely deexcites through one or more unobserved low-energy
transitions with large conversion coefficients, accounting for their absence
in the spectra. Similar considerations, as those outlined above for 204Pb,
have been employed in the case of 205Bi, where the 2442-482-295 keV cascade
feeds the previously established 4696-keV, 37/2- level Byrne1989_2 . From the
present work, the energy of this level is inferred to be about 1 keV lower
i.e., 4695 keV. The 2442-keV $\gamma$ ray feeds this level, and a similar
calculation as in 204Pb leads to the inference of its $E3$ character.
Therefore, the level at 7136 keV deexcited by the 2442-keV $\gamma$ ray is
assigned Iπ = (43/2+). Intensity balance considerations imply $M1$ character
for the 295-keV transition. The 482-keV $\gamma$ ray may have either $M1$ or
$E3$ character, with the latter being excluded by the prompt decay of the
associated level. The 2442-482-295 keV cascade is therefore assigned E3-M1-M1
multipolarity, with the topmost level at 7913 keV having possible Iπ = (45/2+)
or (47/2+). The 8-ms isomer in 205Bi probably decays to this level through an
unobserved transition. It may be noted that there is another level at 7971 keV
in 205Bi which has a prompt decay, and is fed by the decay of the isomer
through an unobserved transition. It is not clear from the data whether the
isomer in 205Bi has two decay paths: one each to the levels at 7913 and 7971
keV, or only one decay to the 7971-keV state, which then deexcites to the
7913-keV level. All of the above considerations will be described in our
detailed future paper Wahid2022 . Regarding the excitation energy of the 8-ms
isomer in 205Bi, a value 7913+$x$ keV is listed, where $x$ $<$ 150 keV. This
upper limit has been estimated taking into account the statistics in the data,
inferred transition probabilities, theoretical conversion coefficients of the
expected $E3$ or $M2$ transitions Kibedi2008 , and the efficiency of the
detector array. A transition of 150 keV would have theoretical total
conversion coefficients of 18.9 and 18.8 for $M2$ and $E3$ multipolarities,
respectively. The available statistics in the data and the efficiency of the
array at 150 keV would imply 2-3 counts for such a $\gamma$ ray, with 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 Wahid2022 .
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) $E$3 and/or $M$2 transitions.

Prior to this work, metastable states reported in this region beyond Ex = 7
MeV, with the highest half-lives, were in the Rn-Fr-Ra isotopes Dracoulis2016
; Walker1999 ; Byrne1990 ; Byrne1989 . The ones identified in Tl-Pb-Bi
isotopes prior to this work were primarily at lower excitation Wrzesinski2003
; Broda2011 ; Szpak2011 ; Wrzesinski2015 ; Broda2018 , except the states at
very high excitation in 208Pb Broda2017 . The primary differences in the
nature of the isomers in the above two regions are evident from an inspection
of: (i) excitation energy ($E_{x}$) as a function of $I(I+1)$, where $I$ is
the spin, and (ii) reduced $E$3 transition probabilities [$B(E3)$] for the
decay of these isomers. As demonstrated in Fig. 5(a), the Iπ = (22+) isomeric
state in 204Pb follows the trajectory of the lowest-energy levels at lower
spin, as is also the case for others in neighboring nuclei. However, the Iπ =
(34+) isomeric level in 212Fr [Fig. 5(b)] is found to lie distinctly lower in
energy at the given spin in relation to the trajectory defined by the lower-
lying states, attesting to its nature as a “spin-trap” isomer, similar to the
situation in neighboring isotopes of Rn, Fr and Ra. Another striking
difference is evident in the $B(E3)$ values for the decay of the isomers in
these two regions [Figs. 5(c) and 5(d)]. In the Tl-Pb-Bi region, including the
isomers newly identified from this work, the $B(E3)$ values are found to be in
the vicinity of those expected from Weisskopf single-particle transition rates
[Weisskopf units (W.u.)], or to be significantly lower. In the Rn-Fr-Ra
region, an increase ranging from 20-40 units in comparison to the single-
particle transition rates is visible in the $B(E3)$ values. This is attributed
to transitions involving a change $\Delta$j = $\Delta$l = 3 between states
Dracoulis2016 . The relatively lower half-lives in this region can be
explained in terms of the resultant enhancement in the $E$3 transition
probabilities. In the Tl-Pb-Bi region though, no such enhancement is visible,
and for the isomers reported in the present work, the half-lives are
considerably larger. It is relevant to mention here that $E3$ decays from the
23+ and 28- isomers at 11.4 MeV and 13.7 MeV in 208Pb have been observed to be
enhanced by factors of 32 and 56 W.u., respectively Broda2017 , similar to the
15/2- $\rightarrow$ 9/2+ transition in 209Pb which has a strength of 26(7)
W.u. This enhancement is similar to that observed in the Rn-Fr-Ra region and
may be attributed to the very high excitation in 208Pb which makes it possible
to sample the j15/2 neutron orbital, resulting in transitions of the
$\nu$j15/2 $\rightarrow$ $\nu$g9/2 type. At low spin, in 209Pb, the 15/2-
level is 1.42 MeV above the 9/2+ ground state, with these levels resulting
from the occupation of the j15/2 and g9/2 orbitals, respectively, therefore
the half-life of the 15/2- level is only 1.36(30) ns NDS209 . 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
fusion-evaporation 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 204Pb and 205Bi using the KHH7B effective interaction
in the model space $Z$ = 58-114 and $N$ = 100-164 around doubly-magic 208Pb
using the OXBASH code Brown2004 . 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) Hosaka1985 , while the proton-neutron
hole-hole and particle-particle TBMEs are from the Kuo-Herling interaction
KuoH1971 , with modifications included later WarBrown1991 . For 204Pb, two
sets of calculations were performed with $t=0$ and $t=1$, where $t=0$
represents no excitation across the $Z=82$ and $N=126$ shell gaps. In the
$t=1$ case, the calculations involve the excitation of one nucleon across the
$Z=82$ and $N=126$ shell gaps. Mixing between $t=0$ and core-excited
configurations is blocked in these calculations. For 205Bi, the $1d_{5/2}$,
$0h_{11/2}$, $1d_{3/2}$ and $2s_{1/2}$ proton orbitals are completely filled,
with the unpaired proton occupying either the $0h_{9/2}$, $1f_{7/2}$ or
$0i_{13/2}$ orbitals. The 22 valence neutrons have been allowed to occupy only
the $0i_{13/2}$, $2p_{3/2}$, $1f_{5/2}$ and $2p_{1/2}$ orbitals below $N=126$.
Results of shell-model calculations using the KHH7B interaction for other
nuclei in this region have been recently reported Wahid2020 ; Wilson2015 ;
Berry2019 ; Anil2021 .

In 204Pb, the shell-model calculations indicate the presence of multiple $t=1$
states with spin-parity quantum numbers 19- and 20-, and excitation energy
$\approx$ 7-8 MeV. A 20+ state with a $\nu i^{-4}_{13/2}$ 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 $\hbar$ can arise in either of two ways viz., the
$\pi(h^{-1}_{11/2}$, $h_{9/2})\otimes\nu(i^{-2}_{13/2})$ and the
$\pi(h^{-1}_{11/2}$, $h_{9/2})\otimes\nu(f^{-1}_{5/2}$, $p^{-1}_{1/2}$,
$i^{-2}_{13/2})$ 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 205Bi, 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
$\leq$ 47/2 $\hbar$ since, in that case, relatively fast $E$2 or $M$2
transitions of several hundred keV would deexcite to levels with spin up to
43/2 $\hbar$, 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 $\pi i_{13/2}\otimes\nu(f^{-1}_{5/2},i^{-3}_{13/2})$
configuration, is low enough in energy to be consistent with the experimental
value. Four other 51/2- states, all involving the $\nu g_{9/2}$ 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 $\pi i_{13/2}\otimes\nu(i^{-4}_{13/2})$
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 $\pi
i_{13/2}\otimes\nu(f^{-1}_{5/2},i^{-3}_{13/2})$ configuration.

In the previous work on 206Bi Cieplicka2012 , configuration assignments for
the isomers with Iπ = (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
$\pi i_{13/2}\otimes\nu[i_{13/2}^{-3},(p_{1/2}^{-1},g_{9/2})]_{43/2-}$
configuration, with the (26+) state to which it decays having a $\pi
h_{9/2}\otimes\nu[i_{13/2}^{-3},(p_{1/2}^{-1},g_{9/2})]_{43/2-}$ one. Thus,
the isomerism would be associated with the $\pi i_{13/2}$ $\rightarrow$ $\pi
h_{9/2}$ transition with a strength $B(M2)$ = 0.028(3) W.u., consistent with
hindered $M$2 decays in this region. There are two possibilities for the
configuration of the (31+) isomer: either a neutron core excitation, $\pi
i_{13/2}\otimes\nu[i_{13/2}^{-3},(p_{1/2}^{-1},j_{15/2})]_{49/2+}$, or a
proton core excitation,
$\pi[i_{13/2},(h_{11/2}^{-1},h_{9/2})]\otimes\nu(i_{13/2}^{-3})$. The measured
half-life leads to $B(E3)$ = 0.0276(21) W.u., consequently the latter scenario
(proton core excitation) seems more likely, since in the former instance, the
$\nu j_{15/2}\rightarrow\nu g_{9/2}$, $\Delta$j = $\Delta$l = 3, $E$3
transition would be expected to have a transition probability $B(E3)$ $>$ 20
W.u., far from the value deduced from the present data.

The new discoveries from the present work have direct implications for
understanding the structure of nuclei in the vicinity of the heaviest, doubly-
magic nucleus, 208Pb. The identification of isomers at high excitation with
complex core-excited configurations, where the excitation energy and spin-
parity are established firmly from experiment, challenges large-scale shell-
model calculations using available interactions. Additionally, with a precise
knowledge of the half-lives of the isomers and the decay paths, tests of the
predicted electromagnetic properties are also feasible. Further, long-lived
isomeric states in general, and particularly in the present cases, tend to
have relatively pure configurations, and are, therefore, more suitable to
discriminate between different theoretical predictions. As stated earlier, the
character of the isomers at high spin in the Tl-Pb-Bi region is different from
that of the long-lived states previously established in the Rn-Fr-Ra one
(which are yrast spin-traps, and have enhanced $E3$ transition rates).
Therefore, different considerations have to be factored in their respective
descriptions. At present, the commonly used effective interactions in this
region are the: (a) KHHE (Z = 58-82, N = 82-126), (b) KHH7B (Z = 58-114, N =
100-164), (c) KHPE (Z = 82-126, N = 126-184), (d) $V_{low-k}$ (Z = 82-126, N =
126-184), and (e) KHM3Y (Z = 50-126, N = 82-184). It is recognized that, while
these interactions have satisfactory predictive power at low to intermediate
excitation, there are major limitations in the description of high-spin
phenomena, as for example, outlined in the previous work on 206Bi
Cieplicka2012 . The present results, viz., the excitation energy, spin-parity
and electromagnetic properties of the three longest-lived metastable states at
high excitation observed thus far in the periodic chart constitute an
important contribution which should improve our understanding considerably.

To summarize, metastable states have been established in 205Bi, 204Pb and
206Bi, with half-lives of 8(2) ms, 0.22(2) ms and 0.027(2) ms, respectively,
constituting the three highest values of half-lives above an excitation energy
of 7 MeV across the nuclear chart. This suggests that nuclear isomerism built
on core-excited configurations is quite robust even under such extreme
conditions. The emergence of a new frontier of metastable states in nuclei
with T1/2 $\gg$ 1 $\mu$s at high excitation, with the hindrance attributable
to the difference in the configurations of isomeric states and the levels to
which they decay, close to the line of $\beta$-stability in the region around
208Pb, is indicated. These results constitute a fertile testing ground for
large-scale shell-model calculations, along with available effective
interactions. 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
$\gamma$ 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.

The authors would like to thank I. Ahmad, J.P. Greene, A.J. Knox, D. Peterson,
X. Wang and C.M. Wilson for assistance during the experiment, and M. Hemalatha
for insightful comments. S.G.W. acknowledges support from the DST-INSPIRE
Ph.D. Fellowship of the Department of Science and Technology, Government of
India (Fellowship No. IF150098); S.K.T. from the University Grants Commission,
India, under the Faculty Recharge Programme, and S.S. from the DST-INSPIRE
Ph.D. Fellowship of the Department of Science and Technology, Government of
India (Fellowship No. IF170965). P.C.S. acknowledges a research grant from
SERB (India), CRG/2019/000556. This work is supported by the U.S. Department
of Energy, Office of Science, Office of Nuclear Physics, under award numbers
DE-FG02-94ER40848, DE-FG02-94ER40834 (UML), DE-FG02-97ER41041 (UNC) and DE-
FG02-97ER41033 (TUNL), and contract number DE-AC02-06CH11357 (ANL). The
research described here utilized resources of the ATLAS facility at ANL, which
is a DOE Office of Science user facility.

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Figure 1: Coincidence spectra illustrating $\gamma$ rays observed in the
deexcitation of the T1/2 = 0.22(2) ms and 8(2) ms isomers in (a) 204Pb and (b)
205Bi, respectively. Transitions with energy $>$ 2 MeV are displayed in the
insets. Asterisks and hash marks designate unplaced and contaminant $\gamma$
rays, respectively. The ones in black font were established earlier
Byrne1989_2 ; Linden1978 , while those in red have been identified from the
present work. Figure 2: Summed coincidence delayed spectra illustrating the
decay of the isomer in 204Pb: (a) the 2520-keV transition in coincidence with
the previously established 1006-325-618-1046 keV cascade (Linden1978 ), (b)
the 1304-keV $\gamma$ ray in coincidence with the 1006-325-618-1046-316-433
cascade identified earlier. It is evident that, in the former instance, the
481-keV $\gamma$ ray is the only newly identified one in addition to the
gating transition at 2520 keV. In the latter instance, only the 501- and
948-keV transitions are newly established. The arrow indicates the absence, in
the delayed data, of the 277-keV, Ex = 8126 keV to 7849 keV $\gamma$ ray
observed in the prompt data from the previous work. This $\gamma$ ray is
clearly visible in the present prompt data, but not in the delayed spectrum.
The 481-, 501- and 948-keV peaks are evident only in the delayed spectra. The
present analysis, with the observed coincidence relationships, and the energy
sums for the above three parallel decay paths, unambiguously establish the
excitation energy of the isomer in 204Pb as 8349 keV.

Figure 3: Time distributions for the decay of isomers with excitation energy
$\geq$ 8 MeV in: (a) 204Pb, (b) 205Bi, and (c) 206Bi. The integral counts,
along with the half-lives inferred from the fits, are displayed. Figure 4:
Long-lived states (T1/2 $>$ 1 $\mu$s) above an excitation energy of 7 MeV in
nuclides across the nuclear chart. Note that the half-lives are displayed on a
logarithmic scale. The large difference between the half-lives of the isomers
in 205Bi and 204Pb established from this work, and those in other nuclei, is
evident.

(a)

(b)

Figure 5: (a), (b) Locations of isomers in 204Pb and 212Fr in the excitation
energy ($E_{x}$) - angular momentum ($I$) plane. The dashed lines are intended
to guide the eye. (c), (d) Reduced $E$3 transition probabilities [$B(E3)$] for
isomer decays in the Tl-Pb-Bi and Rn-Fr-Ra region, respectively. The evidently
different nature of these two types of isomers is discussed in the text.