# Isomers in 203Tl and core excitations built on a five-nucleon-hole structure

V. Bothe  School of Physical Sciences, UM-DAE Centre for Excellence in Basic
Sciences, Mumbai 400098, India  S.K. Tandel  Electronic address:
<EMAIL_ADDRESS><EMAIL_ADDRESS>School of Physical Sciences, UM-
DAE Centre for Excellence in Basic Sciences, Mumbai 400098, India  Department
of Physics, University of Massachusetts Lowell, Lowell, Massachusetts 01854,
USA  S.G. Wahid  School of Physical Sciences, UM-DAE Centre for Excellence in
Basic Sciences, Mumbai 400098, India  P.C. Srivastava  Department of Physics,
Indian Institute of Technology Roorkee, Roorkee 247667, India  Bharti Bhoy
Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667,
India  P. Chowdhury  Department of Physics, University of Massachusetts
Lowell, Lowell, Massachusetts 01854, 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  F.G. Kondev  Argonne
National Laboratory, Argonne, Illinois 60439, 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

Isomers with three- and five-nucleon-hole configurations have been established
in 203Tl. These include newly identified levels with a three-nucleon
structure: Iπ = (15/2-) with T1/2 = 7.9(5) ns, and Iπ = (35/2-) with T1/2 =
4.0(5) ns. In addition, five-quasiparticle states: Iπ = (39/2-) with T1/2 =
1.9(2) ns, and Iπ = (49/2+) with T1/2 = 3.4(4) ns have also been established.
The previously determined long-lived decay [T1/2 = 6.6(3) $\mu$s from this
work] is associated with isomerism of the Iπ = (29/2+) state. Levels above
this long-lived isomer have been identified through a delayed-prompt
coincidence measurement. Five-nucleon-hole states with excitation energies Ex
$\approx$ 7 MeV have been established as well as possible octupole excitations
of the 208Pb core built on these levels. The level scheme of 203Tl is extended
up to Ex $\approx$ 11 MeV with the inclusion of 25 new transitions. Empirical
and shell-model calculations have been performed to aid in the description of
the observed states which are found to be predominantly of intrinsic
character.

###### pacs:

21.10.Re, 21.60.Ev, 23.20.Lv, 27.80.+w

##  I Introduction

The occurrence of metastable states in nuclei with proton or neutron numbers
in the vicinity of shell closures is well established as arising from the
presence of adjacent excited levels with a relatively large difference in
angular momentum and small difference in energy. Isotopes of Hg (Z = 80) and
Tl (Z = 81) with A $\approx$ 200, lying just below the doubly-magic 208Pb
nucleus in the periodic chart, are therefore good candidates for the
observation of metastable states or isomers Hausser ; Wrzesinski1 ; Broda ;
Szpak ; Wrzesinski2 . The proton-rich isotopes of Tl (A $<$ 200) are
characterized by moderate oblate deformation on account of a significant
number of valence neutrons leading to a small degree of collectivity Kreiner1
; Lawrie . However, when approaching the N = 126 shell gap, collective
behavior is no longer evident. This is the case for isotopes of Tl near the
line of stability, where 203Tl and 205Tl are the two stable isotopes Hausser ;
Wrzesinski1 ; Broda ; Wahid1 ; Slocombe . The nucleus 203Tl, with N = 122, is
only one proton and four neutron holes away from doubly-magic 208Pb and, as a
result, its structure is expected to be dominated by single-particle
excitations. The available valence orbitals are the proton s1/2, d3/2, d5/2
and h11/2 states and the neutron p1/2, p3/2, f5/2 and i13/2 ones. The presence
of the unique-parity $\pi$h11/2 and $\nu$i13/2 orbitals allows for the
realization of yrast, high-spin states, some of which may be of isomeric
character, owing to hindrance induced by the angular momentum selection rule
or a change in configuration.

The systematic delineation of isomers along an isotopic chain, most of which
have relatively pure intrinsic character, provides a host of nuclear structure
information, among which figure residual interactions between nucleons
occupying different subshells. Heavy-ion and $\alpha$-induced reactions have
been used to populate excited states at high spin in proton-rich Tl isotopes
Lawrie ; Kreiner2 . However, in order to study isotopes near the line of
stability, different reaction mechanisms such as inelastic excitation and
multi-nucleon transfer may be utilized. In order to populate states with high
spin, heavy projectiles with above-barrier energies are required. The isotopes
of Tl approaching the shell closure at N = 126, particularly 204,205Tl Broda ;
Wrzesinski1 , have been studied up to high spin and several metastable states
established. In contrast, there was limited knowledge on isomers in 200-203Tl
prior to investigations by this collaboration. Recently, the observation of
isomers with half-lives ranging from a few nanoseconds to hundreds of
microseconds in 200Tl Roy  and 202Tl Wahid1  were reported. The existing
information on 203Tl prior to the present work is limited, with levels up to
possible spin (17/2) $\hbar$ and excitation energy $\approx$3 MeV established
through a deuteron-induced reaction Slocombe , while a microsecond isomer was
identified using projectile fragmentation Pfutzner . In the former instance,
the presence of a nanosecond isomer has been inferred, but its location was
not established. In the latter case, no level scheme is reported, and a
tentative assignment of Iπ = (25/2+) and a three-nucleon-hole character for
the microsecond isomer is proposed. The motivation for the present work was to
obtain unambiguous information on the structural aspects mentioned above in
order to advance the understanding of the structure of 203Tl. An additional
goal was to extend the level scheme of 203Tl to also encompass levels arising
from the maximum possible number of nucleon-hole excitations, which is five in
this case, which allows for discriminating tests of interactions used in
shell-model calculations. Furthermore, it was also proposed to investigate the
presence of possible octupole core excitations in 203Tl which would be built
on five-nucleon-hole configurations. In this region, such excitations have
thus far been observed only in 203Hg Szpak .

##  II Experiment and Data Analysis

Multi-nucleon transfer reactions were used to populate excited states in
203Tl, with a 1450-MeV 209Bi beam from the ATLAS accelerator at Argonne
National Laboratory, incident on a thick, 50 mg/cm2 Au target. Gamma-ray
coincidence data were recorded with the Gammasphere array comprising of 100
Compton-suppressed high-purity germanium detectors Lee ; Janssens . In
addition to prompt coincidence events, delayed data from the decay of isomeric
levels were also recorded. In the first instance, the 209Bi beam, with the
natural 82.5 ns pulsing from the ATLAS superconducting linear accelerator, was
incident on the target for $\approx$1 ns, and then swept away for a 825-ns off
period. Three- and higher-fold coincidence events were recorded within a 1
$\mu$s coincidence window, allowing for the measurement of half-lives ranging
from a few to several hundred nanoseconds. Later, two- and higher-fold
coincidence data were collected only during beam-off periods by sweeping the
beam with an ON/OFF ratio of 200 $\mu$s/800 $\mu$s via a free-running external
clock, enabling the study of isomers with long ($\mu$s) half-lives.

The coincidence data were sorted into a variety of histograms in order to
establish the level structure and determine the half-lives of isomers using
the TSCAN Jin  and Radware Radford  suite of programs. Three-dimensional
histograms of prompt and delayed coincidence events were created and analyzed,
corresponding to detection of all three $\gamma$ rays within $\pm$40 ns and
50-650 ns of the trigger, respectively. To identify $\gamma$ rays feeding the
$\mu$s isomer, a three-dimensional histogram requiring two delayed transitions
together with a prompt one, was constructed. The centroid-shift method was
used to determine half-lives ranging between $\approx$1-10 ns using an energy-
gated two-dimensional histogram with energy on one axis and time difference of
the associated transitions on the other. The coincidence relationships between
$\gamma$ rays deexciting the $\mu$s isomer were also analyzed with the help of
a three-dimensional energy histogram consisting of transitions detected in the
800 $\mu$s beam-off period. To determine the half-life of the $\mu$s isomer,
several three-dimensional histograms spanning suitable time intervals within
the 800 $\mu$s beam-off period were created. Further details of data analysis
methods are described elsewhere Tandel1 ; Tandel2 ; Wahid2 .

##  III Results

Excited states in 203Tl up to medium spin and excitation energy of $E_{x}$
$\approx$ 3 MeV had been identified earlier through the 204Hg(d,3n) reaction
with an incident deuteron energy of $\approx$ 25 MeV Slocombe , and projectile
fragmentation using a 1 GeV/nucleon 238U beam on a thick 9Be target Pfutzner .
In the former, a cascade of $\gamma$ rays with transition energies of 588,
533, 328, 350 and 265 keV were placed, in that order, above the 11/2- level at
1450 keV. The presence of an isomer with T1/2 = 7.9${}^{+10}_{-13}$ ns had
been inferred, however its precise location had not been determined. From the
projectile fragmentation work, feeding from a long-lived, T1/2 = 7.7(5) $\mu$s
isomer was reported and a spin-parity, Iπ = (25/2+), was suggested. Though the
above $\gamma$ rays were observed, a level scheme was not reported.

The level scheme for 203Tl deduced from the present work is shown in Fig. 1.
The presence of the two previously reported isomers is confirmed, and a
slightly improved value of half-life is deduced for the $\mu$s isomer. The
placement of the previously reported $\gamma$ rays and level energies above
the 588-keV, 13/2- $\rightarrow$ 11/2- transition, have been revised as
described below, based on observed $\gamma$ rays and their coincidence
relationships in the three-dimensional energy histogram. A new level with
$E_{x}$ = 2048 keV and possible spin-parity Iπ = (15/2-) is established.
Several decay branches are observed from this state, including the 598-, 486-
and 477-keV $\gamma$ rays, along with an unobserved 10-keV transition to the
Iπ = 13/2- level. From previous work Slocombe ; Pfutzner , the 350- and
265-keV $\gamma$ rays were inferred to be in cascade above the 328- and
533-keV transitions. The present data unambiguously indicate that these 350-
and 265-keV $\gamma$ rays are not in mutual coincidence although they are
coincident with all lower- and higher-lying transitions (Fig. 2). The presence
of an unobserved 85-keV transition in cascade with the 265-keV line, but not
with the 350-keV transition, was ascertained. One key evidence leading to the
revised placements was the observation of a weak 798-keV $\gamma$ ray which is
found to be coincident with the 328-keV and all lower-lying transitions, but
not with the 533-, 350- and 265-keV ones (Fig. 3). Another crucial indicator
is the observation of a weak 334-keV transition in coincidence with all
$\gamma$ rays except with the 328-keV one (Fig. 4). The 334-keV transition is
clearly visible in the delayed spectra but not in the prompt ones. These
coincidence relationships, along with intensity balance arguments from the
delayed data, justify the revision in the relative placement of the
transitions. Further, inspection of the prompt spectra reveals that the
intensity of the transitions reduces approaching closer to the (29/2+) isomer,
in the order 588, 350, 533, and 328 keV, respectively. The 334- and 798-keV
$\gamma$ rays may not have been identified in the previous work on account of
their low intensity and proximity of the 798-keV $\gamma$ ray to the strong,
7/2+ $\rightarrow$ 3/2+, 795-keV transition. The newly determined levels above
the $E_{x}$ = 2048-keV state are, therefore, the ones with $E_{x}$ = 2134,
2399, 2932, 3260 and 3266 keV and Iπ = (19/2-), (19/2-), (23/2-), (25/2+) and
(29/2+), respectively (Fig. 1). The 328-keV $\gamma$ ray deexciting the
3260-keV level is assigned $E1$ character from intensity balance
considerations, as determined in the delayed spectra, with the 3/2+
$\rightarrow$ 1/2+, 279-keV transition (using its measured conversion
coefficient) and the 5/2+ $\rightarrow$ 1/2+, 681-keV $\gamma$ ray. Similar
considerations lead to the determination of $E2$ and $M1$ character for the
350- and 265-keV transitions, and rule out other multipolarities. As stated
above, the presence of an unobserved, 85-keV transition linking the 2134- and
2048-keV levels is inferred. For the isomeric, 334-keV $\gamma$ ray, a (29/2+)
$\rightarrow$ (23/2-), $E3$ assignment is implied. The presence of an
unobserved 6-keV, (29/2+) $\rightarrow$ (25/2+), $E2$ transition, also
deexciting the isomer is inferred. The $\gamma$ rays observed following the
deexcitation of the Iπ = (29/2+) isomer are listed in Table I.

The Iπ = (15/2-) state at $E_{x}$ = 2048 keV is determined to be isomeric with
T1/2 = 7.9(5) ns, in agreement with the previously reported value Slocombe .
The histogram of time difference of $\gamma$ rays below and above this state
and a comparison with prompt transitions of similar energy can be found in
Fig. 5. Additionally, the data indicate the possibility of isomerism of the
2134-keV level, with a half-life up to several nanoseconds, however the low
intensity and energy of the transitions involved do not allow for precise
estimation of the value. All $\gamma$ rays below the (29/2+) state are found
to exhibit delayed feeding in the 800 $\mu$s beam-off period. The integral
variation in intensity with time of summed coincidence counts, with gates on
the 232-, 265-, 279-, 328-, 533-, 588- and 795-keV $\gamma$ rays is
illustrated in Fig. 6. A value of T1/2 = 6.6(3) $\mu$s is obtained, with an
uncertainty that is slightly below the quoted one in the previous work, i.e.
7.7(5) $\mu$s Pfutzner . The measured value is associated with the half-life
of the Iπ = (29/2+) state.

Typically, the presence of an intervening long-lived ($\sim$ $\mu$s or
greater) isomer prevents the identification of $\gamma$ rays feeding such a
level. In this case, with the 1 $\mu$s Gammasphere coincidence window and the
6.6(3) $\mu$s half-life, only a small number of coincidence events comprising
$\gamma$ rays below and above the isomer were recorded. By summing coincidence
spectra with gates on two strong delayed transitions below the isomer in a
three-dimensional histogram, several prompt $\gamma$ rays feeding the isomer
could be identified [Fig. 7(a)]. The following $\gamma$ rays were found to be
in coincidence with the delayed transitions as well as with each other: 965,
211, 530, 288, 947, 438 and 313 keV. Their ordering is based on total
intensities inferred from $\gamma$-ray intensities, and multipolarities which,
for low-energy transitions, are determined from intensity balance
considerations after gating on the higher-lying, 2306-keV line, combined with
theoretical conversion coefficients Kibedi . Detailed information on these
transitions is presented in Fig. 1 and Table II. Though some random
contaminant transitions are also present in Fig. 7(a), their origin was
accounted for in terms of the deexcitation of low-lying states from the strong
reaction channels observed in the data. The spin-parity assignments of the
levels above the (29/2+) state are based on systematics Linden  as described
later and should be considered tentative. Figure 7(b) is the prompt
coincidence spectrum with gates on the 530- and 965-keV transitions.
Additionally, four other significantly weaker $\gamma$ rays, with energies
466, 756, 1089 and 2306 keV, were also visible in prompt coincidence, and are
found to be enhanced in the summed prompt coincidence spectrum with gates on
transitions between the (29/2+) and (49/2+) levels [Fig. 7(c)]. The 2306-keV
$\gamma$ ray is found to be coincident with all the above prompt transitions
and is placed above the (49/2+) level based on intensity considerations. It is
worth noting that similar transitions with energies 2207 and 2256 keV are
observed above the four- and three-nucleon-hole states in 204Tl and 205Tl,
respectively Broda ; Wrzesinski1 .

The presence of three isomers above the Iπ = (29/2+) state (Fig. 1) with half-
lives in the range of a few nanoseconds is deduced from an inspection of time
differences of $\gamma$ rays between the (29/2+) and (49/2+) levels (Fig. 8),
and the following values have been obtained:

  1. 1.

$E_{x}$ = 4442 keV, Iπ = (35/2-), T1/2 = 4.0(5) ns

  2. 2.

$E_{x}$ = 4972 keV, Iπ = (39/2-), T1/2 = 1.9(2) ns

  3. 3.

$E_{x}$ = 6957 keV, Iπ = (49/2+), T1/2 = 3.4(4) ns

It may be noted that the Iπ = (29/2+) state in 203Tl is the analog of the
isomeric 9- levels in Pb isotopes Linden ; Lutter ; Rosengard .

##  IV Discussion

###  IV.1 Isomeric states and configurations

The high-spin isomers in Tl isotopes can be understood as resulting from the
coupling of the h11/2 proton hole to specific neutron configurations in the
corresponding Pb isotones with, in particular, a major contribution from
neutrons occupying the i13/2 subshell. The low-lying two-neutron-hole
configurations in even-A Pb isotopes are the $\nu$(i${}_{13/2}^{-1}$,
p${}_{1/2}^{-1}$), $\nu$(i${}_{13/2}^{-1}$, f${}_{5/2}^{-1}$) and
$\nu$i${}_{13/2}^{-2}$ ones leading to the realization of isomeric Iπ = 7-, 9-
and 12+ states Linden ; Lutter . The corresponding states in odd-A Tl isotones
have the configurations $\pi$h${}_{11/2}^{-1}$ $\otimes$ $\nu$2(7-),
$\pi$h${}_{11/2}^{-1}$ $\otimes$ $\nu$2(9-), and $\pi$h${}_{11/2}^{-1}$
$\otimes$ $\nu$2(12+) leading to Iπ = 25/2+, 29/2+ and 35/2- levels. The 25/2+
and 35/2- states in 205Tl have been determined to be isomeric with T1/2 = 2.6
$\mu$s and T1/2 = 235 ns, respectively Wrzesinski1 . Since the 29/2+
$\rightarrow$ 25/2+ $E2$ transition in 205Tl has an energy of 328 keV, the
decay of the 29/2+ level has been found to be prompt Wrzesinski1 . Analogous
isomeric levels have not been identified in lighter, odd-A Tl isotopes with
mass A $\leq$ 199, most likely due to the underlying weak oblate deformation
and resultant collective structures. In 201Tl, the presence of such isomeric
states has not yet been established Dasgupta , however their existence cannot
be ruled out. In 203Tl, under discussion here, the observed long-lived decay,
with T1/2 = 6.6 $\mu$s, is assigned to the 29/2+ level. The excitation
energies of the 25/2+ levels in 203,205Tl are quite similar (3260 and 3291
keV, respectively). This may be understood as follows: the $\pi$h11/2 and
$\nu$p1/2 quasiparticle energies in the two isotopes are quite similar,
however the $\nu$i13/2 one in 203Tl is lower by virtue of its relative
proximity to the neutron Fermi level in comparison to 205Tl. This difference
is compensated to a significant extent by the fact that the neutron pair-gap
energy in 205Tl is lower than that in 203Tl Moller , leading to the observed
similarity of the excitation energies of the 25/2+ levels in the two isotopes.
The small separation (6 keV) between the 25/2+ and 29/2+ levels in 203Tl is
mirrored in 204Pb, where the 7- and 9- levels are 79 keV apart Linden . An
important difference is that the 9- state is lower in 204Pb in contrast to the
25/2+ level in 203Tl. The identification of the closely-spaced pair of levels
with Iπ = 25/2+ and 29/2+ in 203Tl thus provides insight into the difference
of the magnitude of residual interactions of the h11/2 proton with the
respective two-neutron-hole configurations in 204Pb. The transition rates for
the Iπ = 29/2+ isomeric decays are consistent with Weisskopf estimates and
those in neighboring nuclei, e.g., $B(E3)$[334 keV] = 5.8 W.u. The unhindered
$E3$ decay likely implies a configuration change from $\pi$h${}_{11/2}^{-1}$
$\otimes$ $\nu$2(9-) to $\pi$d${}_{5/2}^{-1}$ $\otimes$ $\nu$2(9-) for the
29/2+ $\rightarrow$ 23/2- transition in 203Tl.

In 203Tl, there are four neutron holes in contrast to only two in 205Tl.
Consequently, levels with one-proton and four-neutron-hole configurations are
possible in 203Tl, unlike in 205Tl where only two neutron holes are present.
As a result, in 205Tl, there is no intervening level between the 29/2+ and
35/2- states, and the 35/2- state decays by a 1217-keV, $E3$ transition, and
is characterized by a half-life of T1/2 = 235(10) ns Wrzesinski1 . The Iπ =
35/2- state represents the maximum spin achievable from a three-nucleon-hole
configuration, resulting from one h11/2 proton and two i13/2 neutrons. This
state is found to be isomeric in 203Tl as well, with T1/2 = 4.0(5) ns. It
decays to the 33/2+ level which has a five-nucleon-hole configuration, with
likely mixed character comprising $\pi$h${}_{11/2}^{-1}$ $\otimes$
$\nu$(i${}_{13/2}^{-1}$, f${}_{5/2}^{-2}$, p${}_{1/2}^{-1}$) and
$\pi$h${}_{11/2}^{-1}$ $\otimes$ $\nu$(i${}_{13/2}^{-1}$, f${}_{5/2}^{-1}$,
p${}_{3/2}^{-1}$, p${}_{1/2}^{-1}$) configurations. All the levels above the
35/2- state must have configurations involving five or more nucleons. The
observed isomerism of the 39/2- state may be qualitatively understood in terms
of the hindrance induced by the change of two neutrons in the configurations
of the initial and final states in each of these cases. The Iπ = 49/2+ state
most likely results from the coupling of $\pi$h${}_{11/2}^{-1}$ $\otimes$
$\nu$2(19-), with the neutron configuration corresponding to the relevant
level established in the 204Pb isotone Linden . It is noteworthy that the
level structure of 203Tl above the 29/2+ state inferred from the present work
is quite similar to the one associated with the strongest cascade above the
analogous 9- level in 204Pb (Fig. 9).

###  IV.2 “Empirical” calculations

“Empirical” calculations, based on near-neighbor systematics, have been
performed to estimate the energies of isomeric states. For this purpose, the
average of 1-quasineutron energies from neighboring, odd-A Pb isotopes
(203,205Pb), and 1-quasiproton energies derived from the corresponding excited
levels in 203Tl, were used ENSDF1 ; ENSDF2 ; ENSDF3 . The neutron pair-gap
energies were obtained using the five-point formula involving odd-even mass
differences Moller . To calculate the energies of states with multi-nucleon
configurations, the relevant 1-quasiparticle energies were summed with the
pair-gap energy, and appropriate corrections were incorporated for the
residual interactions. The magnitude of residual interactions was determined
from isomeric configurations in neighboring Tl and Pb isotopes and the
following values were obtained: 15/2- (119 keV): $\pi$h${}_{11/2}^{-1}$
$\otimes$ $\nu$(f${}_{5/2}^{-1}$, p${}_{1/2}^{-1}$); 25/2+ (204 keV):
$\pi$h${}_{11/2}^{-1}$ $\otimes$ $\nu$(i${}_{13/2}^{-1}$, p${}_{1/2}^{-1}$);
29/2+ (160 keV): $\pi$h${}_{11/2}^{-1}$ $\otimes$ $\nu$(i${}_{13/2}^{-1}$,
f${}_{5/2}^{-1}$); 35/2- (13 keV): $\pi$h${}_{11/2}^{-1}$ $\otimes$
$\nu$i${}_{13/2}^{-2}$. The calculated energies of the above mentioned states
and a comparison with experimental values is displayed in Fig. 10. Sufficient
experimental data are not available to determine the residual interactions for
the five-nucleon configuration responsible for the 49/2+
[$\pi$h${}_{11/2}^{-1}$ $\otimes$ $\nu$(i${}_{13/2}^{-3}$, f${}_{5/2}^{-1}$)]
state. Therefore, the energy for this state has been obtained by summing the
experimental value of the 29/2+ state in 203Tl with that of the
$\nu$i${}_{13/2}^{-2}$, 12+ level in 204Pb Linden . While the empirical
calculations underestimate the experimental energies in most cases, there is
fair agreement between the two, with the deviations being less than 300 keV
for all states.

###  IV.3 Shell-model calculations

Shell-model calculations have been performed for 203Tl employing the KHH7B
Herling  effective interaction. Since proton excitations across the Z = 82
shell gap and neutron ones across the N = 126 one were not allowed, the active
orbitals in the shell-model calculations are d5/2, h11/2, d3/2 and s1/2 for
protons, and i13/2, p3/2, f5/2, and p1/2 for neutrons. The shell-model code
Oxbash Brown  was used for the diagonalization of the matrices of interest.
The deviations of the predicted energies from the experimental values range
between a few hundred keV to 0.5 MeV. The 29/2+ state is calculated to be
lower in energy than the 25/2+ level, unlike what is displayed by the data
(Fig. 10). A comparison of the excitation energies from experiment and those
from both empirical and shell-model calculations is presented in Table III,
along with the primary underlying configurations. The significant disagreement
between the experimental and calculated values for the 29/2+ and 35/2- states
indicates the need for improving the interactions used in the shell-model
calculations.

###  IV.4 Octupole core excitations

The level with $E_{x}$ = 9263 keV is assigned Iπ = (55/2-) and interpreted as
the octupole excitation of the 208Pb core built on the $\pi$h${}_{11/2}^{-1}$
$\otimes$ $\nu$(i${}_{13/2}^{-3}$, f${}_{5/2}^{-1}$), Iπ = 49/2+
configuration. The energy of the 55/2- $\rightarrow$ 49/2+ transition (2306
keV) is consistent with this interpretation, as described below. Following the
prescription outlined previously Wrzesinski1 ; Broda ; Kadi , the expected
transition energy for the $E3$ excitation built on the five-nucleon hole,
49/2+ state can be estimated. While the unperturbed energy of the $E3$
excitation in 208Pb would be 2615 keV, energy shifts would result from the
coupling to configurations involving multiple nucleons. These can be expressed
as the sum of energy shifts corresponding to the individual constituents of
such a configuration. For instance, as described previously Broda ; Kadi ,
energy shifts of $\Delta$E = -150 keV and +40 keV are obtained based on the
following transitions: 17/2+ $\rightarrow$ 11/2- (2465 keV) in 207Tl, and
11/2+ $\rightarrow$ 5/2- (2655 keV) in 207Pb, respectively. These transitions
represent the stretched $E3$ excitations built on the $\pi$h${}_{11/2}^{-1}$
and $\nu$f${}_{5/2}^{-1}$ states in 207Tl and 207Pb, respectively. For the
$\nu$i${}_{13/2}^{-3}$ configuration, an energy shift of -262 keV has been
estimated Broda  since the $E3$ excitation built on the
$\nu$i${}_{13/2}^{-3}$, Iπ = 33/2+ state has not been identified yet. Thus,
for the $\pi$h${}_{11/2}^{-1}$ $\otimes$ $\nu($i${}_{13/2}^{-3}$,
f${}_{5/2}^{-1}$) configuration, an addition of the above mentioned energy
shifts yields a value of -372 keV, implying an estimated 55/2- $\rightarrow$
49/2+, 2243-keV transition energy. This estimated value is lower than the
observed one by only 63 keV. The situation is similar to that observed for the
$\pi$h${}_{11/2}^{-1}$ $\otimes$ $\nu$(i${}_{13/2}^{-2}$, f${}_{5/2}^{-1}$),
Iπ = 20+ configuration in 204Tl Broda  where the estimated value is 61 keV
lower than the experimental one. It is worth noting that even better agreement
(within several keV) between estimated and experimental values is seen for the
22+ state in 204Tl Broda  and 35/2- level in 205Tl Wrzesinski1 , e.g.,
excitations involving high-j orbitals only. This likely suggests an
underestimation of the magnitude of the repulsive interaction of the
stretched-$E3$ excitation with the f5/2 neutron hole. On the other hand, the
reasonable agreement between estimated and experimental values appears to
validate the assignment of the 2306-keV transition in 203Tl as the octupole
core excitation built on the 45/2+ state.

##  V Summary

The excited level structure of 203Tl has been considerably expanded and is now
established up to high spin with the inclusion of 25 new transitions, five
isomeric states, and octupole core excitations built on a five-nucleon-hole
configuration. Isomeric states with Iπ = (15/2-), (35/2-), (39/2-) and
(49/2+), and respective half-lives of T1/2 = 7.9(5) ns, 4.0(5) ns, 1.9(2) ns,
and 3.4(4) ns, have been identified. The half-life of the previously
determined long-lived decay is revised from 7.7(5) to 6.6(3) $\mu$s, and is
associated with the Iπ = (29/2+) state. The structure of the levels fed by
this long-lived decay is significantly modified. Gamma rays feeding the 6.6
$\mu$s isomer have been identified through delayed-prompt coincidence
measurements. Of particular note is the observation of octupole core
excitations built on a five-nucleon hole configuration. “Empirical”
calculations, based on near-neighbor systematics, are able to satisfactorily
reproduce key states in the experimental level scheme, while those using the
shell model appear to significantly underestimate the state energies in two
instances. These results contribute valuable information towards improving the
understanding of nuclear structure in the vicinity of the heaviest doubly-
magic nucleus, 208Pb.

##  VI Acknowledgments

The authors wish to thank I. Ahmad, J.P. Greene, T.L. Khoo, A.J. Knox, C.J.
Lister, D. Peterson, U. Shirwadkar, X. Wang and C.M. Wilson for assistance
during the experiment. V.B. acknowledges assistance under the INSPIRE
fellowship of the Department of Science and Technology, Government of India.
S.K.T. would like to acknowledge support from the University Grants
Commission, India, under the Faculty Recharge Programme. 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). This work is
supported by the U.S. Department of Energy, Office of Science, Office of
Nuclear Physics, under award numbers DE-FG02-94ER40848 and 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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Energies and intensities of $\gamma$ rays, and excitation energies and spins
of initial and final states in 203Tl up to the 6.6 $\mu$s isomer. Transition
energies are accurate to within 0.5 keV. Statistical uncertainities on
$\gamma$-ray intensities are listed. Relative intensities have been obtained
from data in the delayed regime. Transition multipolarities determined from
intensity balance considerations are noted.

Eγ (keV) $E_{i}$ (keV) $\rightarrow$ $E_{f}$ (keV) I${}^{\pi}_{i}$
$\rightarrow$ I${}^{\pi}_{f}$ Iγ Multipolarity

c c c c c c c c c (6)
&$3266$$\rightarrow$$3260$$(29/2^{+})$$\rightarrow$$(25/2^{+})$ $-$

(10) $2048$$\rightarrow$$2038$$(15/2^{-})$$\rightarrow$$(13/2^{-})$ $-$

(33) $1218$$\rightarrow$$1184$$9/2^{+}$$\rightarrow$$7/2^{+}$ $-$

(85) $2462$$\rightarrow$$2376$$(19/2^{-})$$\rightarrow$$(15/2^{-})$ $-$

114.9 $2048$$\rightarrow$$1933$$(15/2^{-})$$\rightarrow$$-$ $-$

143.5 $1218$$\rightarrow$$1074$$9/2^{+}$$\rightarrow$$7/2^{+}$ $11(3)$

232.1 $1450$$\rightarrow$$1218$$11/2^{-}$$\rightarrow$$9/2^{+}$ $84(5)$

265.0 $2399$$\rightarrow$$2134$$(19/2^{-})$$\rightarrow$$(19/2^{-})$ $27(3)$
M1

279.3 $279$$\rightarrow$$0$$3/2^{+}$$\rightarrow$$1/2^{+}$ $84(4)$

327.9 $3260$$\rightarrow$$2932$$(25/2^{+})$$\rightarrow$$(23/2^{-})$ $100(5)$
E1

333.7 $3266$$\rightarrow$$2932$$(29/2^{+})$$\rightarrow$$(23/2^{-})$ $4(1)$

350.2 $2399$$\rightarrow$$2048$$(19/2^{-})$$\rightarrow$$(15/2^{-})$ $54(4)$
E2

362.1 $1933$$\rightarrow$$1571$$-$$\rightarrow$$-$ $-$

378.3 $1562$$\rightarrow$$1184$$-$$\rightarrow$$7/2^{+}$ $-$

387.1 $1571$$\rightarrow$$1184$$-$$\rightarrow$$7/2^{+}$ $3(1)$

401.4 $681$$\rightarrow$$279$$5/2^{+}$$\rightarrow$$3/2^{+}$ $10(2)$

477.3 $2048$$\rightarrow$$1571$$(15/2^{-})$$\rightarrow$$-$ $7(2)$

485.8 $2048$$\rightarrow$$1562$$(15/2^{-})$$\rightarrow$$-$ $4(1)$

488.2 $1562$$\rightarrow$$1074$$-$$\rightarrow$$7/2^{+}$ $-$

496.8 $1571$$\rightarrow$$1047$$-$$\rightarrow$$7/2^{+}$ $7(2)$

503.8 $1184$$\rightarrow$$681$$7/2^{+}$$\rightarrow$$5/2^{+}$ $6(1)$

533.1 $2932$$\rightarrow$$2399$$(23/2^{-})$$\rightarrow$$(19/2^{-})$ $85(6)$
E2

537.3 $1218$$\rightarrow$$681$$9/2^{+}$$\rightarrow$$5/2^{+}$ $10(2)$

588.5 $2038$$\rightarrow$$1450$$(13/2^{-})$$\rightarrow$$11/2^{-}$ $90(6)$

598.5 $2048$$\rightarrow$$1450$$(15/2^{-})$$\rightarrow$$11/2^{-}$ $4(1)$

680.6 $681$$\rightarrow$$0$$5/2^{+}$$\rightarrow$$1/2^{+}$ $5(1)$

794.8 $1074$$\rightarrow$$279$$7/2^{+}$$\rightarrow$$3/2^{+}$ $65(5)$

797.6 $2932$$\rightarrow$$2134$$(23/2^{-})$$\rightarrow$$(19/2^{-})$ $14(3)$

905.2 $1184$$\rightarrow$$279$$7/2^{+}$$\rightarrow$$3/2^{+}$ $22(3)$

Energies and intensities of $\gamma$ rays, and excitation energies and spins
of initial and final states in 203Tl above the 6.6 $\mu$s isomer. Transition
energies are accurate to within 0.5 keV. Statistical uncertainities on
$\gamma$-ray intensities are listed. Relative intensities have been obtained
primarily from data in the prompt regime. The intensities in Tables I and II
should be read independently of each other.

Eγ (keV) $E_{i}$ (keV) $\rightarrow$ $E_{f}$ (keV) I${}^{\pi}_{i}$
$\rightarrow$ I${}^{\pi}_{f}$ Iγ

c c c c c c c c 211.0
$4442$$\rightarrow$$4231$$(35/2^{-})$$\rightarrow$$(33/2^{+})$ $68(9)$

287.7 $5260$$\rightarrow$$4972$$(41/2^{-})$$\rightarrow$$(39/2^{-})$ $32(2)$

312.7 $6957$$\rightarrow$$6644$$(49/2^{+})$$\rightarrow$$(45/2^{+})$ $17(2)$

437.6 $6644$$\rightarrow$$6207$$(45/2^{+})$$\rightarrow$$(43/2^{-})$ $26(2)$

466.0 $9729$$\rightarrow$$9263$$-$$\rightarrow$$(55/2^{-})$ $-$

530.3 $4972$$\rightarrow$$4442$$(39/2^{-})$$\rightarrow$$(35/2^{-})$ $66(4)$

755.6 $11107$$\rightarrow$$10352$$-$$\rightarrow$$-$ $-$

947.2 $6207$$\rightarrow$$5260$$(43/2^{-})$$\rightarrow$$(41/2^{-})$ $31(3)$

965.2 $4231$$\rightarrow$$3266$$(33/2^{+})$$\rightarrow$$(29/2^{+})$ $100(16)$

1088.9 $10352$$\rightarrow$$9263$$-$$\rightarrow$$(55/2^{-})$ $-$

2305.7 $9263$$\rightarrow$$6957$$(55/2^{-})$$\rightarrow$$(49/2^{+})$ $11(3)$

Energies and spins of isomeric levels in 203Tl from experiment, “empirical”
and shell-model calculations (see text for details).

I${}^{\pi}_{i}$ T1/2 Configuration $E_{exp}$(keV) $E_{emp}$(keV) $E_{SM}$(keV)

c c c c c c $15/2^{-}$ 7.9(5) ns $\pi s^{-1}_{1/2}$ $\nu p^{-1}_{1/2}$
$i^{-1}_{13/2}$ $2048$ $2185$ $1827$

$29/2^{+}$ 6.6(3) $\mu$s $\pi h^{-1}_{11/2}$ $\nu f^{-1}_{5/2}$
$i^{-1}_{13/2}$ $3266$ $2999$ $2803$

$35/2^{-}$ 4.0(5) ns $\pi h^{-1}_{11/2}$ $\nu i^{-2}_{13/2}$ $4442$ $4148$
$3899$

$49/2^{+}$ 3.4(4) ns $\pi h^{-1}_{11/2}$ $\nu f^{-1}_{5/2}$ $i^{-3}_{13/2}$
$6957$ $6782$ $6627$

Figure 1: Partial level scheme of 203Tl obtained from the present work. The
transitions and levels above the (29/2+) isomeric state, and several below it
(marked in red), are newly established. Figure 2: Double-gated summed
coincidence spectra showing $\gamma$ rays in coincidence with the: (a) 533-
(b) 265- (c) 350-keV transitions, together with any of the 232, 328 and
588-keV transitions. It is evident that the 265 and 350 keV transitions, the
positions of which are marked with arrows in the middle and lower panels, are
not coincident with each other as previously proposed Slocombe ; Pfutzner .
Figure 3: Double-gated coincidence spectra, with gates on the transitions
indicated in the panels, illustrating that the newly observed 798-keV $\gamma$
ray is coincident with the 588- and 328-keV transitions, but not with the
533-keV one (arrow). Figure 4: Double-gated coincidence spectra, with gates on
the $\gamma$ rays indicated in the panels, highlighting the presence of the
334-keV isomeric transition in the 350- and 533-keV gated spectra, and its
absence in the 328-keV gated spectrum. Figure 5: Half-life of the Iπ = (15/2-)
level measured using the centroid-shift method. The time difference between
the 588- and 350-keV transitions, below and above this state, respectively, is
displayed in red, while that of two prompt $\gamma$ rays with similar energies
is shown in blue. A value of T1/2 = 7.9(5) ns is inferred. Figure 6: Variation
with time of the cumulative intensity of $\gamma$ rays from the long-lived,
$\mu$s decay. A half-life of 6.6(3) $\mu$s is deduced for the (29/2+) state.

(a)  (b)

Figure 7: (a) Summed delayed-prompt coincidence spectrum with gates on the
232-, 265-, 328-, 533-, 588- and 795-keV transitions in the delayed regime.
Prompt $\gamma$ rays, feeding the $\mu$s isomer, observed in coincidence with
these delayed transitions, are displayed. The hash marks indicate strong
transitions deexciting the isomer while the asterisks denote known contaminant
$\gamma$ rays from other reaction channels. (b) Prompt coincidence spectrum
with a double gate on the 530- and 965-keV transitions. (c) Double-gated
prompt coincidence spectrum obtained by summing gates on strong transitions
above the $\mu$s isomer and below the (49/2+) level. Figure 8: Half-lives of
the Iπ = (35/2-), (39/2-) and (49/2+) levels determined using the centroid-
shift method. In panels (a) and (b), the histogram in red (solid line)
indicates the time difference of $\gamma$ rays below and above the relevant
states while the one in blue (dashed line) corresponds to that of prompt
transitions with similar energy. Values of T1/2 = 4.0(5) ns and 1.9(2) ns are
determined for the (35/2-) and (39/2-) levels based on the observed centroid
shifts. In panel (c), the time difference between the 947- and 2306-keV
$\gamma$ rays and vice versa are compared which is equal to twice the mean
life of the Iπ = (49/2+) level, leading to a value of T1/2 = 3.4(4) ns for
this state. Figure 9: Comparison of the level structure above the analogous
29/2+ and 9- isomeric states in 203Tl and 204Pb, respectively. Figure 10:
Excitation energies of selected states in 203Tl obtained from experiment and
their comparison with empirical and shell-model calculations discussed in the
text.