# Single Particle Configurations of the Excited States of 203Po

S. Chatterjee  UGC-DAE Consortium for Scientific Research, Kolkata Centre,
Kolkata 700098, India  A. Ghosh  Present Address: ONGC, Cinnamara Complex,
Jorhat, Assam 785704, India  UGC-DAE Consortium for Scientific Research,
Kolkata Centre, Kolkata 700098, India  D. Arora  Present Address: Inter
University Accelerator Centre, New Delhi 110067, India  UGC-DAE Consortium for
Scientific Research, Kolkata Centre, Kolkata 700098, India  S. Das  UGC-DAE
Consortium for Scientific Research, Kolkata Centre, Kolkata 700098, India  B.
Mondal  UGC-DAE Consortium for Scientific Research, Kolkata Centre, Kolkata
700098, India  S. Samanta  UGC-DAE Consortium for Scientific Research, Kolkata
Centre, Kolkata 700098, India  R. Raut  Corresponding Author:
<EMAIL_ADDRESS>UGC-DAE Consortium for Scientific Research, Kolkata
Centre, Kolkata 700098, India  S. S. Ghugre  UGC-DAE Consortium for Scientific
Research, Kolkata Centre, Kolkata 700098, India  P. C. Srivastava  Department
of Physics, Indian Institute of Technology, Roorkee, Roorkee 247667, India  A.
K. Sinha  Presently: Hon. Adjunct Professor, Department of Physics, Savitribai
Phule Pune University, Pune, India  UGC-DAE Consortium for Scientific
Research, University Campus, Khandwa Road, Indore 452017, India  U. Garg
Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556  H.
K. Singh  Department of Physics, Indian Institute of Technology, Bombay,
Mumbai 400076, India  Neelam  Department of Physics and Astrophysics,
University of Delhi, New Delhi 110007, India  K. Rojeeta Devi  Department of
Physics and Astrophysics, University of Delhi, New Delhi 110007, India  A.
Sharma  Department of Physics, Himachal Pradesh University, Shimla 171005,
India  S. S. Bhattacharjee  Inter University Accelerator Centre, New Delhi
110067, India  R. Garg  Inter University Accelerator Centre, New Delhi 110067,
India  I. Bala  Inter University Accelerator Centre, New Delhi 110067, India
R. P. Singh  Inter University Accelerator Centre, New Delhi 110067, India  S.
Muralithar  Inter University Accelerator Centre, New Delhi 110067, India

###### Abstract

Excited states of the 203Po ($Z=84,N=119$) have been investigated after
populating them through 194Pt(13C,4n) fusion-evaporation reaction at Ebeam =
74 MeV and using a large array of Compton suppressed HPGe clover detectors as
the detection setup for the emitted $\gamma$-rays. Standard techniques of
$\gamma$-ray spectroscopy have been applied towards establishing the level
structure of the nucleus. Twenty new $\gamma$-ray transitions have been
identified therein, through $\gamma-\gamma$ coincidence measurements, and
spin-parity assignments of several states have been determined or confirmed,
following the angular correlation and linear polarization measurements on the
observed $\gamma$-rays. The excited states have been interpreted in the
framework of large basis shell model calculations, while comparing their
calculated and experimental energies. They have been principally ascribed to
proton population in the $h_{9/2}$ and $i_{13/2}$ orbitals outside the $Z=82$
closure and neutron occupation of the $f_{5/2}$, $p_{3/2}$ and $i_{13/2}$
orbitals in the $N=126$ shell.

###### pacs:

23.20.Lv,21.10.Hw,21.60.Cs

##  I Introduction

The shell model of the nucleus has remained its most credible microscopic
description through more than seven decades now. Testing the model across the
nuclear chart and refining the inputs, towards accomplishing better overlap
with data, has been an agenda of nuclear structure studies through their
evolving practice. The exercise is facilitated by developments in
computational resources that help circumvent the dimensional challenges
incurred in the application of shell model, particularly to heavier systems
such as those around Pb ($Z=82$). It may be noted that the very validity of
the shell model for describing level structures around the proton $Z=82$
closure was a subject of early investigations in the region. While the closure
at $Z=82$ was identified to be sufficiently stable against collective
excitations Rahkonen et al. (1985), it was also observed that light Hg
($Z=80$) isotopes do exhibit collectivity and there were predictions of
similar phenomena in the proton-rich side of the ($Z=82$) closure, for the
light Po ($Z=84$) nuclei Weckström et al. (1985). The studies undertaken
towards resolving the proposition, however, froze on describing the
excitations of light-Po isotopes, such as 199-201Po, within the framework of
the shell model. This was also commensurate with the systematically calculated
Weckström et al. (1985) shapes of the Pb isotopes starting from 208Pb
($Z=82,N=126$) and extending to the lighter ones. The doubly-magic 208Pb,
quite expectedly, exhibited deep energy minimum for a spherical shape; the
minimum became shallower for lighter systems in the isotopic chain and
eventually evolved into a double minima corresponding to both prolate and
oblate deformations for nuclei as light as 190Pb ($Z=82,N=108$). Such a
scenario, however, wasn’t established in 198Pb or 202Pb that still manifested
near spherical shapes and it was found valid to interpret the excitation
schemes of the neighboring light Po isotopes from the perspectives of the
shell model. The merits of such interpretation notwithstanding, it was largely
extracted from the evolution of experimentally observed level energies and
their spacings across the isotopic and/or the isotonic chains. That was
presumably owing to the limited wherewithal then available for computational
endeavors but, nevertheless, could provide insights into the particle
excitations underlying the level scheme of the nuclei being studied. The
experimental findings in these studies mostly followed population of the
nuclei of interest in $\alpha$\- or heavy-ion induced fusion-evaporation
reactions and detection of the $\gamma$-rays using modest setups of few Ge
detectors and, at times, using conversion electron measurements alongwith.

The only existing precedence of spectroscopic study of the 203Po
($Z=84,N=119$) nucleus, following its population in a fusion-evaporation
reaction, was by Fant et al. Fant et al. (1986). The nucleus was populated
using $\alpha$-induced reaction on 204Pb and the de-excitation $\gamma$-rays
were detected using small planar Ge(Li) detectors, large coaxial Ge(Li)
detectors and intrinsic Ge detectors. Conversion electrons were also measured
in conjunction. The level scheme of the nucleus was established upto an
excitation energy of $\sim$ 4.4 MeV and spin $\sim$ 18$\hbar$. However, only a
selected number of $\gamma$-ray transitions, presumably the strongest ones,
and levels were identified above the 25/2+ state; the spin-parity assignments
were considerably tentative therein. The configurations of the excited states
were largely ascribed to the coupling of an odd neutron hole to the
excitations of the even 204Po-core ($Z=84,N=120$). Two configurations, based
on proton excitations outside the closed proton shell of the 208Pb-core, were
identified in the latter. These were $\pi h_{9/2}^{2}$ and $\pi
h_{9/2}i_{13/2}$ that resulted in maximum spins 8 and 11 respectively. The
available single particle orbitals for the odd neutron are
$2f_{7/2},1h_{9/2},1i_{13/2},3p_{3/2},2f_{5/2},3p_{1/2}$ and the first
$5/2^{-},3/2^{-},1/2^{-},13/2^{+}$ states, in 203Po, were identified with
single neutron excitations therein. The 17/2+, 21/2+, and 25/2+ yrast states
in odd-A Po isotopes were attributed to the odd neutron hole $\nu
i_{13/2}^{-1}$ coupled to the excitations of the corresponding Pb-core or of
the two valence protons of the Po-core, resulting in states 2+ \- 8+. This
followed the systematics of the yrast states in odd-A Pb and Po isotones. It
may be noted that the yrast 17/2+ and the 21/2+ states in isotopes 199-205Pb
had been ascribed to pure neutron excitations, such as $\nu
p_{1/2}^{-1}f_{5/2}^{-1}i_{13/2}^{-1}$ and $\nu f_{5/2}^{-2}i_{13/2}^{-1}$.
However, such (pure neutron) excitations would result into states of higher
excitation energies than those of the yrast 17/2+ and the 21/2+ levels in
odd-A Po isotopes. It was thus found reasonable to assign the pure neutron
excitations to the respective non-yrast states. The 27/2+ and the 29/2+ levels
in the odd Po nuclei were identified with three-quasiparticle configurations
$\pi h_{9/2}^{2}\otimes\nu i_{13/2}^{-1}$. The configurations for the isomeric
25/2- and 29/2- were derived from their overlap with the systematics of these
states observed in the Pb isotopes. Accordingly, their configuration in 203Po
was identified to be similar to that in 201Pb and the same is
$(\pi(h_{9/2}^{2})_{0^{+}}\otimes\nu
p_{1/2}^{-2}f_{5/2}^{-3}(i_{13/2}^{-2})_{12^{+}})_{25/2^{-}29/2^{-}}$. The
findings in 203Po thus upheld the interpretation of its excitation scheme
within the framework of the single particle excitations, as had been
established for the still lighter isotopes of the nucleus Weckström et al.
(1985). This was also a continuing trend from the heavier isotopes such as
205,207Po Rahkonen et al. (1985). The absence of collectivity was further
corroborated by the absence of enhanced B(E2) in these nuclei Fant et al.
(1986).

The present paper reports a spectroscopic investigation of the level structure
of 203Po, using updated experimental facilities as well as contemporary
framework for shell model calculations. The objective was to explore possible
features in the excitation scheme of the nucleus, through the use of a large
array of high-resolution gamma-ray detectors in the setup, and to test the
reproducibility of the observed level energies in the calculations of the
interacting shell model. The computational exercise is a validation of the
model Hamiltonian used for the purpose as well as of facility in identifying
and quantifying the single particle excitations that contribute to the
observed level scheme.

##  II Experimental Details and Data Analysis

Excitations of the 203Po nucleus were investigated following its population in
the 194Pt(13C,4n) reaction at $E_{lab}$ = 74 MeV. The target was 13 mg/cm2
thick self-supporting foil of enriched (99%) 194Pt. The beam was delivered by
the 15 UD Pelletron at IUAC, New Delhi and the beam energy was so chosen after
an excitation function measurement at the commencement of the experiment. As
per the predictions of the statistical model calculations, at this beam
energy, the aforementioned reaction would be of dominant cross section amongst
the possible compound nucleus fusion-evaporation channels while the fission
(exit) channel would amount to $\sim$ 25% of the total fusion cross-section.
Indeed, the yield of 203Po was observed to be maximum when compared to the
other fusion-evaporation products, that principally included isotopes of Po
($Z=84$), Bi ($Z=83$) and Pb ($Z=82$), as illustrated in Fig. 1. The detection
system was the Indian National Gamma Array (INGA) setup at IUAC Muralithar et
al. (2010) and (then) consisted of eighteen Compton suppressed HPGe clover
detectors positioned at 148o (4 detectors), 123o (4 detectors), 90o (6
detectors), 57o (2 detectors), and 32o (2 detectors). An assembly of three
absorber sheets of lead, tin, and copper was afixed on the face of the
heavymet collimator of the Anti Compton Shield (ACS) in each detector. The
absorbers facilitated in reducing the intensity of the X-rays, from the thick
target, being incident on the detectors (and thus contributing in the event
trigger). Data was principally acquired under the condition that at least two
Compton suppressed HPGe clover detectors needed to fire in coincidence for
generating the event trigger. The two- and higher-fold events acquired was
$\sim$ 2$\times$109.

Figure 1:  Part of the $\gamma$-ray spectrum corresponding to the full
projection of a $\gamma$-$\gamma$ symmetric matrix and illustrating the
different product nuclei populated in the present experiment.

The data was sorted into spectra, symmetric and asymmetric (angle dependent)
$\gamma$-$\gamma$ matrices as well as $\gamma$-$\gamma$-$\gamma$ cube using
SPRINGZ Das et al. (2017) and INGASORT Bhowmik et al. (2001) codes and
subsequently analyzed using the RADWARE Radford (1995) package. The
methodology and the objectives of the exercise were identical to that of any
regular investigation of nuclear level structure using $\gamma$-ray
spectroscopy. These have been detailed in numerous papers, such as Ref.
Samanta et al. (2018, 2019), and are briefly mentioned herein. The coincidence
relationships between the observed $\gamma$-ray transitions were extracted
from the symmetric $\gamma$-$\gamma$ matrix and $\gamma$-$\gamma$-$\gamma$
cube. The coincidences along with the intensity considerations were applied
for the placement of the $\gamma$-ray transitions in the level scheme of the
nucleus. The assignment of multipolarities of the $\gamma$-rays followed
determination of their $R_{ADO}$ (Ratio of Angular Distribution from Oriented
Nuclei) values using

$R_{ADO}=\frac{I_{\gamma 1}\ at\ 32^{o}\ (Gated\ by\ \gamma_{2}\ at\ all\
angles)}{I_{\gamma 1}\ at\ 123^{o}\ (Gated\ by\ \gamma_{2}\ at\ all\ angles)}$
(1)

where $I$ is the intensity of the transition (of interest, $\gamma_{1}$ in the
above equation) in the relevant gated spectrum that is generated from the
appropriate angle dependent matrix. As far as this analysis is concerned, the
$R_{ADO}$ value for the stretched dipole ($\Delta$J = 1) transitions is
0.73$\pm$0.01 while for the stretched quadrupole ($\Delta$J = 2) ones, it is
1.34$\pm$0.01. These values were derived from $R_{ADO}$s of transitions with
previously established multipolarities and belonging to other Po isotopes
populated in the same experiment. The $R_{ADO}$ values determined for
different $\gamma$-ray transitions, observed in this study, are represented in
Fig. 2.

Figure 2: $R_{ADO}$ values for transitions of 203Po, as determined in the
current analysis. Those for selected transitions of 202,204Po are plotted as
reference.

Figure 3: (a) Plot of geometrical asymmetry as a function of $\gamma$-ray
energy. (b) Polarization asymmetry of transitions of 203Po. (c) Linear
polarization values for transitions of 203Po along with the corresponding
theoretical estimates for some of them (of pure multipolarity). The $\Delta$
and $P$ values for selected transitions of other isotopes, that were populated
in the same experiment, are included for validation.

The electromagnetic nature of the transitions were assigned on the basis of
their polarization asymmetry evaluated using,

$\Delta=\frac{aN_{\perp}\ -\ N_{\parallel}}{aN_{\perp}\ +\ N_{\parallel}}$ (2)

where $N_{\perp}$ and $N_{\parallel}$ are respectively the number of photons
of the $\gamma$-ray of interest that are scattered perpendicular to and
parallel to the reference plane. The latter is defined by the beam direction
and the direction of emission of the $\gamma$-ray. Each of the four crystals
of a HPGe clover detector operates as scatterer while the two adjacent ones,
parallel and perpendicular to the scatterer, operate as absorbers and
facilitate in identifying the scattering events in the respective directions.
The asymmetry between the two scattering possibilities is known to be maximum
at 90o. Thus, the $N_{\perp}$ ($N_{\parallel}$) for $\gamma$-rays is extracted
from a matrix that has been constructed with the perpendicular (parallel)
scattering events in the detectors at 90o on one axis and the coincident
detections in detectors at all other angles on the other axis. The
coincidences aid in the unambiguous identification of the $\gamma$-ray
transition being analyzed. The $a$ in Eq. (2) represents the asymmetry that is
characteristic to the geometry of the detection setup. It was determined from
the asymmetry between $N_{\perp}$ and $N_{\parallel}$ for $\gamma$-rays of
(unpolarized) radioactive sources, such as 152Eu, and using
$a=N_{\parallel}/N_{\perp}$. The typical plot of $a$, as a function of
$\gamma$-ray energy, for the present setup is illustrated in Fig. 3(a). The
observed asymmetry between $N_{\perp}$ and $N_{\parallel}$ for polarized
$\gamma$-rays, such as those emitted by spin oriented ensemble of nuclei
produced in fusion-evaporation reactions, depends on the degree of their
polarization ($P$) and the sensitivity ($Q$) of the measurement setup. These
are related through,

$P=\frac{\Delta}{Q}$ (3)

with,

$Q(E_{\gamma})=Q_{0}(E_{\gamma})(CE_{\gamma}\ +\ D)$ (4)

where,

$Q_{0}(E_{\gamma})=\frac{\alpha+1}{\alpha^{2}+\alpha+1}$ (5)

$\alpha$ being $E_{\gamma}/m_{e}c^{2}$, $m_{e}c^{2}$ is the electron rest mass
energy. The $C$ and $D$ parameters for the purpose were adopted from those
following the work by Palit et al. Palit et al. (2000) and are $C=0.000099\
keV^{-1}$ and $D=0.446$.

As per the regular methodology of nuclear structure studies, using
$\gamma$-ray spectroscopy, the information on coincidence relationships
between the $\gamma$-rays along with their intensities, multipolarities and
electromagnetic nature, as resulting from the aforementioned analysis, were
used to identify the excitation scheme of the nucleus and the same is
discussed in the next section.

##  III Results

Figure 4:  Excitation scheme of 203Po following the present work. The
$\gamma$-ray transitions that have been newly identified in this study are
indicated in red.

The excitation scheme of 203Po, as established or confirmed in the present
investigation, is illustrated in Fig. 4. Figs. 5 and 6 illustrate the
representative gated spectra respectively projected from $\gamma$-$\gamma$
matrix and $\gamma$-$\gamma$-$\gamma$ cube. The observed coincidences have
been used to identify the placement of transitions in the level scheme. Twenty
new $\gamma$-ray transitions have been placed in the level scheme of the
nucleus and the following modifications have been made in the existing Fant et
al. (1986); nnd  assignments therein. The details of the $\gamma$-ray
transitions are recorded in Table I. (The energies of the transitions and the
levels are rounded off to the nearest integer in the discussions herein.)

Figure 5: Representative spectra projected out of $\gamma$-$\gamma$ matrix
with gate on transitions of 203Po, as indicated in the inset of the respective
spectrum. The $\gamma$-rays newly identified in the present work are marked
with *. Those resulting from overlapping coincidences in other nuclei,
populated in the same experiment, are also labeled accordingly. Figure 6:
Representative spectrum projected out of $\gamma$-$\gamma$-$\gamma$ cube with
double gate on transitions of 203Po, as indicated in the inset of the
spectrum. The $\gamma$-rays newly identified in the present work are marked
with *.

  1. 1.

The placement of 397-keV transition has been changed with respect to that
assigned in the literature, as de-exciting a $\sim$ 1527-keV level Semmes et
al. (1987). The level and the $\gamma$-ray was not reported by Fant et al.
while in the present study the placement of the transition has been modified
to one de-exciting the $\sim$ 3264-keV state. The level has been marked as a
new one in the level scheme (Fig. 4) while the $\gamma$-ray transition is
identified to have been observed previously, albeit with a different
placement.

  2. 2.

The 219-keV transition de-exciting the 2274-keV level has been identified as a
M1 and the state has been identified to be of spin-parity 27/2+. There was no
spin-parity assignment for this level, identified as $\sim$ 2277-keV by Fant
et al. nnd , in the previous studies.

  3. 3.

The 959-keV transition, de-exciting the 3014-keV state, has been assigned a
mixed M1+(E2) nature, following the present measurements. Accordingly, the
state has been assigned a spin-parity of 27/2+ that is at variance with the
assignment by Fant et al. nnd . The latter had identified the $\gamma$-ray as
a pure E2 one and had tentatively assigned the spin-parity of the state
($\sim$ 3018-keV, as per Fant et al.) as (29/2+).

  4. 4.

The 543-keV $\gamma$-ray, from the 3066-keV state, has been assigned a
multipolarity of E1 in this study. It was tentatively identified as M1, by
Fant et al., and the spin of the level (at $\sim$ 3070-keV, as per Fant et
al.) was accordingly assigned to be 29/2.

  5. 5.

The 585-keV transition de-exciting the 3108-keV state has been established as
a pure dipole in this study. However, the electromagnetic nature of the same
could not be unambiguously determined in the present investigation. The
multipolarity of the transition was undetermined in the work by Fant et al.
and consequently there was no spin assignment for the state (at $\sim$
3112-keV, as quoted by Fant et al.) therein.

  6. 6.

The spin-parity of the 3236-keV state, de-excited by the 369-keV transition,
has been confirmed to be 33/2+ in this study. The assignment for the level (at
$\sim$ 3241-keV, as per Fant et al.) was only tentative in the previous work
nnd .

  7. 7.

The spin-parity of the 3712-keV level has been assigned as 33/2+ in this work,
following the E2 assignment of the 845-keV $\gamma$-ray that de-excites the
state. There was no multipolarity assignment for the transition or spin-parity
assignment for the state (at $\sim$ 3717-keV, as per Fant et al.) in the
previous studies nnd .

  8. 8.

The 3877-keV state has been assigned spin-parity of 33/2-, in this
measurement. This is following the identification of the 450-keV transition,
that de-excites the level, as an E2 one herein. Previously nnd , the
transition was assigned as M1 and the spin-parity of the state (at $\sim$
3882-keV, as quoted by Fant et al.) as 31/2-. Fig. 7 represents the spectra of
the transition corresponding to the perpendicular and the parallel scattering
events and illustrates the dominance of the former that leads to positive
value of polarization asymmetry (Eq. 2) or polarization (Eq. 3).

  9. 9.

The spin-parity of the 4352-keV level has been confirmed to be 35/2- in the
present work. The assignment was tentative for the state (at $\sim$ 4358-keV,
quoted by Fant et al.) in the previous studies. The 476-keV transition, de-
exciting the state, has been identified as M1 in this study and this is
different from the E2 assignment by Fant et al..

An additional proposition can be put forth on the multipolarity assignment of
the 182-keV transition de-exciting the 2156-keV state. Since the state is
known to be an isomer of $T_{1/2}$ $>$ 200 ns Fant et al. (1986), the
multipolarity of the transition could not be ascertained from its $ADO$ ratio
and its polarization asymmetry. These measurements are valid for transitions
emitted by spin oriented ensemble of nuclei, such as produced in fusion-
evaporation reactions, while the aforementioned isomeric lifetime is
sufficient to induce dealignment. If the observed intensity of this 182-keV
transition is corrected for electron conversion, using codes such as BrICC
Kibédi et al. (2008), it is $\sim$ 60% increased if the transition is an E2
one and $\sim$ 300% enhanced if it is a M1. The latter would result in an
unbalanced intensity across the 1975-keV state that is fed by the 182-keV
transition and de-excited by the 596-keV one. If the 182-keV transition is
thus interpreted to be of E2 nature, the 2156-keV level can be assigned a
spin-parity of 25/2+. However, since there is no direct experimental evidence
for the same, this proposition has not been indicated in the level scheme
(Fig. 4) and the assignment has not been included in the table (Table I). The
sharp decrease in the relative intensity of the $\gamma$-ray transitions
across the 2156-keV state is also noteworthy and can be ascribed to the state
being an isomer of T1/2 $>$ 200 ns Fant et al. (1986).

Figure 7: Spectra of 450-keV transition peak corresponding to the
perpendicular and the parallel scattering events in the HPGe clover detectors
at 90o.

Previous studies Fant et al. (1986, 1990) on the Po isotopes had reported a
number of isomers therein. Some of these, with half-lives around few ns, have
been reexamined in the current study using the centroid shift method Madhu et
al. (2022); Yadav et al. (2022). In the present implementation of the
technique, the time difference between the feeding and the decaying
$\gamma$-ray transitions of a state is histogrammed alternately by defining
one as the start (stop) and the other as stop (start). The difference between
the centroids of the two distribution is known to be 2$\tau$, $\tau$ being the
average lifetime of the state. Fig. 8 illustrates the time difference spectra
between the (i) 788- and 262-keV transitions that respectively feeds and de-
excites the 3387-keV state in 204Po Fant et al. (1990), also populated in the
present experiment, and (ii) 637- and 304-keV transitions that respectively
feeds and de-excites the 2789-keV state in 203Po. The half-life of the
3387-keV state in 204Po was determined by Fant et al. Fant et al. (1990) as
9$\pm$3 ns, presumably following an analysis of the time profile of the
decaying transition with respect to the RF of the accelerator. The present
analysis has resulted in T1/2 = 6.2$\pm$0.8 ns, that is within the limits of
uncertainty on the previous estimate and validates the present analysis. The
latter carried out for the 2789-keV state in 203Po yields its T1/2 =
7.1$\pm$0.1 ns that is lesser than the previous value, also reported by Fant
et al. Fant et al. (1986), of 12$\pm$2 ns.

Figure 8: (Color online) Time difference spectra between transitions indicated
in the inset, for determining isomeric lifetimes. The upper panel corresponds
to the state at 3387-keV state in 204Po while the bottom panel is for 2789-keV
state in 203Po. (Please refer to the text for details.)

The experimentally observed level scheme of the 203Po nucleus has been
interpreted through single particle excitations in the framework of the shell
model. The same is detailed in the next section.

Table 1: Details of the levels and the $\gamma$-ray transitions of 203Po nucleus observed in the present work. The energy of a $\gamma$-ray transition is the weighted average of its value in multiple gates. The relative intensities ($I_{\gamma}$) of the $\gamma$-ray transitions are normalized with respect to the intensity of 466-keV transition as observed in 612-keV gated spectrum. The ADO ratios($R_{ADO}$), polarization asymmetry ($\Delta_{pol}$), and linear polarization ($P$) of the transitions are determined using the procedure described in Section II. The $N$ and $a$ superscripts indicate the assignments that have been respectively adopted from NNDC nnd  and/or Fant et al. Fant et al. (1986). $E_{i}(keV)$ | $E_{\gamma}(keV)$ | $I_{\gamma}$ | $J_{i}^{\pi}$ | $J_{f}^{\pi}$ | $R_{ADO}$ | $\Delta_{pol}$ | P | Multipolarity
---|---|---|---|---|---|---|---|---
638.7 $\pm$0.1 | 577.2$\pm$0.1 | 11$\pm$1 | 7/2- | (3/2${}^{-})$ |  |  |  | E2N
| 638.7$\pm$0.1 | 48$\pm$1 | 7/2- | $5/2^{-}$ |  |  |  | M1N
641.7 $\pm$0.2 | 641.7$\pm$0.2 |  | 13/2+ | $5/2^{-}$ |  |  |  | M4N
1055.2 $\pm$0.1 | 416.5$\pm$0.1 | 59$\pm$1 | (11/2${}^{-})^{a}$ | $7/2^{-}$ |  |  |  | M1+E2N
1254.0 $\pm$0.2 | 612.3$\pm$0.1 |  | 17/2+ | $13/2^{+}$ |  |  |  | E2N
1378.8 $\pm$0.3 | 737.1$\pm$0.2 | 127$\pm$3 | (17/2${}^{+})^{a}$ | $13/2^{+}$ |  |  |  | (E2)N
1697.1 $\pm$0.8 | 318.3$\pm$0.7 | 23$\pm$6 |  | ($17/2^{+})^{a}$ |  |  |  |
1719.8 $\pm$0.2 | 465.8$\pm$0.1 | 1000 | 21/2+ | $17/2^{+}$ |  |  |  | E2N
1974.5 $\pm$0.3 | 595.7$\pm$0.1 | 251$\pm$2 | (21/2${}^{+})^{a}$ | $(17/2^{+})$ |  |  |  | E2N
2054.7 $\pm$0.2 | 334.9$\pm$0.1 | 643$\pm$14 | 25/2+ | $21/2^{+}$ |  |  |  | E2N
2077.0 $\pm$0.2 | 356.8$\pm$0.1 | 64$\pm$2 | 21/2+ | $21/2^{+}$ |  |  |  | M1N
2156.4 $\pm$0.3 | 181.9$\pm$0.1 | 156$\pm$1 |  | $(21/2^{+})^{a}$ |  |  |  |
2184.4 $\pm$0.7 | 805.6$\pm$0.6 | 4$\pm$1 |  | ($17/2^{+})^{a}$ |  |  |  |
2273.6 $\pm$0.2 | 219.1$\pm$0.1 | 58$\pm$1 | 27/2+ | $25/2^{+}$ | 0.75$\pm$0.01 | -0.16$\pm$0.09 | -0.43$\pm$0.24 | M1
2404.2 $\pm$0.2 | 349.2$\pm$0.1 | 36$\pm$1 | 25/2+ | $25/2^{+}$ |  |  |  | M1N
| 684.1$\pm$0.1 | 71$\pm$2 | 25/2+ | $21/2^{+}$ |  |  |  |
2485.8 $\pm$0.2 | 408.6$\pm$0.2 | 21$\pm$1 | 23/2+ | $21/2^{+}$ |  |  |  | M1N
| 765.9$\pm$0.1 | 76$\pm$2 | 23/2+ | $21/2^{+}$ |  |  |  | M1N
2500.2 $\pm$0.2 | 780.1$\pm$0.1 | 40$\pm$1 | 23/2+ | $21/2^{+}$ |  |  |  | (M1)N
2523.0 $\pm$0.2 | 468.3$\pm$0.1 | 176$\pm$4 | 27/2+ | $25/2^{+}$ |  |  |  | M1N
2527.6 $\pm$0.7 | 1148.8$\pm$0.6 |  |  | (17/2${}^{+})^{a}$ |  |  |  |
2765.1 $\pm$0.4 | 710.4$\pm$0.3 | 8$\pm$1 |  | 25/2+ |  |  |  |
2789.1 $\pm$0.2 | 289.3$\pm$0.1 | 74$\pm$2 | 25/2- | 23/2+ |  |  |  | (E1)N
| 303.5$\pm$0.1 | 102$\pm$2 | 25/2- | 23/2+ |  |  |  | E1N
| 385.1$\pm$0.1 | 54$\pm$2 | 25/2- | 25/2+ |  |  |  | E1N
2820.9 $\pm$0.2 | 297.7$\pm$0.1 | 28$\pm$1 | 29/2- | 27/2+ |  |  |  | (E1)N
2863.0 $\pm$0.2 | 589.4$\pm$0.1 | 55$\pm$2 | 31/2+ | 27/2+ | 1.05$\pm$0.05 | 0.05$\pm$0.04 | 0.21$\pm$0.17 | E2+M3
2867.2 $\pm$0.2 | 812.5$\pm$0.1 | 226$\pm$5 | 29/2+ | 25/2+ | 1.34$\pm$0.01 | 0.06$\pm$0.01 | 0.32$\pm$0.05 | E2
2950.0 $\pm$0.4 | 793.6$\pm$0.2 |  |  |  | 0.70$\pm$0.03 |  |  | D
2976.7 $\pm$0.3 | 922.2$\pm$0.2 | 13$\pm$1 | 27/2+ | 25/2+ | 0.82$\pm$0.06 | -0.05$\pm$0.06 | -0.31$\pm$0.37 | M1
3013.5 $\pm$0.2 | 959.1$\pm$0.1 | 44$\pm$1 | 27/2+ | 25/2+ | 0.83$\pm$0.02 | -0.01$\pm$0.03 | -0.06$\pm$0.19 | M1+(E2)
3066.1 $\pm$0.2 | 542.7$\pm$0.1 | 46$\pm$1 | 29/2- | 27/2+ | 0.81$\pm$0.01 | 0.04$\pm$0.03 | 0.16$\pm$0.12 | E1
3093.2 $\pm$0.4 | 1038.5$\pm$0.3 | 16$\pm$3 | 29/2 | 25/2+ | 1.24$\pm$0.09 |  |  | Q
3107.5 $\pm$0.2 | 584.5$\pm$0.1 | 21$\pm$1 | 29/2 | 27/2+ | 0.66$\pm$0.02 |  |  | D
3108.3 $\pm$0.4 | 704.1$\pm$0.3 | 11$\pm$1 |  | 25/2+ |  |  |  |
3220.5 $\pm$0.4 | 1165.8$\pm$0.3 | 6$\pm$1 |  | 25/2+ |  |  |  |
3231.8 $\pm$0.2 | 364.5$\pm$0.1 | 40$\pm$1 | 31/2+ | 29/2+ | 0.79$\pm$0.02 | -0.04$\pm$0.03 | -0.13$\pm$0.10 | M1
3236.3 $\pm$0.2 | 368.8$\pm$0.1 | 79$\pm$2 | 33/2+ | 29/2+ | 1.39$\pm$0.03 | 0.03$\pm$0.02 | 0.10$\pm$0.06 | E2
3241.9 $\pm$0.2 | 374.7$\pm$0.1 | 15$\pm$1 | 33/2+ | 29/2+ | 1.41$\pm$0.04 | 0.08$\pm$0.10 | 0.26$\pm$0.32 | (E2)
3254.4 $\pm$0.2 | 390.9$\pm$0.1 | 18$\pm$1 | 33/2- | 31/2+ | 0.97$\pm$0.05 | 0.08$\pm$0.07 | 0.26$\pm$0.23 | E1+M2
3262.9 $\pm$0.2 | 196.6$\pm$0.1 | 16$\pm$1 | 33/2 | 29/2- | 1.28$\pm$0.04 |  |  | Q
3264.0 $\pm$0.2 | 397.0$\pm$0.1 | 22$\pm$1 | 33/2+ | 29/2+ | 1.20$\pm$0.04 | 0.05$\pm$0.06 | 0.17$\pm$0.20 | (E2)
3292.0 $\pm$0.3 | 1237.2$\pm$0.2 | 5$\pm$1 |  | 25/2+ |  |  |  |
3416.1 $\pm$0.3 | 627.4$\pm$0.2 | 17$\pm$1 |  | 25/2- |  |  |  |
3426.5 $\pm$0.2 | 637.3$\pm$0.1 | 140$\pm$3 | 29/2- | 25/2- | 1.39$\pm$0.02 | 0.08$\pm$0.01 | 0.35$\pm$0.05 | E2
3443.2 $\pm$0.3 | 211.4$\pm$0.2 | 29$\pm$1 | 33/2 | 31/2+ | 0.72$\pm$0.02 |  |  | D
3456.2 $\pm$0.2 | 192.3$\pm$0.1 | 11$\pm$1 | 35/2 | 33/2+ | 0.68$\pm$0.05 |  |  | D
3488.8 $\pm$0.3 | 234.3$\pm$0.2 | 15$\pm$1 | 35/2 | 33/2- | 0.69$\pm$0.01 |  |  | D
3603.8 $\pm$0.3 | 1329.9$\pm$0.2 | 9$\pm$1 |  | 27/2+ |  |  |  |
3711.9 $\pm$0.2 | 844.7$\pm$0.1 | 29$\pm$1 | 33/2+ | 29/2+ | 1.25$\pm$0.05 | 0.04$\pm$0.02 | 0.22$\pm$0.11 | E2
3741.7 $\pm$0.2 | 315.1$\pm$0.1 | 34$\pm$1 | 31/2- | 29/2- | 0.98$\pm$0.04 | -0.08$\pm$0.05 | -0.24$\pm$0.15 | M1+E2
3876.6 $\pm$0.2 | 450.3$\pm$0.1 | 97$\pm$2 | 33/2- | 29/2- | 1.33$\pm$0.01 | 0.07$\pm$0.02 | 0.25$\pm$0.07 | E2
3934.7 $\pm$0.3 | 491.5$\pm$0.2 | 21$\pm$1 | 37/2 | 33/2 | 1.36$\pm$0.07 |  |  | Q
3979.4 $\pm$0.3 | 742.9$\pm$0.2 | 23$\pm$1 | 35/2+ | 33/2+ | 0.77$\pm$0.03 | -0.04$\pm$0.03 | -0.20$\pm$0.15 | M1
4146.2 $\pm$0.2 | 891.8$\pm$0.1 | 24$\pm$1 | 35/2+ | 33/2- | 0.82$\pm$0.03 | 0.01$\pm$0.03 | 0.06$\pm$0.18 | (E1)
4352.3 $\pm$0.2 | 475.9$\pm$0.1 | 27$\pm$1 | 35/2- | 33/2- | 0.77$\pm$0.04 | -0.06$\pm$0.02 | -0.22$\pm$0.07 | M1
4528.2 $\pm$0.4 | 175.9$\pm$0.3 | 13$\pm$1 |  | 35/2- |  |  |  |
4612.0 $\pm$0.3 | 735.4$\pm$0.2 | 26$\pm$1 | 35/2- | 33/2- | 0.90$\pm$0.04 | -0.05$\pm$0.07 | -0.25$\pm$0.35 | M1+E2
4623.3 $\pm$0.4 | 746.7$\pm$0.3 | 8$\pm$1 |  | 33/2- |  |  |  |
4645.6 $\pm$0.2 | 1189.3$\pm$0.1 | 24$\pm$1 | 37/2 | 35/2 | 0.73$\pm$0.04 | -0.03$\pm$0.07 | -0.24$\pm$0.56 | (M1)
4929.8 $\pm$0.5 | 1053.2$\pm$0.4 |  |  | 33/2- |  |  |  |

##  IV Discussions

One of the objectives of this endeavor has been to probe the efficacy of the
shell model in interpreting the excitation scheme of the nuclei in the A
$\sim$ 200 region. There have been similar efforts, in recent times, wherein
level structures of nuclei around the 208Pb-core are calculated in the shell
model framework. Bothe et al. Bothe et al. (2022) have reported such
calculations for the isomeric states in 203Tl ($Z=81,N=122$) while Yadav et
al. Yadav et al. (2022) and Madhu et al. Madhu et al. (2022) have used them
for deciphering the particle excitations associated with the observed states
of 215,216Fr ($Z=87,N=128,129$) nuclei. These studies have identified a
general overlap, between the experimental and the calculated level energies,
of within $\sim$ 250-keV as reasonable.

Large basis shell model calculation has been carried out in the present work
using KHH7B Herling and Kuo (1972) Hamiltonian in the model space spanning
$Z=58-114$ and $N=100-164$. The latter includes proton orbitals $d_{5/2}$,
$h_{11/2}$, $d_{3/2}$ and $s_{1/2}$ below $Z=82$ and the $h_{9/2}$, $f_{7/2}$,
and $i_{13/2}$ above; the neutron orbitals are $i_{13/2}$, $p_{3/2}$,
$f_{5/2}$, and $p_{1/2}$ below $N=126$ and the $g_{9/2}$, $i_{11/2}$, and
$j_{15/2}$ above. Proton excitations across $Z=82$ closure and neutron
excitations across the closure at $N=126$ have not been allowed in the
calculations. The matrix diagonalization has been carried out using the OXBASH
Brown (2004) code. The comparison between the calculated and the experimental
level energies is illustrated in Figs. 9 and 10. The dominant particle
configurations along with the energy values of the states are recorded in
Table II.

Figure 9: Comparison between the calculated and the experimental level
energies of the negative parity states in 203Po. Figure 10: Comparison between
the calculated and the experimental level energies of the positive parity
states in 203Po.

The calculated energies of the negative parity states with spin $<$ 29/2 are
excellent overlap with their experimental values, even within $\sim$ 100-keV
for some of them. The 25/2- level is an exception for which the theoretical
and the measured level energies differ by $\sim$ 800 keV. The dominant
particle configurations associated with these states negative parity states
have been calculated to be
$\pi(h_{9/2}^{2})\otimes\nu(f_{5/2}^{3,2}p_{3/2}^{2,3}i_{13/2}^{14})$. The
negative parity states at higher spins, $\geq$ 31/2, are poorly represented in
the calculations wherein their energies are deviant by as much as 500-keV -
1-MeV with respect to the experimental values. The energy of the calculated
yrast 33/2- state, however, reasonably overlaps with the measured energy
within $\sim$ 250-keV. The most probable particle configurations for the
negative parity states at higher spins correspond to
$\pi(h_{9/2}^{1}i_{13/2}^{1})\otimes\nu(f_{5/2}^{2}p_{3/2}^{4}i_{13/2}^{13})$.
However, those of the yrare 33/2- and the 35/2- are different
($\pi(h_{9/2}^{2})\otimes\nu(f_{5/2}^{3}p_{3/2}^{4}i_{13/2}^{12})$ but, as
indicated by the widely deviant calculated energies vis-a-vis the experimental
ones, these configurations do not appropriately represent the relevant states,
similar to the other high spin levels of odd parity.

Table 2: Main partitions of wave functions of the positive and negative parity states in 203Po for KHH7B interaction |  | Level Energy |  | $J^{\pi}$ | Probability | Proton | Neutron |
---|---|---|---|---|---|---|---|---
| EXPT |  | SM |  |  |  |  |
|  |  |  |  | NEGATIVE PARITY |  |  |
| 0 |  | 0 | $5/2^{-}$ | 29.33 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{3}p_{3/2}^{2}p_{1/2}^{0}i_{13/2}^{14}$ |
| 62 |  | 181 | $(3/2^{-})$ | 39.21 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{3}p_{1/2}^{0}i_{13/2}^{14}$ |
| 639 |  | 755 | $7/2^{-}$ | 19.96 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{3}p_{1/2}^{0}i_{13/2}^{14}$ |
| 1055 |  | 993 | $(11/2^{-})$ | 37.64 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{3}p_{1/2}^{0}i_{13/2}^{14}$ |
| 2789 |  | 1987 | $25/2^{-}$ | 39.78 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{3}p_{3/2}^{2}p_{1/2}^{0}i_{13/2}^{14}$ |
| 2821 |  | 2715 | $29/2^{-}$ | 70.95 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{3}p_{3/2}^{2}p_{1/2}^{0}i_{13/2}^{14}$ |
| 3066 |  | 2758 | $29/2^{-}$ | 31.65 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{3}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{12}$ |
| 3254 |  | 2999 | $33/2^{-}$ | 26.06 | $h_{9/2}^{1}f_{7/2}^{0}i_{13/2}^{1}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 3427 |  | 2812 | $29/2^{-}$ | 24.93 | $h_{9/2}^{1}f_{7/2}^{0}i_{13/2}^{1}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 3742 |  | 2851 | $31/2^{-}$ | 25.53 | $h_{9/2}^{1}f_{7/2}^{0}i_{13/2}^{1}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 3877 |  | 3402 | $33/2^{-}$ | 42.34 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{3}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{12}$ |
| 4352 |  | 3465 | $35/2^{-}$ | 24.51 | $h_{9/2}^{1}f_{7/2}^{0}i_{13/2}^{1}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 4612 |  | 3671 | $35/2^{-}$ | 29.32 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{3}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{12}$ |
|  |  |  |  | POSITIVE PARITY |  |  |
| 642 |  | 700 | $13/2^{+}$ | 24.13 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 1254 |  | 1365 | $17/2^{+}$ | 28.43 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 1379 |  | 1861 | ($17/2^{+}$) | 23.95 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 1720 |  | 1745 | $21/2^{+}$ | 23.00 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 1975 |  | 1947 | ($21/2^{+}$) | 30.87 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{4}p_{3/2}^{2}p_{1/2}^{0}i_{13/2}^{13}$ |
| 2055 |  | 1981 | $25/2^{+}$ | 32.32 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 2077 |  | 2023 | $21/2^{+}$ | 27.80 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 2404 |  | 2347 | $25/2^{+}$ | 35.75 | $h_{9/2}^{1}f_{7/2}^{0}i_{13/2}^{1}$ | $f_{5/2}^{3}p_{3/2}^{2}p_{1/2}^{0}i_{13/2}^{14}$ |
| 2486 |  | 2001 | $23/2^{+}$ | 12.82 | $h_{9/2}^{0}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{0}p_{3/2}^{0}p_{1/2}^{0}i_{13/2}^{0}$ |
| 2500 |  | 2337 | $23/2^{+}$ | 19.05 | $h_{9/2}^{0}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{0}p_{3/2}^{0}p_{1/2}^{0}i_{13/2}^{0}$ |
| 2274 |  | 2318 | $27/2^{+}$ | 22.42 | $h_{9/2}^{1}f_{7/2}^{0}i_{13/2}^{1}$ | $f_{5/2}^{1}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{14}$ |
| 2523 |  | 2375 | $27/2^{+}$ | 26.22 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 2977 |  | 2667 | $27/2^{+}$ | 31.61 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{3}p_{3/2}^{3}p_{1/2}^{0}i_{13/2}^{13}$ |
| 2867 |  | 2620 | $29/2^{+}$ | 35.78 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 2863 |  | 2758 | $31/2^{+}$ | 53.28 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 3232 |  | 2949 | $31/2^{+}$ | 32.75 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{4}p_{3/2}^{2}p_{1/2}^{0}i_{13/2}^{13}$ |
| 3236 |  | 2782 | $33/2^{+}$ | 52.68 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 3242 |  | 3185 | $33/2^{+}$ | 57.96 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{3}p_{3/2}^{3}p_{1/2}^{0}i_{13/2}^{13}$ |
| 3264 |  | 3226 | $33/2^{+}$ | 30.14 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 3979 |  | 3230 | $35/2^{+}$ | 51.41 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{2}p_{3/2}^{4}p_{1/2}^{0}i_{13/2}^{13}$ |
| 4146 |  | 3517 | $35/2^{+}$ | 54.27 | $h_{9/2}^{2}f_{7/2}^{0}i_{13/2}^{0}$ | $f_{5/2}^{3}p_{3/2}^{3}p_{1/2}^{0}i_{13/2}^{13}$ |

The calculated level energies for most of the positive parity states with spin
$<$ 27/2 are in excellent overlap, within or around 100-keV, with their
experimental values. The yrare 17/2+ state is an exception for which the
calculated and the experimental energies differ by $\sim$ 500-keV. However, it
is noteworthy that the spin-parity assignment of the 1379-keV state as second
17/2+ was by Fant et al. Fant et al. (1986) and is tentative. This could not
be confirmed in the present study. If the parity assignment of the state is
changed, it would be the yrast (and only observed) 17/2- level with calculated
energy of 1214-keV that is in reasonable overlap with the experimental value.
It is noted that, in such a scenario, the 737-keV (17/2- $\rightarrow$ 13/2+)
and 596-keV (21/2+ $\rightarrow$ 17/2-) transitions would be M2 ones and,
according to the Weisskopf estimate, would translate into lifetimes of $\sim$
few ns for the states they de-excite. These lifetimes are much less than the
$\gamma$-$\gamma$ coincidence window (200 ns) of the experiment and, thus,
will not impact the observed intensity of the transitions. The yrast and the
yrare 23/2+ state respectively exhibit differences of $\sim$ 500-keV and
$\sim$ 200-keV between their theoretical and measured values. While the latter
can still be perceived as a reasonable overlap, a deviation of the calculated
energy by $\sim$ 500-keV with respect to the experimental one indicates an
aberrant representation of the state in the framework of the shell model
calculations. It is also noteworthy that the yrast 23/2+ state is calculated
to be of substantially mixed configurations, compared to the other states of
the nucleus, and the numerically dominant partition is only of 13%
probability. As far as the positive parity states of spin $\gtrsim$ 29/2 are
concerned, the overlap of experimental and calculated energies is of
considerable variance. While they excellently agree for the yrast 31/2+, the
yrare and the third 33/2+ levels, within $\sim$ 100-keV, the difference is
$\sim$ 250-450 keV for the 29/2+ and the yrast 31/2+ and 33/2+. It is still
higher, $\sim$ 700-keV, for 35/2+. Such deviations, at the highest excitations
observed in the nucleus, can be ascribed to the limitations of the model
calculations in representing the associated multiparticle configurations based
on the high-j orbitals (that characterize the relevant model space). Most of
the positive parity states have been calculated to be of dominant
configuration
$\pi(h_{9/2}^{2})\otimes\nu(f_{5/2}^{2-4}p_{3/2}^{2-4}i_{13/2}^{13}$. The
exceptions are the yrare 25/2+ state, for which the calculated dominant
configuration is
$\pi(h_{9/2}^{1}i_{13/2}^{1})\otimes\nu(f_{5/2}^{3}p_{3/2}^{2}i_{13/2}^{14}$,
and the yrast 27/2+ state, for which the most probable configuration is
$\pi(h_{9/2}^{1}i_{13/2}^{1})\otimes\nu(f_{5/2}^{1}p_{3/2}^{4}i_{13/2}^{14}$.
It is noteworthy that the calculated and the experimental energies of these
states agree within $\sim$ 50-keV that presumably vindicates the
interpretation of their underlying excitations.

If the 2156-keV state is assigned a spin-parity of 25/2+, as discussed in the
previous section, following an E2 assignment for the 182-keV transition (that
de-excites the level), the level is then the yrare 25/2+ and exhibits a
reasonable overlap, within $\sim$ 200 keV, with the calculated energy
(2347-keV). The current yrare 25/2+ at 2404-keV is then the third 25/2+ state
and its energy is in excellent agreement with the theoretical value of
2383-keV. Once again, since there is no direct experimental evidence to
corroborate the spin-parity assignment of the state at 2156-keV, this has not
been included in the table.

It may thus be summed up that the observed excitation scheme of the 203Po
nucleus could be satisfactorily interpreted within the framework of the large
basis shell model calculations. The specific deviations might have resulted
from the limitations of the Hamiltonian that requires further refinements. The
latter is expected to be facilitated by the availability of experimental data
through endeavors such as the present study.

##  V Conclusion

The level structure of the 203Po nucleus has been probed following its
population in 194Pt(13C,4n) reaction at Elab = 74 MeV. The excitation scheme
of the nucleus has been established upto $\sim$ 5 MeV and spin $\sim$
18$\hbar$. Twenty new $\gamma$-ray transitions have been added in the level
scheme of the the nucleus and spin-parity assignments have been either made or
confirmed for a number of states therein. The observed level scheme has been
satisfactorily interpreted within the framework of large basis shell model
calculations wherein the excited states of the nucleus have been ascribed to
proton excitations in $h_{9/2}$ and $i_{13/2}$ orbitals outside the $Z=82$
closure and neutron excitations in $f_{5/2}$, $p_{3/2}$ and $i_{13/2}$
orbitals in the $N=126$ shell. The overlap between the experimental and the
calculated level energies, of 203Po, upholds the credibility of the shell
model in catering to a microscopic description of the excitation scheme even
for heavy nuclei in the $A\sim 200$ region and in model space consisting of
high-j orbitals. Further refinements in the model calculations are envisaged
to follow the availability of experimental data.

## Acknowledgments

The authors wish to thank the staff associated with the Pelletron Facility at
IUAC, New Delhi, for their help and support during the experiment. We record
our deepest gratitude for Late Prof. Asimananda Goswami and Mr. Pradipta Kumar
Das, of the Saha Institute of Nuclear Physics (SINP), Kolkata, for their
guidance, help and active contribution in the target preparation. Help and
support received from Mr. Kausik Basu (UGC-DAE CSR, KC) during the experiment,
is appreciated. Help of V. Vishnu Jyothi during the experiment is also
acknowledged. P.C.S. acknowledges a research grant from SERB (India),
CRG/2019/000556. B.M. acknowledges the support from Department of Science and
Technology, Government of India through DST/INSPIRE Fellowship (IF200310).
U.G. acknowledges the support from US National Science Foundation through
Grant No. PHY1762495. This work is partially supported by the Department of
Science and Technology, Government of India (No. IR/S2/PF-03/2003-II).

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