Study of Yrast Spectra, Yrast Energy Splitting and Backbanding for 130 Te, 130 I, 130 Xe within the framework of Projected Shell Model

Abstract

The new technology developments are helping up in setting various ββ decay experiments across the world to estimate half-life of many ββ decay candidates. The experimental achievements of ββ decay processes may help in establishing the properties of neutrinos. Theoretically, various mean field approximations are being used to estimate the (Nuclear Matrix Element) of ββ decay processes. The accuratly obtained NMEs should be helpful for extraction of half-life of ββ decay processes and neutrino mass from experimental data. Therefore accurate information of nuclear structure properties of ββ candidates is very important in extracting half-life and〈mν〉from experimental data.
The Projected Shell Model[1] is being used by so many theoretical teams to explain nuclear structure properties. In the present paper, we intend to employ PSM to estimate NMEs of various ββ decay candidates, so we are discussing nuclear structure properties such as yrast spectrum, yrast energy splitting and backbanding of 130Te , 130I , 130Xe respectively.

Full text

Study of Yrast Spectra, Yrast Energy Splitting and
Backbanding for 130Te,130I,130Xe within the framework of
Projected Shell Model
Vikesh Kumar1,∗Pankaj Kumar2,†and Shashi K Dhiman3‡
Department of Physics, Himachal Pradesh University, Shimla - 171005, INDIA
Introduction
The new technology developments are help-
ing up in setting various ββ decay experi-
ments across the world to estimate half-life of
many ββ decay candidates. The experimen-
tal achievements of ββ decay processes may
help in establishing the properties of neutri-
nos. Theoretically, various mean field approx-
imations are being used to estimate the (Nu-
clear Matrix Element) of ββ decay processes.
The accuratly obtained NMEs should be help-
ful for extraction of half-life of ββ decay pro-
cesses and neutrino mass from experimental
data. Therefore accurate information of nu-
clear structure properties of ββ candidates is
very important in extracting half-life and hmνi
from experimental data.
The Projected Shell Model[1] is being used by
so many theoretical teams to explain nuclear
structure properties. In the present paper,
we intend to employ PSM to estimate NMEs
of various ββ decay candidates, so we are
discussing nuclear structure properties such
as yrast spectrum, yrast energy splitting and
backbanding of 130Te,130I,130Xe respectively.
Theoretical Framework
In PSM[1] calculations, the Shell Model
truncation is first achieved within the quasi-
particle (qp) states with respect to the de-
formed Nilsson+BCS vacuum |φi, then rota-
tional symmetry are restored for these states
by standard projection techniques to form a
spherical basis in the laboratory frame. Fi-
∗Electronic address: vickyrao955@gmail.com
†Electronic address: pankajdhiman659@gmail.com
‡Electronic address: shashi.dhiman@gmail.com
0
5
10
15
Energy [MeV]
PSM
Expt.
0
2
4
6
8
10
Energy [MeV]
PSM
Expt.
0 2 4 68 10 12 14 16 18 20 22 24 26 28 30
I(h
_)
0
5
10
15
20
Energy [MeV]
PSM
Expt.
130Te78
130I77
130Xe76
52
53
54
FIG. 1: Comparison of PSM and Expt data[2] for
yrast bands of 130Te,130I,130Xe.
nally the shell model Hamiltonian is diagonal-
ized in the basis. The set of multi-qp states
relevant to the present study (even-even) and
(odd-odd) system is
|φki=na†
ν1a†
ν2|0i, a†
π1a†
π2|0i, a†
ν1a†
ν2a†
π1a†
π2|0io
(1)
|φki=a†
νa†
π|0i(2)
Proceedings of the DAE Symp. on Nucl. Phys. 63 (2018) 262
Available online at www.sympnp.org/proceedings

0 1 2 3 4 5 6 78 9 10 11 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27
I (h
_)
0
0.2
0.4
0.6
0.8
Eγ[MeV]
PSM
Expt.
130I7753
FIG. 2: Comparison of PSM and Experimental
data[2] for Yrast energy splitting between [Eγ][2]
and I(~) for 130I.
0
50
100
150
200
2I/h
_2
PSM
Expt.
00.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65
(h
_ω)2
0
50
100
150
200
2I/h
_2
PSM
Expt.
130Te78
130Xe76
52
54
FIG. 3: Comparison of PSM and Experimental
data[2] for Backbanding between 2I/~2and (~ω)2
for 130Te and 130Xe.
where ν0s(π0s) denote the neutron (pro-
ton) Nilsson quantum numbers which run over
properly selected (low-lying) quasi-particle
states.
In PSM calculations, we use Hamiltonian of
separable forces
ˆ
H=ˆ
H0−1
2χX
µ
ˆ
Q†
µˆ
Qµ−GMˆ
P†ˆ
P−GQX
µ
ˆ
P†
µˆ
Pµ
(3)
Where ˆ
H0is the spherical single particle
hamiltonian. The second term in the Hamilto-
nian is the quadrupole-quadrupole (Q-Q) in-
teraction and the last two terms are monopole
and quadrupole pairing interactions respec-
tively. The coupling constants for the
monopole pairing force GMis taken as[1]
GM=G1∓G2
N−Z
A1
A(MeV ) (4)
where -(+) sign for neutron (proton) and G1,
G2coupling constants are taken as 20.70,
12.12 for 130I[3] and 20.12, 12.12 for 130 Te and
130Xe. The ratio of GQ/GMis taken as 0.16
for 130I[3] and 0.18 for 130 Te and 130 Xe.
Results and Discussion
1. Yrast Spectra
In fig.1 we present the Comparison of PSM
results with experimental data for yrast spec-
tra obtained for 130Te, 130I, 130Xe. The (2)
and (4) used for 130Te ,130I, 130Xe calcula-
tions are 0.240, 0.299, 0.212 and 0.001.
2. Yrast energy splitting
In fig.2 we present the Comparison of PSM
results with experimental data for energy
splitting for 130I.
3. Backbanding Phenomena
In fig.3 we present the Comparison of PSM
results with experimental data for moment of
inertia (2I) as a function of square of rota-
tional frequency ~ω2for even-even 130Te (up-
per panel), 130 Xe (lower panel). The effect of
backbanding is attributes to deformation.
Acknowledgments
V.Kumar and P.Kumar are highly thankful
to Himachal Pradesh University and UGC for
providing computational facilities and finan-
cial assistance as JRF.
References
[1] K. Hara and Y.Sun, Int. J. Mod. Phys. E4,
637 (1995);
[2] Balraj Singh, Nuclear Data Sheets, 93 33
(2001);
[3] Dhanvir Singh, Anuradha Gupta, Amit
Kumar. Nucl. Phys. A 952 (2016) 41-46
Proceedings of the DAE Symp. on Nucl. Phys. 63 (2018) 263
Available online at www.sympnp.org/proceedings