118
Proceedings of the DAE-BRNS Symp. on Nucl. Phys. 61 (2016)
Shape Coexistence and bubble structure in Iodine isotopes
Afaque Karim1∗ and Shakeb Ahmad2†
1
Department Of Physics, Aligarh Muslim University, Aligarh-202002,INDIA and
2
Physics section, Women’s College, Aligarh Muslim University, Aligarh-202002,INDIA
∆E(MeV)
Nuclear shape coexistence is one of the very
peculiar phenomenon studied in various mass
regions of the periodic table. Nuclei with two
different shapes within a very narrow energy
range, i.e shape coexistence is an important
challenge for theoreticians as well as experimentalists. A reliable work both theoretical
and experimental has been done for studying
the coexistence of different shapes by different
researchers [1, 2]. The other interesting investigation is bubble structure in atomic nuclei.
The bubble structure is characterized by a depletion of central density in nuclei. In 1940s,
Wilson [3] started the poineering work of bubble structure studies. Now a days, bubbles are
studied in various light, medium, heavy and superheavy nuclei [2–4].
In the present work, isotopes of iodine
(Z=53, N=122-133) has been chosen for study20
18
16
14
12
10
8
6
4
2
0
20
18
16
14
12
10
8
6
4
2
0
-0.6
123
124
I
I
DD-ME1
DD-ME2
DD-PC1
NL3*
125
126
I
I
∆E(MeV)
Introduction
20
18
16
14
12
10
8
6
4
2
0
20
18
16
14
12
10
8
6
4
2
0
-0.6
127
I
128
I
DD-ME1
DD-ME2
DD-PC1
NL3*
129
-0.4
-0.2
0
0.2
130
I
0.4
0.6
-0.6
β2
FIG. 2: PES of
-0.4
-0.2
127−130
0
0.2
I
0.4
0.6
I
ing shape coexistence and bubble structure as
it has been the focal point for large number of experimental studies. We have studied the ground state as well as intrinsic excited state using covariant density functional
theory(CDFT) [5] with different interactions
(DD-ME1, DD-ME2, DD-PC1, NL3*). The
theoretical formalism for CDFT are presented
in Ref. [5]. We have also studied the other
ground state properties like rms radii, charge
radius, quadruple deformation, pairing energy
which are not presented in this paper.
Result and Discussion
A. Shape Coexistence
-0.4
-0.2
0
0.2
0.4
0.6
-0.6
β2
FIG. 1: PES of
∗ Electronic
† Electronic
-0.4
-0.2
123−126
0
I.
address: [email protected]
address: [email protected]
0.2
0.4
0.6
The constraint calculation to obatin potential
energy surface(PES) is done for 123−133 I nuclei. The PES of 123−133 I nuclei presented here
clearly demarcates the shape coexistence behaviour. From PES, it is clear that Iodine isotopes bear two different shapes (i.e. oblate and
prolate) with slight variation in energy.Thus,
one can infer that nucleus can oscillate from
one state to another state by perturbing small
energy. In addition to this, the difference of the
Available online at www.sympnp.org/proceedings
119
0.17
131
132
I
I
0.16
0.15
0.14
123
I
I
I
126
I
127
I
128
I
129
I
130
I
131
I
132
I
132
I
0.13
124
0.12
125
0.11
0.1
-3
22
20
18
16
14
12
10
8
6
4
2
0
22
20
18
16
14
12
10
8
6
4
2
0
-0.6
ρ(r)(fm )
∆E(MeV)
Proceedings of the DAE-BRNS Symp. on Nucl. Phys. 61 (2016)
133
0.09
0.08
0.07
I
0.06
NL3*
DD-ME1
DD-ME2
DD-PC1
0.05
0.04
0.03
0.02
0.01
0
-0.4
-0.2
0
0.2
0.4
0
0.6
β2
FIG. 3: PES of
0.2
0.4
131−133
0.6
0.8
0
1
2
3
4
5
6
7
8
9
10
11
12
13
1
I
FIG. 5: Total density plot of
RMF(NL3*).
123−133
I using
1.2
Conclusion
1.1
1
B.Eg.s(MeV)-B.Ef.e.s(MeV)
0.9
0.8
DD-ME1
DD-ME2
DD-PC1
NL3*
0.7
0.6
The studies based on CDFT using different
interactions predicts the shape coexistence and
bubble structure in 123−133 I nuclei which is
confirmed by different investigations.
0.5
0.4
TABLE I: Depletion factor(in %) for proton,neutron and total nucleon matter.
0.1
Nuclei (D.F )proton (D.F )neutron (D.F )T otal
0
123
I
17.77
9.06
12.18
122
123
124
127
128
129
130
131
132
133
134
125
126
A
124
I
24.04
10.56
20.80
125
I
24.35
12.90
20.86
123−133
FIG. 4: B.E(g.s)-B.E(f.e.s) for
I.
126
I
24.65
15.60
19.38
127
I
24.60
13.86
18.25
128
I
24.13
8.92
15.84
BE(g.s) and BE(f.e.s)(which is ≤ 1 MeV for
129
I
23.17
7.04
13.64
130
all interactions) have been presented in Fig.4
I
21.84
5.21
10.95
131
which also supports the shape coexistence pheI
20.82
4.19
8.80
132
nomenon in iodine isotopes.
I
19.03
3.44
8.31
133
18.62
2.52
7.62
I
0.3
0.2
B. Bubble Structure
We have obtained the neutron, proton and
total density of iodine isotopes using different
interaction but presented only total density obtained using NL3* interaction. From Fig. 5,
one can observe the depletion of central density
which indicates the bubble structure in iodine
isotopes. For quantitative understanding, we
have also calculated Depletion Factor(D.F)(For
expression See Ref. [2]) which is listed in Table
1. From the table 1, it is clear that nuclei posses
bubble structure in their intrinsic states.
References
[1] F. Sarazin et al., Phys. Rev. Lett. 84 (2000)
5062.
[2] S. K. Singh et al., IJMPE 22 (2013)
1350001.
[3] H. A. Wilson, Phys. Rev. C69 (1946) 538.
[4] M. Grasso et al., Phys. Rev. C79 (2009)
034318.
[5] T. Niks̆ić et al., Comp. Phys. Comm. 185,
1808 (2014).
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