1. Semi-magic seniority isomers and the effective interactions
Good evening to all!!
The title of my presentation is “atlas of nuclear isomers and the role of seniority”, under the supervision of Prof. A. K. Jain.
Ashok Kumar Jain
Department of Physics
Indian Institute of Technology, Roorkee

2. Outline Atlas of Nuclear Isomers ~2450 Isomers
Seniority isomers: Where and why??
Semi-magic seniority isomers
Similar excitation energy systematics
Similar half-life systematics
Will large scale shell model calculations be able to explain this??
Alignment properties of the intruder orbital
Neutron-rich Sn-isomers beyond 132Sn and the effective interactions
How a small change in TBME changes seniority mixing?
Summary
This is the outline of this seminar.
First of all, I will introduce with the subject, i.e. “nuclear isomers”.
Then about their well known types.
And then will give you a idea about our atlas of isomers which compiles 2450 isomers with a lower limit on the half-life at 10 ns. It is a kind of first one for the same with this lower limit. As many renown data bases don’t maintain that limit. Even the NUBASE-12 has a lower limit of 100ns. We have also studied the various systematics which can reveal may unique and novel features for the isomers.

3. Fission/ Shape K- Spin isomers
First of all I will start from the introduction of subject which questions that what is a nuclear isomer?
A nuclear isomer in which isomer is a greek word which has been made up by two : iso and mer ;
In which iso means equal and mer means parts. It’s a long lived excited nuclear state having half–life greater than a normal excited state of nucleus.
In 1917, Soddy had given the first statement regarding them. He wrote that we have some isotopes with same chemical character but different stabilities and decay modes.

4. To be published in Nuclear Data Sheets
Lower limit of the half-life : 10 ns
Total no. of isomers = 2448
Even-even = 414
Odd- odd = 800
Even-odd = 640
Odd-even = 594
To be published in Nuclear Data Sheets

5. What is seniority?
In the 1940s Racah had introduced the concept in the atomic context. The third of his seminal series contains the first mention of seniority.
It has been adopted in nuclear physics in a similar fashion.
Seniority (v) may be defined as the number of unpaired nucleons.
Particle number independent energy variation.
Constant pairing gap.
Any interaction between identical fermions in single-j shell conserves seniority if j7/2.
The seniority is conserved up to j=11/2 in Sn-isomers after the mid-shell, where the mixing of other orbitals is negligible.

6. Seniority isomers: Where to find and why??
Seniority: number of unpaired nucleons
Semi-magic isomers : good place to find seniority isomers.
E2 transitions between same seniority states vanish, when the valence shell is close to the half-filled.
[Ref: A. De Shalit and I. Talmi, Nuclear Shell Theory (Dover Publications, New York, 1963). ]
C.T. Zhang et al., PRC 62,

7. Why Z=50, N=82 isomers?? Same spin-parity isomers 11/2−, 10+ and 27/2−
Same available valence-space (50-82)
Observed similar kind of systematic
Half-life
Excitation energies
High-j h11/2 orbital plays the dominant role.
Fascinating to explore their structural properties……

8. Calculated and experimental excitation energies for the Z=50 isomers
~ 4 MeV
~ 3 MeV
Energy transition
g7/2, d5/2
h11/2
v=1
v=4, 5
v=2, 3
SN100PN: 0g7/2, 1d5/2, 0h11/2, 1d3/2, and 2s1/2 orbitals [Ref.: B. A. Brown, et al., Phys. Rev. C 71, (2005). ]
Nushell [Ref.: B. A. Brown and W. D. M. Rae, MSU-NSCL report (2007). ]

9. Calculated and experimental excitation energies for the N=82 isomers
~ 4 MeV
~ 3 MeV
Energy transition
To be published.
g7/2, d5/2
v=4, 5
h11/2
v=2, 3
v=1
v=1
SN100PN: 0g7/2, 1d5/2, 0h11/2, 1d3/2, and 2s1/2 orbitals [Ref.: B. A. Brown, et al., Phys. Rev. C 71, (2005). ]

10. Z=50 and N=82 seniority isomers the configuration lists the unpaired neutrons in the respective orbitals.
10+
11/2-
27/2-
Isotope
Seniority
Configuration
102Sn
104Sn
106Sn
108Sn
110Sn
112Sn 2 4
h11/22
g7/22, d5/22
103Sn
105Sn
107Sn
109Sn
111Sn
113Sn 1
h11/21 3 5
h11/23
g7/22, d5/22, h11/21
114Sn
115Sn
10+
11/2-
27/2-
Isotone
Seniority
Configuration
134Te
136Xe
138Ba
140Ce
142Nd
144 Sm 2 4
h11/22
g7/22, d5/22
135I
137Cs
139La
141Pr
143Pm
145Eu 1
h11/21 3 5
h11/23
g7/22, d5/22, h11/21
146Gd
147Tb

11. Single-particle energies
Z=50 isomers
N=82 isomers
h11/2 orbital comes late in the N=82 isomers compared to the Z=50 isomers.
Therefore, the change in the seniority takes place at different neutron/proton numbers in the two chains.

12. Alignment of the h11/2 orbital after the mid-shell
Isotope
Eγ (2+→ 0+)
Eγ (12+→ 10+)
Eγ (15/2-→ 11/2-)
Eγ (31/2-→ 27/2-)
R (15: 2)
R (31: 12)
112 Sn
1.257
113 Sn
1.168
0.9295
114 Sn
1.300
115 Sn
1.312
1.0089
116 Sn
1.294
117 Sn
1.279
0.9887
118 Sn
1.230
1.237
119 Sn
1.220
1.179
0.9921
0.953
120 Sn
1.171
1.190
121 Sn
1.151
1.083
0.9827
0.910
122 Sn
1.141
1.103
123 Sn
1.107
1.043
0.9706
0.946
124 Sn
1.132
1.047
125 Sn
1.088
0.924
0.9614
0.883
Sn-isotopes
Expt.
Isotope
Eγ (2+→ 0+)
Eγ (12+→ 10+)
Eγ (15/2-→ 11/2-)
Eγ (31/2-→ 27/2-)
R (15: 2)
R (31: 12)
114Sn
1.508
0.853
115Sn
1.463
0.782
0.970
0.916
116Sn
0.878
1.12
117Sn
0.889
0.921
1.012
0.822
118Sn
0.988
1.007
119Sn
0.942
1.011
0.953
1.004
120Sn
0.939
0.905
121Sn
0.872
0.871
0.928
0.962
122Sn
0.888
123Sn
0.827
0.841
0.931
1.023
124Sn
1.093
0.937
125Sn
0.994
0.910
0.966
126Sn
128Sn
1.123
1.197
0.919
0.977
127Sn
129Sn
1.014
1.152
0.903
0.948
~1 value
Theo.

13. Similar alignments in the N=82 isotones
146 Gd
2.212
0.994
147 Tb
2.152
0.920
0.972
0.925
148 Dy
1.088
1.293
149 Ho
1.182
1.501
1.086
1.160
150 Er
1.162
1.090
151 Tm
1.067
1.000
0.918
0.917
152 Yb
1.102
0.981
153 Lu
1.006
0.902
0.913
0.919
154 Hf
1.068
0.923
155 Ta
0.974
0.845
0.912
0.915
156 W
1.279
1.035
157 Re
1.135
0.878
0.887
0.848
158 Os
1.002
~1 value
Theo.
On the basis of the similar behavior in the Z=50 and the N=82 chains,
we can make reliable predictions for some new isomers.

14. Z=50 and Z=82 seniority isomers
coming from their respective intruder orbitals
High seniority
i13/2 orbital
f5/2, p3/2, p1/2 and i13/2
low seniority
High seniority
h11/2 orbital
g7/2, d5/2 and h11/2
low seniority
Different intruder orbitals
Mirror experimental energy systematics
Will large scale scale shell model calculations be able to explain this?

15. Large scale shell model calculations
Nushell [Ref.: B. A. Brown and W. D. M. Rae, MSU-NSCL report (2007). ]
SN100PN: 0g7/2, 1d5/2, 0h11/2, 1d3/2, and 2s1/2 orbitals [Ref.: B. A. Brown, et al., Phys. Rev. C 71, (2005). ]
KHHE: 1h9/2, 2f7/2, 1i13/2, 3p3/2, 2f5/2, and 3p1/2 orbitals [Ref.: E. K. Warburton and B. A. Brown, Phys. Rev. C 43, 602 (1991). ]
Our calculations are able to reproduce the experimental systematics quite well except for the fact that the relative gap of the isomeric states is systematically smaller due to the applied truncations for both the chains.
To be published.

16. Neutron-rich seniority isomers beyond 132Sn and the effective interactions
136,138Sn measured for the first time.
Interpretation in terms of v=2 and v=4 seniority mixing.
6+ isomer has been assigned as v=2 isomer.
Simpson et al. PRL 113, (2014)

17. Simpson et al. PRL 113, (2014)
Realistic Vlowk interaction does not reproduce the expt. BE2 value for 136Sn, even when the core excitations are included.
A reduction of diagonal and non-diagonal υf7/22 TBME by 150 keV generates a seniority-mixed 4+ state equivalent to the reduced pairing, and reproduces the expt. data.

18. 6+ isomers in Sn
B. Maheshwari, A. K. Jain and P. C. Srivastava, Phys. Rev. C 91, (2015)

19. How a small change in TBME changes seniority mixing?
If the seniority is conserved then the BE2 should be almost zero at the mid-shell, 136Sn.
Large nonzero value = Seniority mixing
On modifying the interaction , BE2 increases → seniority mixing increases.
Active orbital: f7/2 orbital
RCDBMO: modified RCDB by reducing the diagonal and non-diagonal υf7/22 TBME by 25 keV.

20. Summary
Data of about 2450 isomers with lower limit as 10 ns have been collected and systematized in different ways.
This helps us in understanding many universal and novel features of nuclear isomers.
It is interesting to observe that the semi-magic seniority isomers show identical energy and half-life systematics.
Large scale shell model calculations are able to reproduce the systematics quite well.
Their systematic studies provide a global understanding of the known isomers and predictions of unknown isomers.
The systematic studies in long chain of isomers are also able to shed light on the nature of the effective interactions, particularly in neutron/proton-rich regions.

21. T h a n k s