Semi-magic seniority isomers and

the effective interactions

Ashok Kumar JainDepartment of Physics

Indian Institute of Technology, Roorkee

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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

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Spin isomers

K- isomers

Fission/Shapeisomers

Shape isomers

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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

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What is seniority?

Any interaction between identical fermions in single-j shell conserves seniority if j7/2.The seniority is conserved up to j=11/2 in Sn-isomers after the mid-shell, where the mixing of other orbitals is negligible.

• Particle number independent energy variation.• Constant pairing gap.

• 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.

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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, 057305

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• 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……

Why Z=50, N=82

isomers??

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Calculated and experimental excitation energies for the Z=50 isomers

Nushell [Ref.: B. A. Brown and W. D. M. Rae, Nushell @MSU, 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, 044317 (2005). ]

~ 4 MeV

~ 3 MeV

Energy transition

g7/2, d5/2 h11/2

v=1

v=4, 5v=2, 3

v=1

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Calculated and experimental excitation energies for the N=82 isomers

To be published.

~ 4 MeV~ 3 MeV

Energy transition

g7/2, d5/2 h11/2

v=1

v=4, 5v=2, 3

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, 044317 (2005). ]

0

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Z=50 and N=82 seniority isomersthe configuration lists the unpaired neutrons in the respective orbitals.

10+ 11/2- 27/2-

Isotope Seniority Configuration Isotope Seniority Configuration Seniority Configuration

102Sn104Sn106Sn108Sn110Sn112Sn

244222

h11/22

g7/22, d5/22

g7/22, d5/22

h11/22

h11/22

h11/22

103Sn105Sn107Sn109Sn111Sn113Sn

111111

h11/21

h11/21

h11/21

h11/21

h11/21

h11/21

355553

h11/23

g7/22, d5/22, h11/21

g7/22, d5/22, h11/21

g7/22, d5/22, h11/21

g7/22, d5/22, h11/21

h11/23

114Sn 2 h11/22 115Sn 1 h11/21 3 h11/23

10+ 11/2- 27/2-Isotone Seniority Configuration Isotone Seniority Configuration Seniority Configuration

134Te136Xe138Ba140Ce142Nd144 Sm

244444

h11/22

g7/22, d5/22

g7/22, d5/22

g7/22, d5/22

g7/22, d5/22

g7/22, d5/22

135I137Cs139La141Pr

143Pm145Eu

111111

h11/21

h11/21

h11/21

h11/21

h11/21

h11/21

355555

h11/23

g7/22, d5/22, h11/21

g7/22, d5/22, h11/21

g7/22, d5/22, h11/21

g7/22, d5/22, h11/21

g7/22, d5/22, h11/21

146Gd 2 h11/22 147Tb 1 h11/21 3 h11/23

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Single-particle energies

• 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.

Z=50 isomers

N=82 isomers

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Alignment of the h11/2 orbital after the mid-shellIsotope Eγ (2+→ 0+) Eγ (12+→ 10+) Isotope 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

Isotope Eγ (2+→ 0+) Eγ (12+→

10+)

Isotope 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 0.916116Sn 0.878 1.12 117Sn 0.889 0.921 1.012 0.822118Sn 0.988 1.007 119Sn 0.942 1.011 0.953 1.004120Sn 0.939 0.905 121Sn 0.872 0.871 0.928 0.962122Sn 0.888 0.822 123Sn 0.827 0.841 0.931 1.023124Sn 1.093 0.937 125Sn 0.994 0.905 0.910 0.966126Sn128Sn

1.1231.197

0.9190.977

127Sn129Sn

1.0141.152

0.871 0.9030.962

0.948

Expt.

Theo.

~1 value

Sn-isotopes

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Similar alignments in the N=82 isotones

Isotone Eγ (2+→ 0+) Eγ (12+→ 10+) Isotone Eγ (15/2-→ 11/2-) Eγ (31/2-→ 27/2-) R (15: 2) R (31: 12)

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 1.279 1.002 Theo.

~1 value 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.

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Z=50 and Z=82 seniority isomerscoming from their respective intruder orbitals

i13/2 orbital

h11/2 orbital

High seniority

High seniority

low seniority

low seniorityf5/2, p3/2, p1/2 and i13/2

g7/2, d5/2 and h11/2

Different intruder orbitals Mirror experimental energy systematics Will large scale scale shell model calculations be able to explain this?

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• Nushell [Ref.: B. A. Brown and W. D. M. Rae, Nushell @MSU, 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, 044317 (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.

Large scale shell model calculations

To be published.

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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, 132502 (2014)

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• 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 υf7/2

2 TBME by 150 keV generates a seniority-mixed 4+

state equivalent to the reduced pairing, and reproduces the expt. data.

Simpson et al. PRL 113, 132502 (2014)

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6+ isomers in 134-138Sn

B. Maheshwari, A. K. Jain and P. C. Srivastava, Phys. Rev. C 91, 024321 (2015)

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How a small change in TBME changes seniority mixing?

Large nonzero value = Seniority mixing

If the seniority is conserved then the BE2 should be almost zero at the mid-shell, 136Sn.

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.

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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.

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