semi-magic seniority isomers and the effective interactions ashok kumar jain department of physics...
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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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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.