cluster states around 16 o studied with the shell model yutaka utsuno advanced science research...
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![Page 1: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba](https://reader033.vdocument.in/reader033/viewer/2022051819/551c55725503469d6a8b4dfd/html5/thumbnails/1.jpg)
Cluster states around 16O studied with the shell model
Yutaka UtsunoAdvanced Science Research Center, Japan Atomic energy Agency
―Collaborator―
S. Chiba (JAEA)
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Introduction• Excited states around 16O
– Plenty of a-cluster or multiparticle-multihole states
• Famous example: 0+2 of 16O located at 6.05 MeV
• Associated with a rotational band (cf. a-gas state)
• Still very difficult to describe with ab initio calculations
• Still difficult to describe with microscopic models
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Previous shell-model studies• Haxton and Johnson (HJ)
– Up to full 4hw states
– Shell gap is determined so as to reproduce the intruder states.
• Warburton, Brown and Millener (WBM)– Model space similar to HJ
– WBT interaction
– In order to reproduce the intruder states, the N=Z=8 shell gap must be narrowed by ~3 MeV from that of the original interaction.
• Can this be justified? → Scope of the present work
• Effect of 6hw and more? W.C. Haxton and C. Johnson, Phys. Rev. Lett. 65, 1325 (1990).
16O
6hw?
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Effect of configurations beyond 4p-4h
• Configurations beyond 4p-4h does not account for the lowering. Any other effect?
0+ of 16O with PSDWBT (in full p-sd shell)
Only ~1 MeV
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Single-particle energy vs. observables
• Usual procedure (Koopmans theorem): SPEs are identified with the energies of the “single-particle states” for 17O and “single-hole states” of 15O measured from the 16O energy. – Correct in the independent-particle limit
– N=Z=8 gap: Sn(16O)-Sn(17O)
– Correlation energy may change Sn’s but not
always does: if the gain in the correlation energy is common, it is cancelled in the expression of separation energy.
Taken from A. Bohr and B.R. Mottelson, Nuclear Structure vol. 1
Sn(16O)
Sn(17O)
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Cross-shell correlation energy
• Cross-shell correlation energy: the energy gained by incorporating the p to sd shell excitation– the same as the usual correlation
energy in 15,16,17O
– Peaked at 16O: 9.4 MeV for 16O, 8.4 MeV for 17O, and for 7.2 MeV 15O
– The 1/2- in 15O has an especially small correlation energy.
– The “experimental shell gap” Sn(16O)-
Sn(17O) increases by 3.2 MeV.
• Need for renormalization of SPE
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What makes the corr. energy of 16O largest?excitation 16O 15O 17Op n0 0 65.9 73.1 68.31 1 23.9 20.1 22.80 2 2.9 1.4 2.52 0 2.9 3.3 3.0
Component of the wave function (%)
blocked orbit
p1/2
p3/2
p1/2
p3/2
16O 17O sdsd
PSDWBT interaction
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Renormalization of SPE
• Energies of 17O(5/2+, 1/2+, 3/2+), 15O(1/2-, 3/2-), 20Ne(0+) and 12C(0+) relative to 16O(0+) are fitted to experiment including correlation energy.
• Seven parameters, SPE’s and overall two-body strengths of p-shell and sd-shell int., are adjusted.
• A much narrower gap is obtained.
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Systematics of the 0+ states
• Comparison with the calculationa. No excitation across the
N=Z=8 gap
b. Full p-sd calc. with the original gap
c. Full p-sd calc. with the reduced gap so as to reproduce the separation energy including correlation
– Missing states are reproduced.
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Breaking of the closure
• Probability of the closure in the ground state of 16O: only 45%– decreased from PSDWBT value 66% due to the narrower shell gap
– Is this reasonable?
• M1 excitation: a good observable to probe the closed shell– No M1 excitations are allowed if 16O were a complete closure.
• 0p-0h state and 2p-2h cannot be connected with a one-body operator.
Experiment CalculationEx. (MeV) B(M1)↑ n-th T Ex. (MeV) B(M1)↑
16.22 0.225(30) 4 1 16.40 0.076
17.14 0.348(51) 7 1 17.46 0.352
18.8 0.129(30) 13 1 18.90 0.208
Exp.) K.A. Snover et al., Phys. Rev. C 27, 1837 (1983).
The calculation also predicts that there are many unobserved1+ states.
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The case of a j-j closure 56Ni• Correlation energy is the
smallest at the core.
• Difference from the L-S closure: parity– Odd-particle excitation is allowed.
– Deformation (in 52Fe)
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Summary
• Cluster (or multiparticle-multihole) states around 16O are investigated with the full p-sd shell-model calculation.
• Correlation energy is peaked at 16O, which works to decrease the bare shell gap from the “observed” shell gap.
• As a result, excited states are pulled down to a right position.
• Large core breaking associated with the narrow gap is supported by strong M1 excitations from the ground state.
• Perspectives: 40Ca– impossible to perform a conventional shell-model calculation with a 1015
m-scheme dimension
– use of the Monte Carlo shell model: see Shimizu’s seminar tomorrow for recent progress
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Selected levels of 16O
• Rotational band (positive parity) and 1p-1h are well reproduced.
Exp. Calc.
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Energy levels of 17O
Exp. Calc.
5p-4h state