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Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research...

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Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba (JAEA)
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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.

Cluster states around 16O studied with the shell model

Yutaka UtsunoAdvanced Science Research Center, Japan Atomic energy Agency

―Collaborator―

S. Chiba (JAEA)

Page 2: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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

Page 3: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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?

Page 4: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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

Page 5: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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)

Page 6: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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

Page 7: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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

Page 8: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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.

Page 9: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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.

Page 10: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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.

Page 11: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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)

Page 12: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

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

Page 13: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

Selected levels of 16O

• Rotational band (positive parity) and 1p-1h are well reproduced.

Exp. Calc.

Page 14: Cluster states around 16 O studied with the shell model Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba.

Energy levels of 17O

Exp. Calc.

5p-4h state


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