Cluster states around 16O studied with the shell model

Yutaka UtsunoAdvanced Science Research Center, Japan Atomic energy Agency

―Collaborator―

S. Chiba (JAEA)

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

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?

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

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)

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

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

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.

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.

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.

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)

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

Selected levels of 16O

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

Exp. Calc.

Energy levels of 17O

Exp. Calc.

5p-4h state