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

2. Introduction Excited states around 16 O – Plenty of  -cluster or multiparticle-multihole states Famous example: 0 + 2 of 16 O located at 6.05 MeV Associated with a rotational band (cf.  -gas state) Still very difficult to describe with ab initio calculations Still difficult to describe with microscopic models

3. 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). 16 O 6hw?

4. Effect of configurations beyond 4p-4h Configurations beyond 4p-4h does not account for the lowering. Any other effect? 0 + of 16 O with PSDWBT (in full p-sd shell) Only ~1 MeV

5. Single-particle energy vs. observables Usual procedure (Koopmans theorem): SPEs are identified with the energies of the “single-particle states” for 17 O and “single-hole states” of 15 O measured from the 16 O energy. – Correct in the independent-particle limit – N=Z=8 gap: S n ( 16 O)-S n ( 17 O) – Correlation energy may change S n ’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 S n ( 16 O) S n ( 17 O)

6. 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 15,16,17 O – Peaked at 16 O: 9.4 MeV for 16 O, 8.4 MeV for 17 O, and for 7.2 MeV 15 O – The 1/2 - in 15 O has an especially small correlation energy. – The “experimental shell gap” S n ( 16 O)- S n ( 17 O) increases by 3.2 MeV. Need for renormalization of SPE

7. What makes the corr. energy of 16 O largest? excitation 16 O 15 O 17 O pn 0065.973.168.3 1123.920.122.8 022.91.42.5 202.93.33.0 Component of the wave function (%) blocked orbit p 1/2 p 3/2 p 1/2 p 3/2 16 O 17 O sd PSDWBT interaction

8. Renormalization of SPE Energies of 17 O(5/2 +, 1/2 +, 3/2 + ), 15 O(1/2 -, 3/2 - ), 20 Ne(0 + ) and 12 C(0 + ) relative to 16 O(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.

9. Systematics of the 0 + states Comparison with the calculation a.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.

10. Breaking of the closure Probability of the closure in the ground state of 16 O: 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 16 O were a complete closure. 0p-0h state and 2p-2h cannot be connected with a one-body operator. ExperimentCalculation Ex. (MeV)B(M1)↑n-thTEx. (MeV)B(M1)↑ 16.220.225(30)4116.400.076 17.140.348(51)7117.460.352 18.80.129(30)13118.900.208 Exp.) K.A. Snover et al., Phys. Rev. C 27, 1837 (1983). The calculation also predicts that there are many unobserved 1 + states.

11. The case of a j-j closure 56 Ni Correlation energy is the smallest at the core. Difference from the L-S closure: parity – Odd-particle excitation is allowed. – Deformation (in 52 Fe)

12. Summary Cluster (or multiparticle-multihole) states around 16 O are investigated with the full p-sd shell-model calculation. Correlation energy is peaked at 16 O, 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: 40 Ca – impossible to perform a conventional shell-model calculation with a 10 15 m-scheme dimension – use of the Monte Carlo shell model: see Shimizu’s seminar tomorrow for recent progress

13. Selected levels of 16 O Rotational band (positive parity) and 1p-1h are well reproduced. Exp.Calc.

14. Energy levels of 17 O Exp. Calc. 5p-4h state