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Cluster states around 16 O studied with the shell model

Cluster states around 16 O studied with the shell model. Yutaka Utsuno Advanced Science Research Center, Japan Atomic energy Agency ―Collaborator― S. Chiba (JAEA). Introduction. Excited states around 16 O Plenty of a -cluster or multiparticle-multihole states

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Cluster states around 16 O studied with the shell model

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

  2. 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

  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? 16O 6hw? W.C. Haxton and C. Johnson, Phys. Rev. Lett. 65, 1325 (1990).

  4. 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

  5. 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. Sn(17O) Sn(16O) Taken from A. Bohr and B.R. Mottelson, Nuclear Structure vol. 1

  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 15,16,17O • 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

  7. What makes the corr. energy of 16O largest? Component of the wave function (%) PSDWBT interaction 16O 17O sd sd blocked orbit p1/2 p1/2 p3/2 p3/2

  8. 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.

  9. Systematics of the 0+ states • Comparison with the calculation • No excitation across the N=Z=8 gap • Full p-sd calc. with the original gap • 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 16O: only45% • 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. The calculation also predicts that there are many unobserved 1+ states. Exp.) K.A. Snover et al., Phys. Rev. C 27, 1837 (1983).

  11. 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)

  12. 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

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

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

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