1. Systematic study of the many- particle and many-hole states in and around the Island of Inversion - #N=Odd system - M. Kimura(Hokkaido)

2. Introduction: Island of Inversion Island of Inversion: N ～ 20 Ne, Na, Mg isotopes Topics: large deformation, mpmh config., shell gap quench N=21 isotone: 31 Ne(binding limit), 33 Mg Topics: spin-parity, p-wave halo, neutron orbital N=21 isotone Odd-mass(neutron) system reveals neutron-orbital, shape coexistence in the Island The last neutron particle (hole) orbital has strong influence on nuclear properties In N=21 isotone, 0f 7/2 and 0d 3/2 orbials take part in the game Island of Inversion

3. Theoretical Framework: AMD A-body Hamiltonian Parity projected Slater determinant Single particle wave packets Variational parameters Gogny D1S

4. Theoretical Framework: AMD Angular momentum projection GCM Generator Coordinate: quadrupole deformation  Hill-Wheeler eq.

5. Energy curves in and around the Island ph configuration depends on neutron # Relative energy between ph states depends on the proton number The Island

6. Spectrum of 32 Mg V. Tripathi, et. al., PRC77034310(2008).

7. Results: 0 + and 2 + states (N=20 isotones) Strongly deformed 2p2h takes over the ground state Note that 0p0h, 2p2h and 4p4h appear in the Island 4p4h (more deformed) also participates in. Some experimental evidences

8. Results: 0 + and 2 + states (Z=10,12 isotopes) 2p2h dominates in N=20, 22 system 4p4h (4h  )appears only in N=20 isotopes Intermediate character of N=18 isotopes Precursor in N=18 system

9. Results: 1 - and 3 - states (N=20 isotones) Great reduction of 3p3h energy 1p1h is not so sensitive to the proton number

10. Results: 1 - and 3 - states (Z=10,12 isotopes) Great reduction of 1h  excitation energy Due to the reduction, de-excitation is also possible in the island Precursor in N=18 system

11. Introduction: Particle Hole Config. (N=19 System) 1p-removal from 32 Al D. Miller, et.al.,Phys. Rev. C 79, 054306 (2009) 31 Mg 0p1h 1p2h 2p3h 3p4h M. K. Phys.Rev. C 75, 041302 (2007)

12. J     -decays 33 Na(N=22,g.s.) → 33 Mg(g.s.) 33 Mg(g.s.) → 33 Al(N=20, g.s.) J    magnetic-moment:  =-0.7456  N 1n-removal: p 3/2 S. Nummela, et. al., PRC64, 054313 (2001) V. Tripathi, et. al., PRL101,142504 (2008) D. T. Yordarov, et. al., PRL99, 212501 (2007) R. Kanungo, et. Al., PLB685, 253 (2010) Introduction: Spin-parity of 33 Mg(N=21)

13. Introduction: 1n Halo of 31 Ne(N=21) 1n-Removal Exp. : Large cross section : Observed large cross section can be explained with small Sn and l=1,2 Large Reaction cross section M. Takechi, et. al., Nucl. Phys. A 834, (2010), 412 T. Nakamura, et. al., PRL103, 262501 (2009) Halo?

14. Results: Energy Curve and PH Config. of 33 Mg 33 Mg 1p0h 2p1h3p2h 4p3h 2p1h1p0h3p2h4p3h

15. Introduction: Particle Hole Config. (N=21 System) 33 Mg 1p0h 2p1h 3p2h 4p3h

16. Results: Spectrum of 33 Mg Consistent with magnetic moment exp. AMD underestimates number of very low-lying states Sn=3.2MeV

17. Results:  -decay and J  assignment 33 Na(4p2h) feeds 4p3h config. 33 Na(4p2h) 33 Mg*(4p3h)

18. Results: B(E2) of 33 Mg Coulomb Excitation Exp. : B.V. Pritychenko, et. al., PRC65, 061304(R) (2002). Large cross section for 485keV state Authors assumed J  =5/2+ for the ground state (no information was available at that time except for  -decay data that suggested positive parity) Large cross section does not contradict to AMD (Further exp. is required.)

19. Results: Spectrum of 31 Ne Sn=250keV Same J  with 33 Mg, but much smaller Sn 3/2+ is almost degenerated (Ex=120keV)

20. Summary and Plan Summary 33 Mg has negative-parity ground state with J=3/2 AMD agrees with magnetic moment and COULEX experiments, but contradict to  -decay  -decay of 33 Na should feeds 4p3h config. of 33 Mg 31 Ne also has negative-parity ground state with J=3/2 and very small Sn. J=3/2- is almost degenerated. Plans Small Sn, but no Halo ! (fault of AMD, RGM calc. to see it) p-n interaction dependence of level-ordering