Shell evolution with tensor and three-body forces

1. Shell evolution with tensor and three-body forces Takaharu Otsuka University of Tokyo / MSU 11th International Conference on Nucleus-Nucleus Collision San Antonio, Texas May 30 (27-June 1), 2012

2. Outline An overview of the evolution of shell structure in exotic nuclei with large asymmetry in N/Z Tensor force : robust effect & persistency 3-body force with D-excitation origin : robust and unique effect effect of continuum how large ? does it maintain features of nuclear forces ?

3. Monopole component of tensor force TO, Suzuki, et al. PRL 95, 232502 - An intuitive picture - At collision point: k1 k2 k = k1 – k2 , K= k1 + k2 k1 k2 large relative momentum k small relative momentum k strong damping loose damping k1 k2 wave function of relative coordinate wave function of relative coordinate k2 k1

4. Response to the renormalization of interactions bare interaction for free space Renormalization processes - short-range correlations - in-medium corrections V = Vc + V LS + VT effective interaction for a model space V’ = V’c + V’ LS + V’T + VNNN + … In general, V’x differs from Vx. If Vx = V’x, Renormalization Persistency holds. • only good approx. at best, but it makes sense • new approach to nuclear forces

5. Treatment of tensor force by V low k and Q box (3rd order) Monopole component of tensor interactions in pf shell Bare(AV8’) short-range correlation by V low k in-medium correction with intermediate states (> 10 hw, 3rd order) V low k : Bogner, Kuo, Schwenk only for comparison TO, Suzuki, et al. PRL 104, 012501 (2010)

6. Two major components in nuclear force + … monopole component of tensor force in nuclear medium Renormalization Persistency almost equal(no renormalization) monopole component of tensor force in free space N.Tsunoda, T.O., K.Tsukiyama, M.H.-Jensen, PRC84,044322 (2011)

7. Shell evolution in exotic nuclei due to tensor + central forces  proton-neutron correlation Changes of single-particle properties due to these nuclear forces

8. p3/2 Otsuka, Suzuki and Utsuno, Nucl. Phys. A805, 127c (2008) exp. N =28 (4+)： RIBF data 2011 f7/2 d3/2 doubly magic ? neutron s1/2 Z =14 d5/2 repulsive 4214Si28 proton attractive Potential Energy Surface full 42Si Tensor force removed from cross-shell interaction Strong oblate Deformation 42Si 2+: Bastin, Grévy et al., PRL 99 (2007) 022503 Other calculations (RMF, Gogny) show oblate shape.

9. w/o tensor force PES of 42Si Tensor force included (as global VMU) oblate with tensor force 42Si spherical prolate

10. d3/2 Spectroscopic factors obtained by (e,e’p) on 48Ca (Kramer et al., NP A679, 267 (2001) NIKHEF) s1/2 d5/2 no tensor in the cross shell part with the same tensor force Exp. Exp. Th. Th.

11. Why is the drip line of Oxygen so near ? Nuclear Chart - Left Lower Part - next issue  oxygen anomaly and continuum v.s. its restoration in fluorine Proton number  Neutron number 

12. Single-Particle Energy for Oxygen isotopes by phenomenological eff. int. by microscopic eff. int. - G-matrix + fit - G-matrix+ core-pol. : Kuo, Brown Utsuno, O., Mizusaki, Honma, Phys. Rev. C 60, 054315 (1999) SDPF-M Vlow-k : Bogner, Kuo, Schwenk Brown and Richter, Phys. Rev. C 74, 034315 (2006) USD-B trend trend

13. The clue : Fujita-Miyazawa 3N mechanism (D-hole excitation) p D particle m=1232 MeV S=3/2, I=3/2 D p N N N

14. Most important message with Fujita-Miyazawa 3NF m’ m Effective monopole repulsive interaction m + D m’ D m m’ m’ m m D Pauli blocking Renormalization of single particle energy same m’ m Monopole part of Fujita-Miyazawa 3-body force

15. Ground-state energies of oxygen isotopes NN force + 3N-induced NN force (Fujita-Miyazawa force) Drip line

16. (i) D-hole excitation in a conventional way • EFT with D D-hole dominant role in determining oxygen drip line (iii) EFT incl. contact terms (N2LO) continuum

17. Continuum-coupled shell model (CCSM) Hamiltonian : approximated by Gaussian basis state-vector (denoted by j ): bound states + discretized continuum states included wall very far (3000 fm, ~3000 basis states) d3/2 r VNN + V s1/2

18. 240 = 220 + 2n in the space ground state : 2n in 1s1/2 excited states of 1+ and 2+ : 1s1/2 : solution of Woods-Saxon potential with observed Sn diagonalize H Eigenfunction :

19. RMS Radius: 16-24O Woods-Saxon s1/2 Harmonic Oscillator d5/2 Exp: Ozawa et al., Nucl. Phys. A693, 32 (2001) Kanungo et al., Phys. Rev. C84, 061304 (2011)

20. Removal of one proton and one neutron from 26F knockout reaction @MSU (2009) 9Be(26F,24O)X less probable <== large s1/2-d3/2 neutron gap C. Hoffman, M. Thoennessen et al. continuum H.O. -p -n 16O 16O 16O 16O 16O bound nucleus 26F doorway state excited states in 24O ground state 1s1/2 is bound. Kanungo et al. (2009)

21. Low-lying Continuum Spectra in 24O Doorway state ==> continuum states in 24O 24O,1+ exp • bound approximation:Normal shell model with the same Hamiltonian : NO continuum effect • CCSM : With continuum effect • incl. residual interaction • no int. : With continuum effect but • no residual interaction. 24O, 2+ 25O, 3/2+ • Continuum effect is about 1 MeV • No bound excited state. • 1+-2+ splitting by 2-body interaction • 1+-2+ splitting is in good agreement • with experiments.

22. Summary of the results

23. Peak Energies of neutron emission SPE as bound state 2 MeV Exp.　：MSU(Hoffman et al), RIKEN(Elekes et al) Lowering due to continuum effect Continuum spectra are consistent with the shell evolution

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25. Neutron single-particle energies at N=20 for Z=8~20 dashed line : central only solid line : full (central + tensor) 20 14 8 16 A proton in d5/2 moves neutron orbits by 20 d3/2 -2.0 MeV 16 s1/2 -1.1 MeV energy (MeV) d5/2 -1.6 MeV 40Ca 29F well bound already by s.p. e. F d5/2 s1/2 d3/2 31,…F bound through mixing with pf shell Z TO, Suzuki, et al. PRL 104, 012501 (2010)

26. Holt, TO, Schwenk, Suzuki, submitted Ca ground-state energy experiment extrapolation NN + 3NF NN only

27. Summary • Shell structure of exotic nuclei changes (or evolves), even in novel • manners some times, due to particular components of nuclear forces •  Mayer-Jensen’s magic numbers disappear and new ones arise • Tensor force : changes spin-orbit splitting • - proton-neutron interaction • - in-medium~bare under the concept Renormalization Persistency • -> many cases from p-shell to superheavy • -> 42Si (Bastin, Grévy, et al. 2007 GANIL, Takeuchi et al. 2011-12 RIKEN) • oblate shape rather than spherical sub-magic of Z=14 and N=28 • Fujita-Miyazawa 3-body force produces repulsive effective interactionbetween valence neutrons in general. • -> oxygen drip line at N=16, similar situations e.g. in Ca isotopes • -> contributes to shell evolution • Continuum effect sizable even for d3/2 (~ 1 MeV shift for oxygen) • shell evolution in continuum … visible and interesting in future • transfer reactions with RI beams are useful

28. Collaborators • N. Tsunoda Tokyo • Tsukiyama Tokyo • M. H.-Jensen Oslo • T. Suzuki Nihon U. • M. Honma Aizu • Y. Utsuno JAEA • B.A. Brown MSU • SchwenkDarmstadt • Holt Oak Ridge • Akaishi RIKEN R. Fujimoto Hitachi (work @Tokyo)