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Structure of Neutron-rich Isotopes and Roles of Three-body Forces Toshio Suzuki Nihon University

Structure of Neutron-rich Isotopes and Roles of Three-body Forces Toshio Suzuki Nihon University Trento, July 13, 2011. ○ Shell-model interactions important roles of tensor force need more repulsion in T=1 monopoles need more attraction in T=0 monopoles

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Structure of Neutron-rich Isotopes and Roles of Three-body Forces Toshio Suzuki Nihon University

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  1. Structure of Neutron-rich Isotopes and Roles of Three-body Forces Toshio Suzuki Nihon University Trento, July 13, 2011

  2. ○ Shell-model interactions important roles of tensor force need more repulsion in T=1 monopoles need more attraction in T=0 monopoles 1. Repusive Corrections in T=1 Monopoles and Structure of C isotopes with the use of a ‘phenomenological’ interaction Three-body forces → repulsion 2. ・Structure of O and Ca isotopes and three-body forces ‘G + FM-3N (Δ excitaions by 2π exchanges)’ ・He, Sn isotopes and remaining problems

  3. Repusive Corrections in T=1 Monopoles • and Structure of C isotopes • ・ Important roles of tensor forces • e.g. a new p-shell Hamiltonian: SFO • ・ Need for repulsion in T=1 monopoles • G-matrix vs. phenomenological interactions • ・ Monopole-based-universal interaction (VMU) • ・ Phenomenological shell model interaction for • neutron-rich carbon isotopes: SFO-tls • ・ Structure of C isotopes

  4. New shell model Hamiltonians → success in better description of spin modes in nuclei ● Important roles of tensor force → SFO (p, p-sd) (Suzuki-Fujimoto-Otsuka) ・Shell evolutions ・GT transitions and magnetic moments ● Monopole-based universal interaction (VMU) Monopole terms in Vnn tensor force

  5. SFO p-sd shell Suzuki, Fujimoto, Otsuka, PR C67 (2003) Tensor components Shell evolution in N=8 isotone N=8 N=6 πp3/2

  6. Magnetic moments of p-shell nuclei B(GT) for 12C →12N SFO present = SFOSuzuki, Fujimoto, Otsuka, PR C67 (2003) PR C55, 2078 (1997) Space: up to 2-3 hw SFO*: gAeff/gA=0.95 B(GT: 12C)_cal = experiment Suzuki, Chiba, Yoshida,Kajino, Otsuka, PR C74, 034307, (2006).

  7. ● Tensor force + repulsive corrections in T=1 monopoles → SFO-tls ・Structure of neutron-rich C isotopes ・Exotic M1 transitions in 17C ● 3 body forces induced by Δ excitations → repulsion in T=1 monopoles more repulsion than G in T=1 more attraction than G in T=0

  8. VMU= Monopole based Universal Interaction Tensor: bare≈renormalized 16 Otsuka, Suzuki, Honma, Utsuno, Tsunoda, Tsukiyama, Hjorth-Jensen PRL 104 (2010) 012501 20

  9. Modification of SFO Full inclusion of tensor force ・p-sd: tensor->p+r LS -> s+r+w ・sd: Kuo G-matrix T=1 monopole terms more repulsive → SFO-tls 3=0d3/2 5=0d5/2 1=1s1/2

  10. neutron ESP N dependent en 0.33 0.27 0.22

  11. M1 transitions in 17C Anomalous suppression of B(M1) strength D. Suzuki et al., PL B666 (2008) Suzuki, Otsuka, PR C78 (2008) 061301(R)

  12. 2. Structure of O and Ca isotopes and three-body forces Shell model G-matrix vs. G-matrix + three-body force G = BonnC, CD-Bonn for Ca; 3rd-order Q-box G = Kuo, BonnC, CD-Bonnfor O Hjorth-Jensen, Kuo, Osnes Phys. Rep. 261 (1995) 125. FM (Fujita-Miyazawa)three-body force Δ-excitation by two-pion exchange ・Effective neutron single-particle energies ・Ground state energies ・Ex (2+) ・M1 transition in 48Ca

  13. +3rd-order core-polarization effects Kuo (HJ): 2nd-order, up to 2hw BonnC: 3rd-order, up to 2-4 hw CD-BonnC: 3rd-order, up to 18hw Hjorth-Jensen et al., Phys. Rep. 261, 125 (1995) T. T. S. Kuo, Nucl. Phys. A103, 71 (1967) etc.

  14. j j’j’ j j’ j Monopole terms from 3-body force induced by Δ excitations and short-range terms j j’ j j’ j j’ repulsive

  15. （A） j j’ j’ j j j’ j j’ （B） j j’ Monopole terms from 3-body force induced by Δ excitations j’ j j’ j j’ j j’ j j j’ （C） j’ j j j’ j j’j j’

  16. ● Oxygen isotopes Monopoles for sd-shell: T=1

  17. ESPE of OxygenIsotopes 3N →repulsion

  18. E(2+)

  19. Multipoles vs. monopoles

  20. Energies of O isotopes 3-body force → drip line at 24O Otsuka, Suzuki, Holt, Schwenk, Akaishi, PRL 105, 032501 (2010)

  21. Effects of breaking of 16O core p-sd p, p-sd: SFO sd: G 0hw 2hw 16O 83% 17% 20O 91% 24O 97% 28O 99% How double magic is 24O? Cal: closed (p-d5/2-s1/2） core 87%

  22. ● Ca isotopes Monopoles 3-body force →repulsion

  23. Energies of Ca isotopes

  24. E(2+) 48 3N →Shell closure at 48Ca

  25. Multipoles vs. monopoles

  26. B(M1) +3N (multipole) → concentration of M1 strength EXP.： Steffen et al. NP A404, 413 (1983)

  27. (A/42)-0.35

  28. Energy levels of odd Ca isotopes Important roles of multipole components

  29. ● He isotopes SPE=PKUO p1/2: 3.8282 MeV p3/2: 1.744 MeV (spe) :p3/2: +0.6MeV

  30. New magic at N=76? Erosion of N=64 magic

  31. Remaining Problems • T=0 monopoles Need attractive correction • Microscopic derivation of single-particle energies (J. D. Holt) • Extension of the configuration space sd -> sd+f7/2,p3/2 (J. D. Holt) fp -> fp+g9/2 (J. D. Holt) G-matrix for non-degenerate orbits (Tsunoda) p-sd, sd-pf, pf-g9/2

  32. － － Monopoles for π(AV8’) Core=4He Monopoles in T=0 Higher order terms T=1 T=0 1 : 3x(-3)=-9

  33. Summary • Three-body force can describe well the g.s. energies of O and Ca (and He) isotopes, drip-line at 24O, shell closure at 48Ca, as well as M1 transition strength in 48Ca. • Structure of C isotopes can be well described by an improved Hamiltonian with proper tensor forces and repulsive corrections in T=1 monopoles.

  34. Collaborators T. Otsuka Univ. of Tokyo J. D. Holt ORNL A. Schwenk Darmstadt

  35. 殻模型 H = T + U(r) + Σi>jVij = H0 + V 　　　一体場　+　残留相互作用 U(r) = Uc(r) +ULS(r)L・S 殻模型相互作用 ・Microscopic interaction derived from NN interaction 1. Renormalization of repulsive core part of NN interaction G-matrix: V_{low-k} integrating out high momentum components of two-nucleon interaction sum of ladders

  36. etc. +3rd-order core-polarization effects Hjorth-Jensen et al., Phys. Rep. 261, 125 (1995) Good energy levels except for a few cases: e.g. closed-shell struture of 48Ca can not be obtained Problems in saturation (binding energies) ・Phenomenological interaction single particle energies + fitted two-body matrix elements e.g. p-shell: Cohen-Kurath p-sd: Millener-Kurath sd: USD

  37. ● Oxygen isotopes Monopoles for sd-shell: T=1

  38. ● Oxygen isotopes Monopoles for sd-shell: T=1

  39. ESPE of OxygenIsotopes 3N →repulsion

  40. ESPE of OxygenIsotopes 3N →repulsion

  41. E(2+)

  42. Energies of O isotopes 3-body force → drip line at 24O Otsuka, Suzuki, Holt, Schwenk, Akaishi, PRL 105, 032501 (2010)

  43. Effects of breaking of 16O core p-sd p, p-sd: SFO sd: G 0hw 2hw 16O 83% 17% 18O 87% 20O 91% 22O 95% 24O 97% 26O 98% 28O 99%

  44. Energies of Ca isotopes

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