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Delta-hole effects on the shell evolution of neutron-rich exotic nuclei

Chiral07 Osaka November 12 - 16, 2007. Delta-hole effects on the shell evolution of neutron-rich exotic nuclei. Takaharu Otsuka University of Tokyo / RIKEN / MSU. Outline. Motivations : Drip line of oxygen isotopes (as an example).

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Delta-hole effects on the shell evolution of neutron-rich exotic nuclei

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  1. Chiral07 Osaka November 12 - 16, 2007 Delta-hole effects onthe shell evolutionof neutron-rich exotic nuclei Takaharu OtsukaUniversity of Tokyo / RIKEN / MSU

  2. Outline • Motivations: Drip line of oxygen isotopes • (as an example) 2. 3-body force : Basically attractive effect 3. D-hole effect on the shell evolution 4. Summary

  3. nuclei (mass number) stable exotic -- with halo A Proton number  Neutron number  Stable Nuclei Nuclear Chart - Left Lower Part - proton halo F (Z=9) O (Z=8) Why is the drip line of Oxygen so near ? Drip Line (Existence Limit of Nuclei) 11Li リチウム１１ neutron halo neutron skin

  4. This is because the neutron d3/2 orbit is high for Oxygen. Neutron orbits in Fluorineisotopes Neutron orbits inOxygenisotopes 1d3/2 neutron threshold 23O15 ~ 24O16 2s1/2 Tensor-force contribution due to a proton in d5/2 17O9 ~ 22O14 1d5/2 16O core 16O core

  5. A reminder of tensor-force effects on the evolution of shell structure One pion exchange ~ Tensor force

  6. To see changes of single-particle energies within the shell model, the monopole interaction is useful • Monopole part of the NN interaction • Angular averaged interaction Isotropic component is extracted froma general interaction.

  7. Effective single-particle energy (ESPE) ESPE is changed by Nvm Monopole interaction, vm N particles ESPE : Total effect on single-particle energies due to interaction with other valence nucleons

  8. Monopole effects due to the tensor force - An intuitive picture - wave function of relative motion spin of nucleon large relative momentum small relative momentum repulsive attractive j> = l + ½, j< = l – ½ TO et al., Phys. Rev. Lett. 95, 232502 (2005)

  9. Robust under-lying mechanism for the gap change d3/2 Tensor force d5/2 TO et al., Phys. Rev. Lett. 87, 082502 (2001) + Phys. Rev. Lett. 95, 232502 (2005)

  10. Neutron orbits in Fluorineisotopes Neutron orbits inOxygenisotopes 1d3/2 neutron threshold 23O15 ~ 24O16 2s1/2 due to a proton in d5/2 17O9 ~ 22O14 1d5/2 Why do those neutrons NOT pull down d3/2 ? 16O core 16O core

  11. Kuo-Brown G-matrix + core-pol. d3/2 d5/2 5 10 15 20 Neutron number (N) Wrong drip line Effective Single-Particle Energy for Oxygen isotopes narrowing

  12. Effective Single-Particle Energy for Oxygen isotopes Kuo-Brown G-matrix + core-pol. Empirical correction USD Less steep d3/2 d5/2 5 10 15 20 5 10 15 20 Neutron number (N) Neutron number (N) Additional repulsion between d5/2 and d3/2 Wrong drip line Not enough narrowing

  13. Effective Single-Particle Energy for Oxygen isotopes Kuo-Brown G-matrix + core-pol. Empirical correction Final correction SDPF-M USD Less steep d3/2 d5/2 5 10 15 20 Neutron number (N) Neutron number (N) Finally flat, d3/2 kept high  correct drip line Neutron number (N) Y. Utsuno, T.O., T. Mizusaki, and M. Honma, Phys. Rev. C 60, 054315 (1999). narrowing

  14. A solution within 2-body interaction is very unlikely (more systematic studies for pf shell)  3-body interaction Question What is the origin of the repulsive modification to T=1 monopole matrix elements ?

  15. Outline • Motivation : Drip line of oxygen isotopes • (as an example) 2. 3-body force : Basically attractive effect 3. D-hole effect on the shell evolution 4. Summary

  16. Nucleons in valence orbits (of low momenta) Nucleons in higher shell (of high momenta) Nucleons in valence orbits (of low momenta) 3N force with short range produces basically more attraction from the 2nd order perturbation

  17. Outline • Motivation : Drip line of oxygen isotopes • (as an example) 2. 3-body force : Basically attractive effect 3. D-hole effect on the shell evolution 4. Summary

  18. D-hole excitation (Fujita-Miyazawa 3N mechanism) is the key. Oset, Tokiand Weise Pionic modes of excitation Phys. Rep. 83, 281 (1982)

  19. D Renormalization of NNinteraction Due to D excitation in the intermediate state T=1 attraction between NN effectively

  20. D D-hole excitation effect on single-particle energy and Pauli blocking m m m’ m’ m’ D D m m Pauli Forbidden D-hole contribution to single-particle energies is suppressed T=1 attraction in NN interaction Renormalization of single particle energy due to core polarization (attractive !)

  21. Possible origin of global T=1 repulsion m m’ m D m’ m’ D m m’ m Pauli forbidden (from previous page) Effective T=1repulsion for monopole Relevant mechanism in Hypernuclei (Akaishi’s talk) • This involves D excitation • from the core • density-dependent • long-ranged effect

  22. Back to the question of high-lying d3/2 Neutron orbits inOxygenisotopes Central : attractive (generally) 1d3/2 neutron threshold Tensor : attractive - 0.9 MeV (next page) 2s1/2 17O9 ~ 22O14 1d5/2 D-hole induced repulsion ( > tensor ) Next page 16O core

  23. Repulsive effective monopole interaction assuming 16O core pexchange with radial cut-off at 0.7 fm , ΔE =293 MeV f_{πNΔ｝/f_{πNN} = \sqrt{9/2} Preliminary result Monopole interaction j j' pion tensor d5/2 d3/2 314 keV d3/2 single-particle energy relative to N=8 +1 MeV S.P.E. neutron number (N) 8 14 D-hole-induced repulsion Tensor

  24. N  D If another nucleon (X) is in state m’and wave functions are coupled antisymmetric (T=1), the effect is vanished.  Repulsive T=1 force Density dependent repulsive force in T=1 channel - Long-ranged due to p exchange - m’ p m p No changes to T=0 monopole interaction

  25. D Suppression of renormalization of NNinteraction included in our results Pauli blocking Related effect was discussed by Frisch, Kaiser and Weise for neutron matter (see next page). See also Nishizaki, Takatsuka and Hiura PTP 92, 93 (1994) Particle in the inert core T=1 interaction between valence particles

  26. D-hole excitation may be crucial to neutron matter property Chiral Perturbation incl. D : Frisch, Kaiser and Weise

  27. m3 m4 D m1 m2 Multipole parts Remark : Multipole interactions …different story m m’ D m m’ Effective T=1repulsion for monopole

  28. D T=1 attraction between NN effectively Effective point coupling ; The present effect cannot be seen. Explicit consideration of D has been crucial

  29. Modifications to effective NN interaction in the valence shell - monopole channel - D T=1 repulsion Likely T=0 attraction Similar magnitudes of opposite sign

  30. Summary • - Pions manifest themselves in the shell structure of exotic nuclei • i) Tensor force changes the shell structure, including • disappearance of magic numbers and appearance of new ones • ii) Repulsive modification to T=1 channel • due to suppression of D-hole effects (Fujita-Miyazawa 3N mechanism).  drip line of Oxygen, neutron matter, etc. • Both should be considered in mean-field theories. • - Explicit treatment of D needed up to the derivation of • effective NN interaction(D can be put aside at a later stage) •  a message to EFT (power counting may differ between • bulkproperties (order of magnitude = 100 MeV) and • single-particle properties (order of magnitude = 100 keV) ). • Related mechanism in Hypernuclei (Akaishi, Dote, et al.)

  31. Collaborators T. Suzuki Nihon U. Y. Akaishi RIKEN

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