Delta-hole effects on the shell evolution of neutron-rich exotic nuclei Takaharu Otsuka University of Tokyo / RIKEN / MSU Chiral07 Osaka November , 2007

Outline 1.Motivations : Drip line of oxygen isotopes (as an example) 2. 3-body force : Basically attractive effect 3.  -hole effect on the shell evolution 4. Summary

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

This is because the neutron d 3/2 orbit is high for Oxygen. 16 O core 1d 5/2 2s 1/2 1d 3/2 17 O 9 ~ 22 O O 15 ~ 24 O 16 Neutron orbits in Oxygen isotopes 16 O core Neutron orbits in Fluorine isotopes neutron threshold Tensor-force contribution due to a proton in d 5/2

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

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

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

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

Tensor force d 5/2 d 3/2 Robust under-lying mechanism for the gap change TO et al., Phys. Rev. Lett. 87, (2001) + Phys. Rev. Lett. 95, (2005)

16 O core 1d 5/2 2s 1/2 1d 3/2 17 O 9 ~ 22 O O 15 ~ 24 O 16 Neutron orbits in Oxygen isotopes 16 O core Neutron orbits in Fluorine isotopes neutron threshold Why do those neutrons NOT pull down d 3/2 ? Why do those neutrons NOT pull down d 3/2 ? due to a proton in d 5/2

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

Effective Single-Particle Energy for Oxygen isotopes Less steep USD Kuo-Brown G-matrix + core-pol. d3/2 d5/2 Neutron number (N) narrowing Empirical correction Additional repulsion between d 5/2 and d 3/2 Not enough Neutron number (N) Wrong drip line

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

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

Outline 1.Motivation : Drip line of oxygen isotopes (as an example) 2. 3-body force : Basically attractive effect 3.  -hole effect on the shell evolution 4. Summary

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 2 nd order perturbation

Outline 1.Motivation : Drip line of oxygen isotopes (as an example) 2. 3-body force : Basically attractive effect 3.  -hole effect on the shell evolution 4. Summary

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

Renormalization of NN interaction Due to  excitation in the intermediate state  T=1 attraction between NN effectively

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

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

16 O core 1d 5/2 2s 1/2 1d 3/2 17 O 9 ~ 22 O 14 Neutron orbits in Oxygen isotopes neutron threshold Back to the question of high-lying d 3/2 Central : attractive (generally) Tensor : attractive MeV (next page)  -hole induced repulsion ( > tensor ) Next page

Repulsive effective monopole interaction assuming 16 O core  exchange 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 d 5/2 d 3/2 314 keV Tensor  -hole-induced repulsion d 3/2 single-particle energy relative to N=8 neutron number (N) MeV S.P.E.

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

Suppression of renormalization of NN interaction T=1 interaction between valence particles  Pauli blocking Particle in the inert core included in our results 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)

 -hole excitation may be crucial to neutron matter property Chiral Perturbation incl.  Frisch, Kaiser and Weise

Remark : Multipole interactions … different story  m4m4 m1m1 m2m2 m3m3 Multipole parts  Effective T=1 repulsion for monopole m m m’

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

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

- 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  -hole effects (Fujita-Miyazawa 3N mechanism).  drip line of Oxygen, neutron matter, etc. Both should be considered in mean-field theories. - Explicit treatment of  needed up to the derivation of effective NN interaction (  can be put aside at a later stage)  a message to EFT (power counting may differ between bulk properties (order of magnitude = 100 MeV) and single-particle properties (order of magnitude = 100 keV) ). - Related mechanism in Hypernuclei (Akaishi, Dote, et al.) Summary

Collaborators T. Suzuki Nihon U. Y. Akaishi RIKEN