Tensor optimized shell model and role of pion in finite nuclei

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Presentation transcript:

Tensor optimized shell model and role of pion in finite nuclei Hiroshi Toki (RCNP/Osaka) In collaboration with Takayuki Myo (Osaka Inst. of Tech.) Kiyomi Ikeda (RIKEN) 09.2.20 toki@seoul

Variational calculation of light nuclei with NN interaction VMC+GFMC VNNN Fujita-Miyazawa C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001) Relativistic We want to calculate heavy nuclei!! 09.2.20 toki@seoul Pion is a key element

General feature of nucleon-nucleon interaction Strong tensor interaction (pion: chiral symmetry) Strong short range repulsion (quark: confinement) Deuteron wave function V 1fm r Strong short range repulsion (Quark structure) s d -50 (MeV) Strong tensor interaction (Pion exchange) 09.2.20 toki@seoul Central dip and D-wave component

If we treat tensor interaction Pion exchange interaction vs. Tensor interaction Pion is a peudoscalar meson (0-)---spin interaction Tensor interaction (high momentum) Delta interaction (short range correlation) Yukawa interaction (low momentum) If we treat tensor interaction we can treat pion 09.2.20 toki@seoul

The property of tensor interaction Centrifugal potential (800MeV@0.5fm) pushes away the L=2 wave function 09.2.20 toki@seoul

Tensor optimized shell model (TOSM) Ground state is obtained by shell model (HF method) Treat tensor interaction explicitly using 2p-2h wave functions (3p-3h, 4p-4h are checked small) The point of success of TOSM is the tensor interaction being of intermediate range 09.2.20 toki@seoul

Tensor optimized shell model Myo, Toki, Ikeda, Kato, Sugimoto, PTP 117 (2006) 0p-0h + 2p-2h (size parameter) Energy variation Gc 09.2.20 toki@seoul

Convergence of tensor correlation Higher L states 4 Gaussian functions 09.2.20 toki@seoul We can completely treat the tensor correlations

5He and spin-orbit splitting due to tensor interaction Myo, Kato, Ikeda, PTP 113 (2005) 09.2.20 toki@seoul

Tensor correlations provide suitable amount of spin-orbit effect Phase shifts in 4He+n Tensor correlations provide suitable amount of spin-orbit effect 09.2.20 toki@seoul

Unitary Correlation Operator Method (UCOM) short-range correlator Bare Hamiltonian Shift operator depending on the relative distance r H. Feldmeier, T. Neff, R. Roth, J. Schnack, NPA632(1998)61 09.2.20 toki@seoul

Short-range correlator : C H. Feldmeier, T. Neff et. al Short-range correlator : C H. Feldmeier, T. Neff et.al., NPA632(1998)61 Hamiltonian in UCOM 2-body approximation in the cluster expansion of operator 09.2.20 toki@seoul

Form of R+ in UCOM Afnan-Tang : central only Function form given by Feldmeier reproducing deuteron wave function 09.2.20 toki@seoul

4He with UCOM 09.2.20 toki@seoul

Correlation Function and Charge form factor (0s)4 x C 09.2.20 toki@seoul

TOSM+UCOM Myo Toki Ikeda, PTP(2008) Use bare NN interaction (AV8’) TOSM for tensor interaction (long range) UCOM for short range repulsion We take one approximation (two body) We consider VNNN ( ) in future 09.2.20 toki@seoul

V coordinate vs. T coordinate TOSM+UCOM with AV8’ (Myo Toki Ikeda) T VLS E VC VT 09.2.20 toki@seoul V coordinate vs. T coordinate

Picture of nucleus proton Snapshot neutron pionic pair 09.2.20 toki@seoul

Summarize TOSM We develop shell model method which describes the strong tensor and short-range correlations explicitly. Tensor correlation Tensor-optimized shell model (TOSM) Short-range correlation Unitary Correlation Operator Method (UCOM) We can describe nuclei starting from the bare interaction. We get a tool to study the importance of pion. (Unification of nuclear physics and hadron physics through chiral symmetry) 09.2.20 toki@seoul

Hypernuclei and pion T=0 J=1/2 Role of pion through N N N N 09.2.20 toki@seoul

4He+Y N p1/2 p3/2 s1/2 N 4He+ 4He+N Large attraction Spin-orbit effect due to blocking of particle states by the valence nucleon Use hole states to utilize pion attraction for lambda binding 09.2.20 toki@seoul

4He+ N N Central Effective int. interaction Hiyama et al. 09.2.20 toki@seoul

Conclusion We develop TOSM to treat nuclei using NN interaction We have to treat pion explicitly for hypernuclei (Binding energy) vs. finite nuclei (spin-orbit) We should develop TOSM for hypernuclei 09.2.20 toki@seoul