Relativistic Mean Field Model for finite nuclei and infinite matter
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1 Relativistic Mean Field Model for finite nuclei and infinite matter Hiroshi Toki (RCNP/Osaka) in collaboration with H. Shen (Nankai/China) L. Geng (Beijing/China) K. Sumiyoshi (Numazu)
2 Supernova explosion February 23, 1987 Before After
3 Supernova explosion and neutrino propagation Fe core Collapse ρ c ~10 10 g/cm3 T c ~1 MeV ν ν-trapping ρ c ~10 12 g/cm3 T c ~2 MeV e-capture ν ν ν ν 1000 km Core Bounce ρ c ~3x10 14 g/cm3 T c ~5 MeV ν ν Explosion ν ν ν Shockwave NS R-process 10 km
4 Bethe-Weizsaecker Mass Formula Liquid drop model h
5 Proton Number Z Proton Number Z Mass as compared with simple BW mass formula Binding Energy difference: Exp.-BW Binding Energy difference: RMF-BW
6 Nuclear matter saturation relativistic Bruckner Hartree-Fock non-relativistic Coester band Empirical saturation Non-relativistic calculations: not successful. relativistic mean field theory Relativistic Bruckner Hartree-Fock calculations: encouraging! The RMF model: parameterized to describe the nuclear matter saturation.
7 Relativistic mean field theory with TM1 parameter Lagrangian Y. Sugahara and H. Toki Nucl. Phys. A579 (1994) free parameters TM1
8 The RMF model Y. Sugahara and H. Toki, Nucl. Phys. A 579 (1994)557
9 Proton Number Z Study all nuclei within RMF Calculate all 7000 Nuclei Deformation and pairing are worked out Many predictions for experiments to come RMF+BCS HFB-2 FRDM
10 Proton separation Energy
11 E/A [MeV] E/A [MeV] E/A [MeV] E/A [MeV] Binding Energy Gd isotopes RMF+BCS Exp Z=64 Z= Dy isotopes RMF+BCS Exp Z=68 Z= Er isotopes RMF+BCS Exp Yb isotopes RMF+BCS Exp
12 Deformation Gd isotopes Dy isotopes RMF+BCS FRDM Exp. Z=64 Z= RMF+BCS FRDM Exp Er isotopes Yb isotopes Z=68 RMF+BCS -0.1 Z=70 FRDM Exp RMF+BCS FRDM Exp
13 R c [fm] R c [fm] R c [fm] R c [fm] Radius Gd isotopes Dy isotopes 5.5 Z=64 Z= RMF+BCS HFBCS-1 Exp RMF+BCS HFBCS-1 Exp Er isotopes Z= Z= RMF+BCS HFBCS-1 Exp Yb isotopes RMF+BCS HFBCS-1 Exp.
14 Proton Number Z Binding energy difference 100 Binding energy differences: B theo. -B exp RMF+BCS
15 Nuclear deformation Exp
16 Summary of RMF for Finite Nuclei The RMF lagrangian is very good for finite nuclei. The isovector interaction is not well controlled yet Rho meson tensor coupling Pion exchange term
17 Thomas-Fermi approximation * body-centered cubic lattice * parameterized nucleon distribution * RMF input E = Ebulk + Esurface+ ECoulomb+ ELattice+ Eelectron assume state minimize free energy favorable state
18 EOS non-uniform matter e+a e+n+a (g/cm ) Shen, Toki, Oyamatsu, Sumiyoshi, Nucl.Phys.A637(1998)435 Prog.Theor.Phys.100(1998)1013
19 EOS for supernova
20 EOS temperature: 0.1 < T < 100 (MeV) density: 10 5 < ρ B < (g/cm 3 ) asymmetry: 0.01 < Y p < nuclei alpha proton neutron electron Shen, Toki, Oyamatsu, Sumiyoshi, Nucl.Phys.A637(1998)435 Prog.Theor.Phys.100(1998)1013
21 Fe-core of 15M solar No explosion even with new EOS (Shen( Shen) collapse shock wave proto-neutron star bounce Sumiyoshi et al. ApJ 629 (2005) 922
22 After bounce: ν-heating effect ν-heating rate at t pb =150ms 1.0 till ~200 msec: Similar dynamics of shock ν-luminosity Temperature ν-energy, flux Cancel out EOS effects heating rate [erg/g/s] x Shen-EOS LS-EOS 200 radius [km] Heating region Sumiyoshi et al. ApJ 629 (2005) 922. ν ν ν n Protoneutron star ν e + n ν e + p p Stalled shock e + p e + + n Fe core
23 X i p Mass fraction nuclei n neutron proton Profiles after bounce:t pb =150ms α alpha temperature [MeV] Temperature Shen-EOS LS-EOS radiusc [km] radiusc [km] Sumiyoshi et al. ApJ 629 (2005) 922
24 ニュートリノがもっとがもっとエネルギー 重力崩壊の全エネルギーがニュートリノで持ち去られう を落としてほしい ν 約 100msec 後 10^53erg (Kamiokande) Rho~1e11g/cm^3 T~3MeV Many Alpha exists ν 約 1% のニュートリノのエネルギーがショックの後ろの物質に落とされる ν ν ν ν km ν-sphere ν-heating
25 Neutrino Alpha interaction At present this rate is set 0 Inelastic excitation Elastic scattering about 0.5MeV is dropped 30MeV 10MeV
26 Conclusion Relativistic EOS for supernova simulation is available Isovecter part is not yet satisfactory (if tensor interaction, the EOS is unchanged) Neutrino alpha interaction is being worked out for supernova explosion
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