Relativistic Chiral Mean Field Model for Finite Nuclei

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Presentation transcript:

Relativistic Chiral Mean Field Model for Finite Nuclei Hiroshi Toki (RCNP/Osaka) in collaboration with Yoko Ogawa (RCNP/Osaka) Setsuo Tamenaga (RCNP/Osaka) Akihiro Haga (Nagoya/RCNP) 2018/11/24 May 19 Shanhai 2006

6500 light year away 1987A is 150,000 light year away From Sumiyoshi From Book by N. Itoh From Gravitation by Misner, Thorn, Wheeler 6500 light year away 1987A is 150,000 light year away 2018/11/24 May 19 Shanhai 2006 From Sumiyoshi

超新星爆発 February 23, 1987 Before After Supernova is not yet exploded by theory!! Neutrino He4 GT reaction is key 2018/11/24 May 19 Shanhai 2006

Ab initio calculation of light nuclei Pion 70 ~ 80 % C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001), nucl-th/0103005 2018/11/24 May 19 Shanhai 2006

Resolution Now and Then Y. Fujita et al., EPJ A 13 (’02) 411. H. Fujita et al., Dr. Th. & PRC 2018/11/24 May 19 Shanhai 2006

Experiments H. Fujita et al (RCNP) 2003 Tamii for (p, p’) High resolution GT (pionic) excitations High resolution (30keV) H. Fujita et al (RCNP) 2003 Tamii for (p, p’) 2018/11/24 May 19 Shanhai 2006

Weinberg transformation Chiral sigma model Y. Ogawa et al. PTP (2004) Pion is the Goldstone boson of chiral symmetry Linear Sigma Model Lagrangian Polar coordinate Weinberg transformation 2018/11/24 May 19 Shanhai 2006

Non-linear sigma model Lagrangian r = fp + j where M = gsfp M* = M + gs j mp2 = m2 + l fp2 ms2 = m2 +3 l fp2 mw = gwfp mw* = mw + gwj ~ 2018/11/24 May 19 Shanhai 2006

Mean Field Equation Surface pion condensation Dirac equation Klein-Gordon equations Surface pion field 2018/11/24 May 19 Shanhai 2006

Nuclear matter Chiral sigma model vs. TM1 Density = 0.1414 fm-3 E/A = -16.14 MeV K = 650 MeV ms = 777 MeV mw = 783 MeV mp = 139 MeV M = 939 MeV fp = 93 MeV l = (ms2 - mp2) / 2fp2 = 33.7847 gs = M / fp = 10.0968 gw = mw / fp = 8.41935 = h gw h = 1.19700 ~ 2018/11/24 May 19 Shanhai 2006

40Ca 56Ni gp = gA/2fp h = 1.17319 with pion (gA = 1.15) without pion 9.2 40Ca N=20 56Ni 9.0 N=28 8.8 8.6 8.4 8.2 8.0 7.8 20 30 40 50 60 70 80 90 N=Z A (Mass number) with pion (gA = 1.15) without pion gp = gA/2fp 2018/11/24 May 19 Shanhai 2006 h = 1.17319

56Ni Magic effect No pion Pion Mean Field Parity mixed Pion produces spin-orbit splitting!! 2018/11/24 May 19 Shanhai 2006

Gamow-Teller transition 2018/11/24 May 19 Shanhai 2006

Relativistic Mean Field Theory with Pion (0-) s, w Parity mixed self-consistent mean field + Single particle state with parity mixing Intrinsic state (parity mixed state !!) H. Toki, S. Sugimoto, and K. Ikeda, Prog. Theor. Phys. 108(2002)903 2018/11/24 May 19 Shanhai 2006

Symmetry projected RMF with pion 2018/11/24 May 19 Shanhai 2006

Charge and parity projected RMF 2018/11/24 May 19 Shanhai 2006

projection -2- 2018/11/24 May 19 Shanhai 2006

Energy components and radius Y. Ogawa et al., PRC73 (2006) 34301 2018/11/24 May 19 Shanhai 2006

Parity projection Wave function 2018/11/24 May 19 Shanhai 2006

Density distribution and form factor 2018/11/24 May 19 Shanhai 2006

He4 and He5 Myo et al (2005) 2018/11/24 May 19 Shanhai 2006

Phase shifts for various partial waves 2018/11/24 May 19 Shanhai 2006

Higher partial waves 2018/11/24 May 19 Shanhai 2006

Conclusion We have developed the relativistic chiral mean field model for finite nuclei Spin and charge projection is essential Chiral symmetry recovery of 20% provides strong attraction for nuclear formation Pion provides a half of spin-orbit splitting We have succeeded to have renormalized chiral meson-baryon Lagrangian (vacuum) 2018/11/24 May 19 Shanhai 2006

Coleman-Weinberg mechanism for Renormalization of Chiral Sigma Model Linear sigma model Work out the nucleon loop and boson loop 2018/11/24 May 19 Shanhai 2006

Total effective potential Final Lagrangian 2018/11/24 May 19 Shanhai 2006

Results Quantum corrections cancel each other and the theory becomes trivial. 2018/11/24 May 19 Shanhai 2006

Coleman-Weinberg Scheme for Chiral Symmetric Lagrangian Massless Fermion-Chiral Boson system There is Fermion-Boson symmetry at m=infinity  No loop corrections Slight symmetry braking provides divergence free reasonable size non-linear effective potential We get now the lagrangian for finite nuclei with the vacuum contribution worked out 2018/11/24 May 19 Shanhai 2006