Relativistic mean field theory and chiral symmetry for finite nuclei

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Relativistic mean field theory and chiral symmetry for finite nuclei Towards unification of hadron and nuclear physics Hiroshi Toki (RCNP-Osaka University) Kiyomi Ikeda (RIKEN & RCNP) Satoru Sugimoto (RIKEN) Yoko Ogawa (RCNP) Setsuo Tamenaga (RCNP) 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Variational calculation of light nuclei Pion 70 ~ 80 % C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001), nucl-th/0103005 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Ｃｈｉｒａｌｐｅｒｔｕｒｂａｔｉｏｎ 0- Ｎ．Ｋａｉｓｅｒ，Ｓ．ＦｒｉｔｓｃｈａｎｄＷ．ＷｅｉｓｅＣｈｉｒａｌ　ｐｅｒｔｕｒｂａｔｉｏｎ 0- Ｎ．Ｋａｉｓｅｒ，　Ｓ．　Ｆｒｉｔｓｃｈ　ａｎｄ　Ｗ．ＷｅｉｓｅＮ．Ｐ．Ａ６９７（２００２）２５５ 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Deuteron Veff(r ; 3S1) = VC(r ; 3E) + DVeff(r ; 3S1), DVeff(r ; 3S1) = VT (r) 8 w(r) u (r) The 3S1-3D1 coupling due to tensor force leads a large attractive force. 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Surface pion condensation by Toki, Sugimoto and Ikeda PTP 108 (2002) 903 Lagrangian Mean field equation Wave function 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Parity Projection 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

O+ and 0- states as brother states 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

5He p1/2 p3/2 s1/2 2 8 20 s1/2 p1/2 p3/2 d3/2 d5/2 f5/2 f7/2 Additional contribution 0- 5He L .S force Full energy gain s1/2 p3/2 p1/2 2 No energy gain blocked 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Weinberg transformation Chiral sigma model Linear sigma model Lagrangian Polar coordinate Weinberg transformation 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

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 ~ 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Without omega mass generation term Equation of motion obtained by using the E-L equation in nuclear matter Without omega mass generation term 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Linear sigma model 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

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 ~ 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Finite nuclei Nucleon Meson 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Finite nuclei h = 1.17319 40Ca 56Ni gp = gA/2fp TM1 9.2 40Ca 56Ni 9.0 8.8 8.6 8.4 8.2 8.0 7.8 20 30 40 50 60 70 80 90 A (Mass number) with pion (gA = 1.15) without pion gp = gA/2fp 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Single particle energy TM1 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Extended sigma model with pion 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

56Ni Gamow-Teller transition j> and j< couple and hence the selection rule is jj, j+-1 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Experiments Gamow-Teller distribution; Quenching factor=0.5 Longitudinal vs. transverse spin responses High resolution GT excitations H. Fujita et al RCNP 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Proton inelastic scattering Analyzed by Y. Fujita 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

S1/2 N=0.7 The upper components of 3j1/2 for 56Ni. 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Magnetic moments for proton 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Magnetic mements for neutron 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

中性子の単一粒子レベル 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Lambda Hypernuclei nucleon lambda OZI rule u u d u d s ＭＭ u u d u d s g(lambda) = 2/3 g(nucleon) No pion lambda coupling 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Ｌａmbｄａｈｙｐｅｒｎｕｃｌei （Ｎｉ５６－Ｌａmbｄａ）Ｙ．Ｏｇａｗａ　ｅｔ　ａｌ．（２００３） 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Conclusion Chiral sigma model is extended to include the mass generation term for the omega meson Saturation property is realized with too large a compressibility The magic number effect is generated by surface pion condensation All observables related with tensor force are to be explained by surface pion condensation 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

The spin-orbit splitting of Lambda hyper nuclei is small – This fact indicates that the nuclear spin- orbit splitting is due to surface pion condensation Pion, which is a Goldstone particle of chiral symmetry, plays the major role for hadron and nuclear physics 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Many home works Parity and charge projection Vacuum polarization Semi-infinite matter Infinite matter with projection Observables Delta and other mesons 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Result for 4He Volkov No. 1 + G3RS unit: MeV xT 1 1.25 1.5 1.75 2 xTE 0.93 0.88 0.81 0.73 0.64 Central 1 -18.36 -17.42 -15.92 -14.16 -12.07 Central ss -11.72 -11.67 -11.52 -11.26 Central tt -10.31 -9.18 -7.43 -5.28 -2.61 Central ss tt -33.21 -31.81 -29.73 -27.39 -24.75 Central sum -73.60 -70.13 -64.75 -58.34 -50.69 Tensor 1 -0.29 -0.36 -0.43 -0.51 -0.59 Tensor tt -11.98 -19.87 -30.16 -43.36 -59.82 Tensor sum -12.26 -20.23 -30.59 -43.86 -60.41 LS 1 0.71 1.18 1.78 2.55 3.49 LS tt 0.04 0.08 0.13 0.18 0.22 LS sum 0.75 1.26 1.91 2.72 3.72 Coulomb 0.85 0.86 0.87 Potential sum -84.27 -88.26 -92.58 -98.62 -106.51 Kinetic 55.81 59.71 64.39 70.52 78.19 Etotal -28.46 -28.55 -28.19 -28.10 -28.32 rms Rm (fm) 1.64 1.61 1.58 1.55 1.51 <Y|P|Y>/<Y|Y> 0.67 0.62 0.57 0.52 P(-) 0.105 0.133 0.161 0.188 0.214 rms Rmexp = 1.570.04 fm (NPA 693 (2001) 32) 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Density of 4He XT=1.5 XTE=0.81 0+ 0+ H-F 0- 11/28/2018 Oct. 1 , 2003 RCNP-Osaka

Surface Pion 11/28/2018 Oct. 1 , 2003 RCNP-Osaka