1 11/20/13 21/11/2015 Jinniu Hu School of Physics, Nankai University Workshop on “Chiral forces and ab initio calculations” Nov. 20- Nov. 22, 2015, Xiamen University The equation of state of nuclear matter from quantum chromodynamics theory

21/11/2015 Outline  The realistic nucleon-nucleon interaction  Nuclear matter with chiral force  Nuclear matter with lattice force  Summary and respective

21/11/2015 Realistic NN interaction History  One pion exchange Yukawa (1935)  Multi-pion Taketani et al. (1951)  Repulsive Jastrow (1951)  One Boson exchange Bonn Group (1970~)  EFT Weinberg (1990)  High precision potentials (1990~)  Lattice (2000~)

Realistic NN interaction  Realistic nucleon-nucleon interaction From the nucleon-nucleon scattering experiment k k’ z θ  Differential scattering cross section 21/11/2015

NN scattering data R. Navarro Pérez, J. E. Amaro, and E. Ruiz Arriola, Phys. Rev. C 89(2014) ! 21/11/2015

Partial wave representation The good quantum numbers in NN scattering problem Momentum k, Total angular momentum J, Total spin S, Total isospin T The wave function of NN scattering states The NN interaction in partial wave representation 21/11/2015

Two nucleon states StatesCentralTensor and spin-orbit J=0, S=0, T=1, L=0 1 S 0 (pp,np,nn)- J=0, S=1, T=1, L=1 3 P 0 (pp,np,nn)- J=1, S=0, T=0, L=1 1 P 1 (np)- J=1, S=1, T=1, L=1 3 P 1 (pp,np,nn)- J=1, S=1, T=0, L=0,2 3 S 1 – 3 D 1 (np) J=2, S=0, T=1, L=2 1 D 2 (pp,np,nn)- J=2, S=1, T=0, L=2 3 D 2 (np)- J=2, S=1, T=1, L=1,3 3 P 2 – 3 F 2 (pp,np,nn) J=3, S=0, T=0, L=3 1 F 3 (np)- J=3, S=1, T=1, L=3 3 F 2 (pp,np,nn)- J=3, S=1, T=0, L=2,4 3 D 3 – 3 G 3 (np) 21/11/2015

Types of realistic NN interaction Phenomenological interaction Based upon the standard non-relativistic operator structure  Gammel-Thaler potential Hard core J. L. Gammel, and R. M. Thaler, Phys. Rev. 107(1957)291  Hamada-Johnston potential Hard core T. Hamada, and I. D. Johnston, Nucl. Phys. 34 (1962)382  Reid potential soft core R.V. Reid, Ann. Phys. (N.Y.) 50(1968)411  Argonne V14 potential R. B. Wiringa, R. A. Smith, and T. L. Ainsworth, Phys. Rev. C 29(1984)1207  Argonne V18 potential R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C 51(1995)38 21/11/2015

Types of realistic NN interaction Relativistic interaction Based upon the quantum field theory  One boson exchange potential R. Machleidt, K. Holinde, and Ch. Elster, Phys. Rep. 149(1987)1  CD Bonn potential R. Machleidt, Phys. Rev. C 63(2001)  Chiral effective potential R. Machleidt, and D. R. Entem, Phys. Rep. 503(2011)1  Lattice QCD potential N. Ishii, S. Aoki, and T. Hatsuda, Phys. Rev. Lett. 99(2007) /11/2015

The shape of NN interaction 21/11/2015

Chiral effective NN interaction  The Lagrangian of chiral effective field theory  The Lagrangian of dynamics among pions  The Lagrangian of pion and nucleon interaction where 21/11/2015

Chiral effective NN interaction 21/11/2015

Chiral effective NN interaction E. Epelbaum, H. Krebs and U. -G. Meissner, PRL115(2015) phase shift differential cross section NLO N 2 LO N 3 LO N 4 LO 21/11/2015

High precision NN interaction AV 18CD-BonnIdaho(N 3 LO) Bochum (N 4 LO) Parameters c 2 /datum(np) (0~100 MeV) c 2 /datum(pp) (0~100 MeV) B d (MeV) P D (%) /11/2015

Lattice QCD NN interaction Sketch of Lattice method  NN wave function is constructed by using lattice QCD.  The NN potential is constructed from the wave function by demanding that the wave function should satisfy the Schrodinger equation. Schematically 21/11/2015

Lattice QCD NN interaction Lattice QCD NN scattering T. Inoue et al, Nuc. Phys. A 881(2012)28 21/11/2015

Outline  The realistic nucleon-nucleon interaction  Nuclear matter with chiral force  Nuclear matter with lattice force  Summary and respective 21/11/2015

BHF theory in nuclear matter 18 Bethe-Goldstone equation in basis space where is the Fermi energy, is the starting energy and are intermediate states. Bethe-Goldstone equation in plane wave basis where is a shorthand notation for and. Matrix inversion method 21/11/2015

BHF theory in nuclear matter Single particle potential Single particle energy Energy per nucleon 21/11/2015

EOSs of symmetric nuclear matter with chiral force 21/11/2015 Nuclear matter in BHF theory E. Epelbaum, H. Krebs and U. -G. Meissner, PRL115(2015)122301

Equation of states of symmetric nuclear matter with chiral force 21/11/2015 Nuclear matter in BHF theory

The partial wave contributions at saturation density for N 4 LO 21/11/2015 Nuclear matter in BHF theory

The partial wave contributions at r=0.4 fm -3 for N 3 LO 21/11/2015 Nuclear matter in BHF theory

The partial wave contributions at r=0.8 fm -3 for N 3 LO 21/11/2015 Nuclear matter in BHF theory

Equation of states of pure neutron matter with chiral force 21/11/2015 Nuclear matter in BHF theory

Equation of states of pure neutron matter with chiral force 21/11/2015 Nuclear matter in BHF theory

BHF theory in nuclear matter Symmetric energy of nuclear matter with chiral force 21/11/2015

21/11/2015 Outline  The realistic nucleon-nucleon interaction  Nuclear matter with chiral force  Nuclear matter with lattice force  Summary and respective

21/11/2015 Lattice potential in r-space

21/11/2015 Lattice potential in p-space

21/11/2015 OBEP from lattice

21/11/2015 EOS from lattice force

21/11/2015 P-waves effect

21/11/2015 Outline  The realistic nucleon-nucleon interaction  Nuclear matter with chiral force  Nuclear matter with lattice force  Summary and respective

21/11/2015 Summary and perspectives  We studied the properties of nuclear matter with chiral effective potential based on chiral symmetry of QCD theory  The properties of nuclear matter with chiral effective force become convergence with the high order term  We also attempt to study the nuclear matter with lattice NN interaction  The Delta isobar effect in nuclear matter  The three-body effect  Perspectives

21/11/2015 Thank you very much for your attention !