1 11/20/13 21/11/2015 jinniu hu school of physics, nankai university workshop on “chiral forces...
DESCRIPTION
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~)TRANSCRIPT
111/20/1321/11/2015 Hu@Xiamen
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 respectiveHu@Xiamen
21/11/2015
Realistic NN interactionHistory
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~)Hu@Xiamen
Realistic NN interaction Realistic nucleon-nucleon interaction From the nucleon-nucleon scattering experiment
k k’z
θ
Differential scattering cross section
21/11/2015 Hu@Xiamen
NN scattering dataR. Navarro Pérez, J. E. Amaro, and E. Ruiz Arriola, Phys. Rev. C 89(2014)064006
8125!21/11/2015 Hu@Xiamen
Partial wave representationThe 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 Hu@Xiamen
Two nucleon states
States Central Tensor and spin-orbit J=0, S=0, T=1, L=0 1S0 (pp,np,nn) -J=0, S=1, T=1, L=1 3P0 (pp,np,nn) -J=1, S=0, T=0, L=1 1P1 (np) -J=1, S=1, T=1, L=1 3P1 (pp,np,nn) -
J=1, S=1, T=0, L=0,2
3S1 – 3D1 (np) 3S1 –
3D1 (np)
J=2, S=0, T=1, L=2 1D2 (pp,np,nn) -J=2, S=1, T=0, L=2 3D2 (np) -
J=2, S=1, T=1, L=1,3
3P2 – 3F2 (pp,np,nn) 3P2 –
3F2 (pp,np,nn)
J=3, S=0, T=0, L=3 1F3 (np) -J=3, S=1, T=1, L=3 3F2 (pp,np,nn) -
J=3, S=1, T=0, L=2,4
3D3 – 3G3 (np) 3D3 –
3G3 (np)
21/11/2015 Hu@Xiamen
Types of realistic NN interaction
Phenomenological interaction Based upon the standard non-relativistic operator structureGammel-Thaler potential Hard core J. L. Gammel, and R. M. Thaler, Phys. Rev. 107(1957)291Hamada-Johnston potential Hard core T. Hamada, and I. D. Johnston, Nucl. Phys. 34 (1962)382Reid potential soft core R.V. Reid, Ann. Phys. (N.Y.) 50(1968)411Argonne V14 potential R. B. Wiringa, R. A. Smith, and T. L. Ainsworth, Phys. Rev. C 29(1984)1207Argonne V18 potential R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C 51(1995)38
21/11/2015 Hu@Xiamen
Types of realistic NN interaction
Relativistic interaction Based upon the quantum field theoryOne 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)024001Chiral effective potential R. Machleidt, and D. R. Entem, Phys. Rep. 503(2011)1Lattice QCD potential N. Ishii, S. Aoki, and T. Hatsuda, Phys. Rev. Lett. 99(2007)022001
21/11/2015 Hu@Xiamen
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
where
21/11/2015 Hu@Xiamen
Chiral effective NN interactionE. Epelbaum, H. Krebs and U. -G. Meissner, PRL115(2015)122301phase shift
differential cross section
NLO
N2LO
N3LO
N4LO
21/11/2015 Hu@Xiamen
High precision NN interaction
AV 18 CD-Bonn Idaho(N3LO)
Bochum (N4LO)
Parameters 40 38 24 26
c2/datum(np)(0~100 MeV) 0.95 0.6 1.7-5.2 0.3
c2/datum(pp)(0~100 MeV) 1.0 0.5 1.5-6.7 0.3
Bd (MeV) 2.224575 2.224575 2.224575 2.224575
PD (%) 5.76 4.85 4.51 4.29
21/11/2015 Hu@Xiamen
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 Hu@Xiamen
Lattice QCD NN interaction
Lattice QCD NN scatteringT. Inoue et al, Nuc. Phys. A 881(2012)28
21/11/2015 Hu@Xiamen
Outline The realistic nucleon-nucleon interaction
Nuclear matter with chiral force
Nuclear matter with lattice force
Summary and respective21/11/2015 Hu@Xiamen
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 Hu@Xiamen
BHF theory in nuclear matter
Single particle potential
Single particle energy
Energy per nucleon
21/11/2015 Hu@Xiamen
EOSs of symmetric nuclear matter with chiral force
21/11/2015 Hu@Xiamen
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 Hu@Xiamen
Nuclear matter in BHF theory
The partial wave contributions at saturation density for N4LO
21/11/2015 Hu@Xiamen
Nuclear matter in BHF theory
The partial wave contributions at r=0.4 fm-3 for N3LO
21/11/2015 Hu@Xiamen
Nuclear matter in BHF theory
The partial wave contributions at r=0.8 fm-3 for N3LO
21/11/2015 Hu@Xiamen
Nuclear matter in BHF theory
Equation of states of pure neutron matter with chiral force
21/11/2015 Hu@Xiamen
Nuclear matter in BHF theory
Equation of states of pure neutron matter with chiral force
21/11/2015 Hu@Xiamen
Nuclear matter in BHF theory
BHF theory in nuclear matterSymmetric energy of nuclear matter with chiral force
21/11/2015 Hu@Xiamen
21/11/2015
Outline The realistic nucleon-nucleon interaction
Nuclear matter with chiral force
Nuclear matter with lattice force
Summary and respectiveHu@Xiamen
21/11/2015
Outline The realistic nucleon-nucleon interaction
Nuclear matter with chiral force
Nuclear matter with lattice force
Summary and respectiveHu@Xiamen
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
Hu@Xiamen