1 11/20/13 21/11/2015 jinniu hu school of physics, nankai university workshop on “chiral forces...

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

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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


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)


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


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


The shape of NN interaction


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


Chiral effective NN interaction


Chiral effective NN interactionE. Epelbaum, H. Krebs and U. -G. Meissner, PRL115(2015)122301phase shift

differential cross section

NLO

N2LO

N3LO

N4LO


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


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


Lattice QCD NN interaction

Lattice QCD NN scatteringT. Inoue et al, Nuc. Phys. A 881(2012)28





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


BHF theory in nuclear matter

Single particle potential

Single particle energy

Energy per nucleon


EOSs of symmetric nuclear matter with chiral force


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



The partial wave contributions at saturation density for N4LO



The partial wave contributions at r=0.4 fm-3 for N3LO



The partial wave contributions at r=0.8 fm-3 for N3LO



Equation of states of pure neutron matter with chiral force



BHF theory in nuclear matterSymmetric energy of nuclear matter with chiral force


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Lattice potential in r-space


Lattice potential in p-space


OBEP from lattice


EOS from lattice force


P-waves effect

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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

21/11/2015

Thank you very much for your attention!

Hu@Xiamen

1 11/20/13 21/11/2015 jinniu hu school of physics, nankai university workshop on “chiral forces...

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