Isospin effect in asymmetric nuclear matter (with QHD II model) Kie sang JEONG

Effective mass splitting from nucleon dirac eq. here energy- momentum relation Scalar self energy Vector self energy (0 th )

Effective mass splitting Schrodinger and dirac effective mass (symmetric case) Now asymmetric case visit Only rho meson coupling + => proton, - => neutron

Effective mass splitting Rho + delta meson coupling In this case, scalar-isovector effect appear Transparent result for asymmetric case

Semi empirical mass formula Formulated in 1935 by German physicist Carl Friedrich von Weizsäcker 4 th term gives asymmetric effect This term has relation with isospin density

QHD model Quantum hadrodynamics Relativistic nuclear manybody theory Detailed dynamics can be described by choosing a particular lagrangian density Lorentz, Isospin symmetry Parity conservation * Spontaneous broken chiral symmetry *

QHD model QHD-I (only contain isoscalar mesons) Equation of motion follows

QHD model We can expect coupling constant to be large, so perturbative method is not valid Consider rest frame of nuclear system (baryon flux = 0 ) As baryon density increases, source term becomes strong, so we take MF approximation

QHD model Mean field lagrangian density Equation of motion We can see mass shift and energy shift

QHD model QHD-II (QHD-I + isovector couple) Here, lagrangian density contains isovector – scalar, vector couple

Delta meson Delta meson channel considered in study Isovector scalar meson

Delta meson Quark contents This channel has not been considered priori but appears automatically in HF approximation

RMF HF If there are many particle, we can assume one particle – external field(mean field) interaction In mean field approximation, there is not fluctuation of meson field. Every meson field has classical expectation value.

RMF HF Basic hamiltonian

RMF HF Expectation value

Hartree Fock approximation Classical interaction between one particle - sysytem Exchange contribution

H-F approximation Each nucleon are assumed to be in a single particle potential which comes from average interaction Basic approximation => neglect all meson fields containing derivatives with mass term

H-F approximation Eq. of motion

Wigner transformation Now we control meson couple with baryon field To manage this quantum operator as statistical object, we perform wigner transformation

Transport equation with fock terms Eq. of motion Fock term appears as

Transport equation with fock terms Following [PRC v64, ] we get kinetic equation Isovector – scalar density Isovector baryon current

Transport equation with fock terms kinetic momenta and effective mass Effective coupling function

Nuclear equation of state below corresponds hartree approximation Energy momentum tensor Energy density

Symmetry energy We expand energy of antisymmetric nuclear matter with parameter In general

Symmetry energy Following [PHYS.LETT.B 399, 191] we get Symmetry energy nuclear effective mass in symmetric case

Symmetry energy vanish at low densities, and still very small up to baryon density reaches the value in this interested range Here, transparent delta meson effect

Symmetry energy Parameter set of QHD models

Symmetry energy Empirical value a 4 is symmetry energy term at saturation density, T=0 When delta meson contribution is not zero, rho meson coupling have to increase

Symmetry energy

Now symmetry energy at saturation density is formed with balance of scalar(attractive) and vector(repulsive) contribution Isovector counterpart of saturation mechanism occurs in isoscalar channel

Symmetry energy Below figure show total symmetry energy for the different models

Symmetry energy When fock term considered, new effective couple acquires density dependence

Symmetry energy For pure neutron matter (I=1) Delta meson coupling leads to larger repulsion effect

Futher issue Symmetry pressure, incompressibility Finite temperature effects Mechanical, chemical instabilities Relativistic heavy ion collision Low, intermediate energy RI beam

reference Physics report 410, PRC V PRC V PRC V36 number1 Physics letters B Arxiv:nucl-th/ v1