Post on 28-Dec-2015
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 (0th )
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 for-mula
• Formulated in 1935 by German physicist Carl Friedrich von Weizsäcker
• 4th 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 sys-tem (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 consid-ered priori but appears automatically in HF approximation
RMF <–> HF
• If there are many particle, we can as-sume 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 be-tween 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, 045203] 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 0.045 in this interested range
• Here, transparent delta meson effect
Symmetry energy
• Parameter set of QHD models
Symmetry energy
• Empirical value a4 is symmetry energy term at saturation density, T=0
When delta meson contribution is not zero, rho meson cou-pling have to increase
Symmetry energy
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 chan-nel
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 re-pulsion 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, 335-466• PRC V65 045201• PRC V64 045203• PRC V36 number1• Physics letters B 191-195• Arxiv:nucl-th/9701058v1