Isospin effect in asymmetric nuclear matter (with QHD II model)
description
Transcript of Isospin effect in asymmetric nuclear matter (with QHD II model)
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