Download Isospin effect in asymmetric nuclear matter

Isospin effect in asymmetric
nuclear matter
(with QHD II model)
Kie sang JEONG
Effective mass splitting
• from nucleon dirac eq. here energymomentum 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
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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
• 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 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, 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 coupling 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 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
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Symmetry pressure, incompressibility
Finite temperature effects
Mechanical, chemical instabilities
Relativistic heavy ion collision
Low, intermediate energy RI beam
reference
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Physics report 410, 335-466
PRC V65 045201
PRC V64 045203
PRC V36 number1
Physics letters B 191-195
Arxiv:nucl-th/9701058v1