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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 (0 th ). Effective mass splitting.

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

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

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

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

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

  5. 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

  6. 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 *

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

  8. 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

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

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

  11. Delta meson • Delta meson channel considered in study • Isovector scalar meson

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

  13. 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.

  14. RMF <–> HF • Basic hamiltonian

  15. RMF <–> HF • Expectation value

  16. HartreeFock approximation Classical interaction between one particle - sysytem Exchange contribution

  17. 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

  18. H-F approximation • Eq. of motion

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

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

  21. Transport equation with fock terms • Following [PRC v64, 045203] we get kinetic equation • Isovector– scalar density • Isovector baryon current

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

  23. Nuclear equation of state • below corresponds hartreeapproximation • Energy momentum tensor • Energy density

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

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

  26. 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

  27. Symmetry energy • Parameter set of QHD models

  28. 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

  29. Symmetry energy

  30. Symmetry energy • Now symmetry energy at saturation density is formed with balance of scalar(attractive) and vector(repulsive) contribution • Isovectorcounterpart of saturation mechanism occurs in isoscalar channel

  31. Symmetry energy • Below figure show total symmetry energy for the different models

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

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

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

  35. reference • Physics report 410, 335-466 • PRC V65 045201 • PRC V64 045203 • PRC V36 number1 • Physics letters B 191-195 • Arxiv:nucl-th/9701058v1

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