Liang-Gang Liu

PION CONDENSATION BASED ON A RELATIVISTIC DESCRIPTION OF PARTICLE-HOLE AND DELTA-HOLE EXCITATIONS

The critical density of neutral pion condensation is reinvestigated based on the relativistic framework and compared with nonrelativistic results. The particle-hole and delta-hole polarizations of the pion selfenergy are calculated in the relativistic way by using a new set of Landau–Migdal parameters derived from recent experimental data. It is concluded that the use of relativistic particle-hole and delta-hole excitations for the pion selfenergy increases the critical density, but still leads to condensation for densities from two to three times the normal nuclear matter density within the random phase approximation.

The dispersion relation of the pion in nuclear matter

Abstract We put forward a formalism to calculate the relativistic particle-hole and delta-hole excitation polarization insertion for pion propagator by using the particle-hole-antiparticle representation of nucleon and delta propagators in nuclear matter. The real and the imaginary part of the polarization insertion and the dispersion relation for pion propagator are calculated numerically. We find that the short range correlation enhances the delta-hole excitation but suppresses the particle-hole excitation, it also suppresses the pion condensation. We find that the effect of the short range correlation on the pion dispersion relation depends very much on the form of the short range correlation and the parameters involved.

NN¯,Δ¯N,ΔN¯excitation for the pion propagator in nuclear matter

The particle-hole and Delta -hole excitations are well-known elementary excitation modes for the pion propagator in nuclear matter. But, the excitation also involves antiparticles, namely, nucleon-antinucleon, anti-Delta-nucleon and Delta-antinucleon excitations. These are important for high-energy momentum as well, and have not been studied before, to our knowledge. In this paper, we give both the formulas and the numerical calculations for the real and the imaginary parts of these excitations.

EFFECTIVE MESON MASS IN NUCLEAR MATTER BASED ON DISPERSION EQUATION INCLUDING

Effective meson masses of σ, ω, ρ and π in nuclear matter are calculated from the meson self-energy of the particle–antiparticle excitations. Instead of the traditional renormalization, the dispersion relation method is used to calculate the real part from the finite imaginary part, since the tensor coupling of the pion and ρ meson is not renormalized in the usual sense. In this paper, we show the effects from antidelta-nucleon and delta-antinucleon excitations in π meson mass beside nucleon–antinucleon excitation. It is also shown that agreement is obtained on the ω meson mass predicted by the subtraction method and ρ meson mass by the QCD sum rule method. It is concluded that the dispersion equation method leads to the fact that all the meson mass decreases as the baryon density increases, and it supports the chiral symmetry restoration.

{\rm N} \bar{\rm N},\ \Delta \bar{\rm N},\ \bar\Delta {\rm N}

The critical density of neutral pion condensation is investigated based on the relativistic framework and compared with nonrelativistic results. The particlehole and delta-hole polarizations of the pion selfenergy are calculated in the relativistic way by using a new set of Landau-Migdal parameters derived from a recent experimental data. It is concluded that the use of relativistic particle-holeand delta-holeexcitations for the pion selfenergy increases the critical density compared with the non-relativistic result, however still leads to condensation for densities from 2 to 4 times normal nuclear matter density.

EXCITATIONS

The particle-hole and Delta -hole excitations are well-known elementary excitation modes for the pion propagator in nuclear matter. But, the excitation also involves antiparticles, namely, nucleon-antinucleon, anti-Delta-nucleon and Delta-antinucleon excitations. These are important for high-energy momentum as well, and have not been studied before, to our knowledge. In this paper, we give both the formulas and the numerical calculations for the real and the imaginary parts of these excitations.

PION CONDENSATION BASED ON RELATIVISTIC FORMULATION

The particle-hole and Delta -hole excitations are well-known elementary excitation modes for the pion propagator in nuclear matter. But, the excitation also involves antiparticles, namely, nucleon-antinucleon, anti-Delta-nucleon and Delta-antinucleon excitations. These are important for high-energy momentum as well, and have not been studied before, to our knowledge. In this paper, we give both the formulas and the numerical calculations for the real and the imaginary parts of these excitations.