Thermodynamic description of pion excitations in nuclear matter

The thermodynamic properties of pion excitations in nuclear matter are studied for variation of its density from normal rhoroughly-equalrho0 to rhoroughly-equal3rho0 and of its temperature T from zero to Tapprox.1m/sub π/c2. From numerical calculations of the polarization operator product of the pion field are found the frequencies ω(k, rho,T), necessary for calculation of the thermodynamic quantities, at which there is a change of sign of ReD-1(ω,k, rho,T): the real part of the pion inverse Green function. Qualitative estimates and a numerical calculation are carried out of the following thermodynamic quantities: the ratio of the density of pion excitations rho/sub π/ to the density of the medium, R = rho/sub π// rho, their entropy S, and the energy density E. The dependence of the results on NN, NΔ, and ΔΔ interactions in nuclear matter is discussed. The role of the effective ππ interaction in nuclear matter is investigated. The qualitative estimates and numerical calculations show that ω(k, rho,T) and R, S, and E can depend substantially on effects, nonlinear in the pion field, of anharmonicity of the pion excitations, allowance for which is accomplished by introduction of an effective ππ interaction. Calculations are carried out for an effective repulsion and attraction and for a ππ interaction similar to the interaction of free pions