Superoperator Approach to the Theory of Hot Nuclei and Astrophysical Applications: I—Spectral Properties of Hot Nuclei

The method of superoperators in Liouville space was applied to study spectral properties of hot nuclei. It is shown that properly defined fermionic superoperators allow us to generalize the equation-of-motion method to hot nuclei. Within the superoperator approach, for the nuclear model with separable particle–hole residual interaction of Landau–Migdal type, we derived the equations of thermal quasiparticle random phase approximation, which allow the spectral densities and strength functions of charge-exchange and charge-neutral excitations of hot nuclei to be calculated in a thermodynamically consistent way, i.e., without violating the principle of detailed balance. For the quasiparticle-phonon nuclear model, a thermodynamically consistent way is proposed for going beyond the random phase approximation by considering the interaction of thermal phonons. Using the Donnelly–Walecka method and the superoperator approach, expressions for cross sections of semileptonic weak reactions with hot nuclei are obtained.