The Strutinsky method and its foundation from the Hartree-Fock-Bogoliubov approximation at finite temperature

Abstract

Strutinsky's shell-correction method is investigated in the framework of the microscopical Hartree-Fock-Bogoliubov method at finite temperature (HFBT). Applying the Strutinsky energy averaging consistently to the normal and abnormal density matrices and to the entropy, we define a self-consistently averaged HFBT system as the solution of a variational problem. From the latter we derive the generalized Strutinsky energy theorem and the explicit expressions for the shell correction of a statistically excited system of BCS quasiparticles. Using numerical results of HF calculations, we demonstrate the convergence of the Strutinsky expansion and estimate the validity of the practical shell-correction approach. We also discuss the close connections of the Strutinsky energy averaging with semiclassical expansions and their usefulness for solving the average nuclear self-consistency problem. In particular we argue that the Hohenberg-Kohn theorem should hold for the averaged HFBT system and we thus provide a justification of the use of semiclassical density functionals.