Self-consistent quasiparticle-phonon coupling for superfluid nuclei

Abstract

The utility of the anomalous Green's function formalism is physically motivated as a description of superfluid finite Fermi systems. The quasiparticle self-energy is then derived from a generalized six-point response function with the assumption that three-body correlations are negligible. An approximate calculation of the self-energy includes the usual core-polarization diagram, a backward-exchange diagram with ground state correlations, and higher-order diagrams that correct for exclusion-principle violations in the propagation of the quasiparticle and the microscopic phonon. Intermediate lines in the self-energy are described self-consistently, thereby including multiple-phonon core excitations. It is shown that the equation for the self-energy may be solved by matrix diagonalization with coupling of the even- and odd-nuclear eigenmodes. Renormalized phonons are calculated by taking into account the distribution of quasiparticle strength in the solution of the Bethe-Salpeter equation. The self-energy and phonon are calculated self-consistently.NUCLEAR STRUCTURE Green's function method with pairing. Self-consistent RPA, collective effects in odd-$A$ nuclei.