Quasiparticle-phonon interaction in the theory of finite Fermi systems

Abstract

Within the Green’s function method and on the basis of the method developed by V.A. Khodel for analyzing anharmonic effects, effects of quasiparticle-phonon interaction in the second order in the amplitude of phonon production are studied in two problems as a natural development of A.B. Migdal’s theory of finite Fermi systems. Transitions between excited states and static moments of magic and nonmagic nuclei in excited states, each of which is described in the random-phase approximation, are considered. The results for this problem are found to differ considerably from those in the quasiparticle random-phase approximation. The inclusion of all second-order anharmonic effects in the extended theory of finite Fermi systems that extends the standard theory of finite Fermi systems to the case of taking into account quasiparticle-phonon interaction in order to describe excited states, but which does not take into account all such effects, is also considered. They are taken into account at a level that makes it possible to calculate static moments of odd nuclei—more precisely, the respective equation for the vertex function, which, in the theory of finite Fermi systems, is a basic ingredient that describes the interaction of a nucleus with an external field, is derived. Some numerical results obtained within the recently implemented self-consistent version of the extended theory of finite Fermi systems are also presented for 15 stable and unstable tin isotopes. These results give sufficient grounds to conclude that phenomenological systematics are inapplicable to giant dipole resonances in neutron-rich isotopes. The cross sections for radiative neutron capture that are calculated by usingmicroscopic strength functions for the neutron-rich isotopes 132Sn and 150Sn differ strongly from the cross sections calculated on the basis of a phenomenological description of giant dipole resonances. These results are of paramount importance for astrophysics and for the theory of nuclear data for reactors since they highlight the inapplicability of phenomenological systematics to giant dipole resonances and the need for self-consistent calculations for neutron-rich nuclei.