Microscopic description of static quadrupole moments of 2 1 + states by time-dependent HF equations

Abstract

Large quadrupole moments of 1-phonon states of sperical nuclei are shown to follow in a simple and direct way from time-dependent HF equations using the self-consistent perturbation expansion. Whereas the first order describes harmonic quadrupole oscillations, anharmonic terms arise in second order. The scattering of quasiparticles by quasi-particle pairs, which is neglected in RPA calculations, but included in this paper, leads to a second order response of the system and is shown to produce a strong enhancement of the quadrupole moments. Explicit results are obtained with a pairing-plus-quadrupole interaction and discussed within a schematic two level model.