Four quasi-particle excitations and two-phonon vibrational states in spherical nuclei — I

Abstract

A formalism is developed which presents a microscopic theory of both one- and two-phonon (many-phonon) type vibrational states of spherical nuclei. The superconducting nature of nuclear structure is taken into account by the Bogoliubov canonical transformation. Two cases are considered: that of an uncorrelated ground state, and that of the ground-state correlations represented by a kind of Second (Higher) Random Phase Approximation on the (Bogoliubov) quasiparticles. Both the one- and the two-phonon type modes emerge as coherent superpositions of the two- and four-quasi-particle components. The respective eigenvalue equations and transition probabilities are discussed.