A generalized RPA theory of the nuclear response function

Abstract

A new method of calculating the response function is proposed. The new method gives the response which is explicitly a generalization of the RPA response in a perturbative sense. When we calculate the transition amplitude of a one-body operator from the ground state to a particle-hole (p-h) state, the new response function provides all the second-order effects in addition to the first-order ones which can be obtained in the RPA theory. The new response function is obtained by the following procedure. Firstly, we consider the second RPA theory which is a generalization of the usual RPA theory. It is found that the second RPA misses some of the second-order effects. Secondly, we formulate a modified second RPA equation from the equation of motion of the operators, and then derive the p-h response function from it. It is found that the newly derived p-h response function is obtained by adding new terms to the self-energy of the p-h response function derived from the second RPA theory. Lastly, we introducd vertex functions which take into account the transitions from a particle (hole) state to a particle (hole) state. Note that the p-h response function deals with only the transition amplitudes from a particle (hole) state to a hole (particle) state.