New results for two-neutrino double beta decay with large particle-particle two body proton-neutron interaction

Abstract

A model many-body Hamiltonian describing an heterogenous system of paired protons and paired neutrons and interacting among themselves through monopole particle-hole and monopole particle-particle interactions is used to study the double beta decay of Fermi type. The states are described by time dependent approaches choosing as trial functions coherent states of the symmetry groups underlying the model Hamiltonian. One formalism, VP1, is fully equivalent with the standard pnQRPA and therefore fails at a critical value of the particle-particle interaction strength while another one, VP2, corresponds to a two step BCS treatment, i.e. the proton quasiparticles are paired with the neutron quasiparticles. In this way a harmonic description for the double beta transition amplitude is provided for any strength of the particle-particle interaction. The approximation quality is judged by comparing the actual results with the exact result as well as with those corresponding to various truncations of the boson expanded Hamiltonian and transition operator. Finally it is shown that the dynamic ground states provided by VP1 and VP2 are reasonable well approximated by solutions of a variational principle. This remark constitutes a step forward finding an approach where the RPA ground state is a solution of a variational principle equation.