New results for 2νββ decay with large particle–particle two-body proton–neutron interaction

Abstract

A model many-body Hamiltonian describing a 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 proton–neutron quasiparticle random phase approximation and therefore fails at a critical value of the particle–particle interaction strength while another one, VP2, corresponds to a two-step Bardeen–Cooper–Schrifed (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 reasonably well approximated by solutions of a variational principle. This remark constitutes a step forward in finding an approach where the random phase approximation ground state is a solution of a variational principle equation.