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A model many-body Hamiltonian describing an heterogenous system of pairedprotons and paired neutrons and interacting among themselves through monopoleparticle-hole and monopole particle-particle interactions is used to study thedouble beta decay of Fermi type. The states are described by time dependentapproaches choosing as trial functions coherent states of the symmetry groupsunderlying the model Hamiltonian. One formalism, VP1, is fully equivalent withthe standard pnQRPA and therefore fails at a critical value of theparticle-particle interaction strength while another one, VP2, corresponds to atwo step BCS treatment, i.e. the proton quasiparticles are paired with theneutron quasiparticles. In this way a harmonic description for the double betatransition amplitude is provided for any strength of the particle-particleinteraction. The approximation quality is judged by comparing the actualresults with the exact result as well as with those corresponding to varioustruncations of the boson expanded Hamiltonian and transition operator. Finallyit is shown that the dynamic ground states provided by VP1 and VP2 arereasonable well approximated by solutions of a variational principle. Thisremark constitutes a step forward finding an approach where the RPA groundstate is a solution of a variational principle equation.Comment: 38 pages, RevTex (preprint form), 11 postscript figure

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