Description of the 2ννββ decay within a gauge restored of a fully renormalized pnQRPA approach

Abstract

A many-body Hamiltonian involving the mean field for a projected spherical single particle basis, the pairing interactions for alike nucleons, the dipoledipole proton-neutron interactions in the particle-hole (ph) channel and the ph dipole-pairing potential is treated by the projected gauge of fully renormalized proton-neutron quasiparticle random phase approximation (PGFRpnQRPA) approach. The resulting wavefunctions and energies for the mother and the daughter nuclei are used to calculate the 2νββ decay rate and the process half life. For illustration, the formalism is applied for the decays 100 Mo→ 100 Ru and 116 Cd→ 116 Sn. The results are in good agreement with the corresponding experimental data. The Ikeda sum rule is obeyed.

FRpnQRPA approach with the gauge symmetry restored. Application for the 2νββdecay

“…Recently [8,9], the results of Ref. [7] were improved in two respects: a) aiming at providing a unitary description of the process for the situations when the involved nuclei are spherical or deformed, here we use a projected spherical single particle basis; b) the space of proton-neutron dipole configurations is split in three subspaces, one being associated to the single β − decay, one to the single β + process, and one spanned by the unphysical states.…”

Interplay of classical and quantal features within the coherent-state model

“…Indeed, in that case quantizing the classical trajectories, the resulting spectrum might be close to that associated to the initial many body Hamiltonian. Such a treatment can be applied also to quadrupole boson Hamiltonians [3,4].…”