Collective motion in iso- and gauge-spaces: Application to 2 νββ-decay transitions

Abstract

The nuclear two-neutrino double-beta decay is a measured process that should be quantitatively understood before the predictions on more exotic, non-standard, double-beta decay processes are fully trusted. In most cases, the current framework for the description of 2 νββ process includes the quasiparticle and random phase approximation (RPA) procedures, which present instabilities in the region of interest. From the point of view of many-body physics, the problem involved is to disentangle the physical effects associated with the lack of conservation of the isospin symmetry in the Hamiltonian, from those arising from the application of the Bogoliubov–Valatin transformation between identical particles. In the present paper, the separation between both effects is accomplished by introducing the collective subspace in isospin and gauge spaces, and restoring the symmetry within such subspace. Explicit, real, isodipole and isoquadrupole mixing terms are subsequently obtained. The problem of the over-completeness of the basis is solved by isolating the spurious sector via the application of the Becchi–Rouet–Stora–Tyutin (BRST) symmetry. The formalism allows to calculate Fermi double-beta-decay transitions which result—as expected—too small in order to be of significance in the double-beta processes. The same procedure is applied to calculate Gamow–Teller double-beta decay transitions and the already known sensitivity to model parameters is recovered. We have calculated two-neutrino double-beta decay transitions in 76Ge, as an example about the use of the formalism.