Limitações impostas por modelos de estrutura nuclear tipo RPA sobre decaimento beta duplo

Abstract

In this work, nuclear moments were obtained for both double beta decay modes, with and without neutrino emission, using nuclear microscopic structure models, of the RPA type (Random Phase Approximation). For this purpose, a new method to implemente the pn-QRPA model was developed (proton-neutron-Quasi-particle Random Phase Approximation) to double beta decay, solving only one pn-QRPA equation for the intermediate nucleus. In addition, the method leads to a partial restoration of SU (4) symmetry to fix the parameters of the residual interaction, making the method predictive, since the nuclear moments obtained are in the same order as the experimental moments for the following nucleus 48 Ca, 76Ge, 82 Se, 96Zr, 100Mo, 128,130Te and 150Nd. It is important to mention that the pn-QRPA model was developed to describe the nuclear structure of the transitions that involves simple charge exchange, (N, Z) → (N ∓ 1, Z ± 1) and, when this is applied to double charge exchange transitions, some limitations arise in describing some observable such as excitation energies of the daughter nucleus, Q values of reaction, and Nuclear Matrix Elements of excited states, besides presenting an extreme sensitivity with the parametrization of the particle-particle channel. To overcome these limitations, we resorted to an extension of the QTDA model (Quasi-particle Tamm-Dancoff Approximation) with four quasi-particles, applied for the first time to double beta decay in this work using the BCS mean-field. This model was named (pn,2p2n)-QTDA and solves the limitations shown by pn-QRPA model. Also it obtains the energies of all excited states 0+ and 2+, giving the energy spectra of the Fermi transitions and Gamow-Teller Double charge exchange transitions,as well as the locations of the corresponding resonances and their sum rules, when this is applied to double beta decay. The last ones are relevant to reactions with the double charge exchange and double beta decay, since the nuclear structure is the same. This correlation does not exist within the pn-QRPA model. Thus, the (pn, 2p2n)-QTDA model is considered a natural extension of the pn-QRPA model, aimed at describing the nuclear phenomena present in Double Charge Exchange transitions. Thus, detailed numerical calculations are shown for processes (N, Z) → (N − 2, Z + 2) in 48Ca →48Ti and the process (N, Z) → (N + 2, Z − 2) in 96Ru →96Mo, involving everyone the final states 0+ and 2+.