Description of the two neutrino double β decay in deformed nuclei with projected spherical single particle basis

Abstract

Using an angular-momentum-projected single-particle basis, a proton-neutron quasiparticle random-phase approximation approach is used to study the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ properties of 10 isotopes, exhibiting various quadrupole deformations. The parent and daughter nuclei exhibit different quadrupole deformations. Since the projected basis enables a unified description of deformed and spherical nuclei, situations where the nuclei involved in the double \ensuremath{\beta} decay process are both spherical, both deformed, or one spherical and the other deformed can be treated through a single formalism. Dependence of single ${\ensuremath{\beta}}^{\ensuremath{-}}$ and ${\ensuremath{\beta}}^{+}$ strength distribution on atomic mass number and nuclear deformation is analyzed. For the double \ensuremath{\beta} decay process, the Gamow-Teller transition amplitudes and half-lives are calculated. Results are compared with experimental data as well as with predictions of other theoretical approaches. The agreement between the present results and experimental data is fairly good.