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

Using an angular-momentum-projected single-particle basis, a proton-neutron quasiparticle random-phase approximation approach is used to study the 2νββ 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 β decay process are both spherical, both deformed, or one spherical and the other deformed can be treated through a single formalism. Dependence of single β- and β+ strength distribution on atomic mass number and nuclear deformation is analyzed. For the double β 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