Quadrupolar correlations and deformation effect on two-neutrino εβ+ and εε modes of 156Dy isotope

The two-neutrino positron double-? decay modes of 156Dy isotope are studied in the projected Hartree?Fock?Bogoliubov framework for the 0+ ? 0+ transition. Theoretically calculated half-lives of electron?positron conversion and double-electron capture modes are presented. The effect of the quadrupolar deformation on the nuclear transition matrix element M2? is also investigated.