Study of the double Gamow-Teller transitions using the shell model approach

The double Gamow-Teller strength distributions in the lightest double beta-decay candidate ${}^{48}$Ca and its isotope ${}^{46}$Ca were calculated using the nuclear shell model by applying the single Gamow-Teller operator two times sequentially on the ground state of parent nucleus. The nuclear matrix element of the double Gamow-Teller transition from the ground state to the ground state that goes into the double beta decay calculation was shown as a small fraction of the total transition.