Realistic shell-model calculations of the 2νββ nuclear matrix elements and the role of the shell structure in intermediate states

Abstract

We discuss two conditions needed for the correct computation of the 2νββ nuclear matrix elements within the realistic shell-model framework. An algorithm in which intermediate states are treated based on Whitehead's moment method is inspected by taking examples of the double GT + transitions 36 Ar → 36 S, 54 Fe → 54 Cr and 58 Ni → 58 Fe. This algorithm yields rapid convergence on the 2νββ matrix elements, even when neither the relevant GT + nor GT − strength distribution is convergent. A significant role of the shell structure is pointed out, which makes the 2νββ matrix elements highly dominated by the low-lying intermediate states. Experimental information of the low-lying GT ± strengths is strongly desired. Half-lives of T 1 2 2ν ( EC/EC; 36 Ar → 36 S ) = 1.7 × 10 29 yr , T 1 2 2ν ( EC/EC; 54 Fe → 54 Cr ) = 1.5 × 10 27 yr T 1 2 2ν ( EC/EC; 58 Ni → 58 Fe ) = 6.1 × 10 24 yr and T 1 2 2ν (β + / EC; 58 Ni → 58 Fe ) = 8.6 × 10 25 yr are obtained from the present realistic shell-model calculation of the nuclear matrix elements.