Realistic shell model calculation of 2νββ nuclear matrix elements and role of shell structure in intermediate states

We discuss two conditions needed for correct computation of 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 36Ar → 36S, 54Fe → 54Cr and 58Ni → 58Fe. This algorithm yields rapid convergence on the 2νββ matrix-elements, even when neither 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 lowlying intermediate states. Experimental information of the low-lying GT strengths is strongly desired. Half-lives of T 2ν 1/2(EC/EC; 36Ar → 36S) = 1.7 × 1029yr, T 2ν 1/2(EC/EC; 54Fe → 54Cr) = 1.5 × 1027yr, T 2ν 1/2(EC/EC; 58Ni → 58Fe) = 6.1 × 1024yr and T 2ν 1/2(β +/EC; 58Ni → 58Fe) = 8.6×1025yr are obtained from the present realistic shell-model calculation of the nuclear matrix-elements.