Double Gamow-Teller Transitions and its Relation to Neutrinoless ββ Decay

We study the double Gamow-Teller (DGT) strength distribution of Ca-48 with state-of-the-art large-scale nuclear shell model calculations. Our analysis shows that the centroid energy of the DGT giant resonance depends mostly on the isovector pairing interaction, while the resonance width is more sensitive to isoscalar pairing. Pairing correlations are also key in neutrinoless beta beta (0 nu beta beta) decay. We find a simple relation between the centroid energy of the Ca-48 DGT giant resonance and the 0 nu beta beta decay nuclear matrix element. More generally, we observe a very good linear correlation between the DGT transition to the ground state of the final nucleus and the 0 nu beta beta decay matrix element. The correlation, which originates on the dominant short-range character of both transitions, extends to heavier systems including several beta beta emitters and also holds in energy-density functional results. Our findings suggest that DGT experiments can be a very valuable tool to obtain information on the value of 0 nu beta beta decay nuclear matrix elements.