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

Abstract

We study the double Gamow-Teller (DGT) strength distribution of ^{48}Ca 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 ββ (0νββ) decay. We find a simple relation between the centroid energy of the ^{48}Ca DGT giant resonance and the 0νββ 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 0νββ decay matrix element. The correlation, which originates on the dominant short-range character of both transitions, extends to heavier systems including several ββ 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 0νββ decay nuclear matrix elements.

Heavy-ion double-charge-exchange and its relation to neutrinoless double- β decay

“…[62], the nuclear matrix elements are computed by means of the microscopic Interacting Boson Model (IBM-2) formalism [63]. [64].…”

Loop-enhanced rate of neutrinoless double beta decay

“…(4) where Λ is, again, mainly determined by the largest mass in the loop-see Eq. (12). However, the neutrino mass m ν in Eq.…”

Double charge-exchange phonon states

“…Hence, CIB interactions will contribute to the quartic commutator in Eq. (9). In addition to that, we note that other types of CIB interactions are given by the operators T ij ≡ t(i) · t(j) − 3t z (i)t z (j), which is a tensor in isospin space, and also by s i s j T ij , where s i = 1 2 σ i , and by S ij T ij , where S ij is the tensor operator analogous to T ij but in spin-space.…”

“…Although many theoretical efforts have been devoted to studies of double β-decays, DGTR strengths corresponding to the double β-decays are still too small to be identified in these experiments. Recently, shell-model calculations were performed to study the DGTR of 48 Ti [9], and also Ti-isotopes [10]. At the same time, other DGTR strength distributions have been studied by using the sum rule approach [11][12][13][14], in order to establish a possible unit cross section of DGTR in comparison with the DIAS.…”