Calculation of the neutrinoless double- β decay matrix element within the realistic shell model

Abstract

We approach the calculation of the nuclear matrix element of the neutrinoless double-β decay process, considering the light-neutrino-exchange channel, by way of the realistic shell model. To this end, we start from a realistic nucleon-nucleon potential and then derive the effective shellmodel Hamiltonian and 0νββ-decay operator within the many-body perturbation theory. We focus on investigating the perturbative properties of the effective shell-model operator of such a decay process, aiming to establish the degree of reliability of our predictions. The contributions of the socalled short-range correlations and of the correction of Pauli-principle violations to the effective shellmodel operator, the latter introduced in many-valence nucleon systems, are also taken into account. The subjects of our study are a few candidates to the 0νββ-decay detection, in a mass interval ranging from A = 48 up to A = 136, whose spin-and spin-isospin-dependent decay properties we have studied in previous works. Our results evidence that the effect of the renormalization of the 0νββ-beta decay operator on the values of the nuclear matrix elements is less relevant than what we have obtained in previous studies of the effective single-body GT transitions operating also in the two neutrinos double-beta decay PACS numbers: 21.60.Cs, 21.30.Fe, 27.60.+j, 23.40-s 1/2 −1/2 . Moreover, combining the calculated nuclear structure factor with neutrino mixing parameters [10] and limits on m ν from current experiments, one may extract an estimation of the half-life an experiment should measure in order to be sensitive to a particular value of the neutrino effective mass [1]. All the above considerations evidence that reliable calculations of M 0ν are of paramount importance, and, currently, various nuclear structure models arXiv:2001.00890v2 [nucl-th] 3 Apr 2020

Perturbative Approach to Effective Shell-Model Hamiltonians and Operators

“…. (89) The minus sign in front is due to the fact that n h = n l = 1 and that an extra phase factor (−1) n ph is needed for the total number of cuts of particle-hole pairs (n ph ) [51], since we have to cut the inner loop to factorize the diagram.…”

“…Reference [89] reports on the calculation of the 0νββ-decay NME for 48 Ca, 76 Ge, 82 Se, 130 Te, and 136 Xe in the framework of the realistic SM, where the H eff 's and 0νββ-decay effective operators are consistently derived starting from a realistic NN potential, the high-precision CD-Bonn potential [90].…”

“…Here we restrict ourselves to the results obtained in reference [89] for the heavy-mass nuclei around 132 Sn, 130 Te, and 136 Xe. At present, these nuclei are under investigation as 0νββ-decay candidates by some large experimental collaborations.…”

“…Before showing the results for the 0νββ NME obtained in reference [89], it is worth checking the reliability of the approach we have adopted. To this end, we present some results obtained from the calculation of quantities for which there exist experimental counterparts to compare with.…”

Weak Transitions in Light Nuclei

“…Ab initio studies in light nuclei allow us to carefully test many-body correlations and electroweak currents and serve as benchmark to approximated many-body methods currently employed to access heavier nuclear systems [30,31]. A study along these lines has been carried out recently in [32].…”