Calculation of the neutrinoless double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay matrix element within the realistic shell model
L. Coraggio, A. Gargano, N. Itaco, R. Mancino, F. Nowacki
Abstract
We approach the calculation of the nuclear matrix element of the neutrinoless double-$\ensuremath{\beta}$ 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 shell-model Hamiltonian and $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ 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 so-called short-range correlations and of the correction of Pauli-principle violations to the effective shell-model 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 $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ 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 provide evidence that the effect of the renormalization of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-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 Gamow-Teller transitions operating also in the two-neutrino double-$\ensuremath{\beta}$ decay