Renormalization of the Gamow-Teller operator within the realistic shell model

Abstract

In nuclear structure calculations, the choice of a limited model space, due to computational needs, leads to the necessity to renormalize the Hamiltonian as well as any transition operator. Here, we present a study of the renormalization procedure and effects of the Gamow-Teller operator within the framework of the realistic shell model. Our effective shell-model operators are obtained, starting from a realistic nucleon-nucleon potential, by way of the many-body perturbation theory in order to take into account the degrees of freedom that are not explicitly included in the chosen model space. The theoretical effective shell-model Hamiltonian and transition operators are then employed in shell-model calculations, whose results are compared with data of Gamow-Teller transition strengths and double-β half-lives for nuclei which are currently of interest for the detection of the neutrinoless double-β decay process, in a mass interval ranging from A = 48 up to A = 136. We show that effective operators are able to reproduce quantitatively the spectroscopic and decay properties without resorting to an empirical quenching neither of the axial coupling constant gA, nor of the spin and orbital gyromagnetic factors. This should assess the reliability of applying present theoretical tools to this problematic.

Realistic shell model and nuclei around 132Sn

“…As mentioned in the Introduction, we discuss here two cases, whose results have been partially reported in previous papers [10][11][12]. Our aim is to show the reliability of our approach as well as to illustrate some inconsistencies whose solution would require further investigations also from the experimental point of view.…”

“…The formalism to construct these operators has been developed by Suzuki and Okamoto [20], who have extended theQ boxplus-folded-diagram method developed for the Hamiltonian to this end. A description of our procedure to calculate the effective transition operators, based on Suzuki and Okamoto method, can be found in [12].…”

“…In Ref. [12] we have reported the Gamow-Teller strength distributions and the calculated nuclear matrix element of the two-neutrino double-β decay for 130 Te and compared them with the experimental data. As for the electromagnetic operators, the Gamow-Teller operator is It is shown that also the decay properties of this nucleus are very well reproduced by the theory, without resorting to an empirical quenching of the axial coupling constant g A .…”

“…In the present work, we report a few examples of our realistic shell-model calculations, which have partially discussed in previous papers [10][11][12]. In particular, we shall focus on very neutron-rich even-even tin isotopes with N > 82, from A = 134 to 140.…”

“…We will also discuss the spectroscopic properties of 130 Te, which as discussed above is a candidate for the observation of the zero-neutrino double-β decay. For this nucleus, whose β decay properties are shown in [12], we shall report the results of a more complete calculation, with effective transition operators derived within a microscopic approach consistent with that employed for the effective shell-model Hamiltonian. Our aim is, in fact, to evaluate the predictive power of our approach, without introducing any adjustable parameters, in order to verify the reliability of our predictions for still unknown quantities, such as the nuclear matrix element involved in the neutrinoless double-β decay.…”