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.

We report on the calculation of Gamow-Teller and double-β decay properties for nuclei around 132 Sn within the framework of the realistic shell model. The effective shell-model Hamiltonian and Gamow-Teller transition operator are derived by way of many-body perturbation theory, without resorting to empirical effective quenching factor for the Gamow-Teller operator. The results are then compared with the available experimental data, in order to establish the reliability of our approach. This is a mandatory step, before we apply the same methodology, in forthcoming studies, to the calculation of the neutrinoless double-β decay nuclear matrix element for nuclei that are currently considered among the best candidates for the detection of this process.

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The structure of neutron-rich isotopes 60Cr and 62Cr was studied via proton inelastic scattering in inverse kinematics. The deformation lengths (delta) for 60Cr and 62Cr were extracted as 1.12(16) and 1.36(14) fm, respectively, providing evidence for enhanced collectivity in these nuclei. An excited state at 1180(10) keV in 62Cr was identified for the first time. We adopted 4;{+} as its spin and parity, leading to the rapid increase of the Ex(4;{+})/E_{x}(2;{+}) ratio, which indicates the development of large deformation in 62Cr near N=40. Importance of the admixture of the gd-shell component above N=40 is also discussed by comparing with a modern shell model calculation.

Extensions of the eikonal approximation to low energy (20 MeV/nucleon typically) are studied. The relation between the dynamical eikonal approximation (DEA) and the continuum-discretized coupled-channels method with the eikonal approximation (E-CDCC) is discussed. When Coulomb interaction is artificially turned off, DEA and E-CDCC are shown to give the same breakup cross section, within 3% error, of 15 C on 208 Pb at 20 MeV/nucleon. When the Coulomb interaction is included, the difference is appreciable and none of these models agrees with full CDCC calculations. An empirical correction significantly reduces this difference. In addition, E-CDCC has a convergence problem. By including a quantum-mechanical correction to E-CDCC for lower partial waves between 15 C and 208 Pb, this problem is resolved and the result perfectly reproduces full CDCC calculations at a lower computational cost.