A low momentum nucleon-nucleon (NN) potential $V_{low-k}$ is derived from meson exchange potentials by integrating out the model dependent high momentum modes of $V_{\mathrm{NN}}.$ The smooth and approximately unique $V_{low-k}$ is used as input for shell model calculations instead of the usual Brueckner G matrix. Such an approach eliminates the nuclear mass dependence of the input interaction one finds in the G matrix approach, allowing the same input interaction to be used in different nuclear regions. Shell model calculations of ${}^{18}\mathrm{O},$ ${}^{134}\mathrm{Te},$ and ${}^{135}\mathrm{I}$ using the same input $V_{low-k}$ have been performed. For cut-off momentum Λ in the vicinity of 2 ${\mathrm{fm}}^{\mathrm{-}1}$, our calculated low-lying spectra for these nuclei are in good agreement with experiments, and are weakly dependent on Λ.

We compute the energy per particle of infinite symmetric nuclear matter from chiral N${}^3\mathrm{LO}$ (next-to-next-to-next-to-leading order) two-body potentials plus N${}^2\mathrm{LO}$ three-body forces. The low-energy constants of the chiral three-nucleon force that cannot be constrained by two-body observables are fitted to reproduce the triton binding energy and the ${}^3\mathrm{H}$-${}^3\mathrm{He}$ Gamow-Teller transition matrix element. In this way, the saturation properties of nuclear matter are reproduced in a parameter-free approach. The equation of state is computed up to third order in many-body perturbation theory, with special emphasis on the role of the third-order particle-hole diagram. The dependence of these results on the cutoff scale and regulator function is studied. We find that the inclusion of three-nucleon forces consistent with the applied two-nucleon interaction leads to a reduced dependence on the choice of the regulator only for lower values of the cutoff.

The $B({E2;0\mathrm{}}^{+}\to 2^{+})$ values for the first $2^{+}$ excited states of neutron-rich ${}^{132,134,136}\mathrm{Te}$ have been measured using Coulomb excitation of radioactive ion beams. The $B\left(E2\mathrm{}\right)$ values obtained for ${}^{132,134}\mathrm{Te}$ are in excellent agreement with expectations based on the systematics of heavy stable Te isotopes, while that for ${}^{136}\mathrm{Te}$ is unexpectedly small. These results are discussed in terms of proton-neutron configuration mixing and shell-model calculations using realistic effective interactions.

We approach the calculation of the nuclear matrix element of the neutrinoless double-$\beta$ 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 $0\nu \beta \beta$ 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 $0\nu \beta \beta$ 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 $0\nu \beta \beta$-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-$\beta$ decay

We calculate the energy per particle in infinite neutron matter perturbatively using chiral N${}^3$LO (next-to-next-to-next-to-leading order) two-body potentials plus N${}^2$LO three-body forces. The cutoff dependence of the predictions is investigated by employing chiral interactions with different regulators. We find that the inclusion of three-nucleon forces, which are consistent with the applied two-nucleon interaction, leads to a strongly reduced regulator dependence of the results.