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.

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.

We calculate the nuclear and neutron matter equations of state from microscopic nuclear forces at different orders in chiral effective field theory and with varying momentum-space cutoff scales. We focus attention on how the order-by-order convergence depends on the choice of resolution scale and the implications for theoretical uncertainty estimates on the isospin asymmetry energy. Specifically we study the equations of state using consistent NLO and ${\mathrm{N}}^2\mathrm{LO}$ (next-to-next-to-leading order) chiral potentials where the low-energy constants $c_D$ and $c_E$ associated with contact vertices in the ${\mathrm{N}}^2\mathrm{LO}$ chiral three-nucleon force are fitted to reproduce the binding energies of ${}^3\text{H}$ and ${}^3\text{He}$ as well as the beta-decay lifetime of ${}^3\text{H}$. At these low orders in the chiral expansion there is little sign of convergence, while an exploratory study employing the ${\mathrm{N}}^3\mathrm{LO}$ two-nucleon force together with the ${\mathrm{N}}^2\mathrm{LO}$ three-nucleon force give first indications for (slow) convergence with low-cutoff potentials and poor convergence with higher-cutoff potentials. The consistent NLO and ${\mathrm{N}}^2\mathrm{LO}$ potentials described in the present work provide the basis for estimating theoretical uncertainties associated with the order-by-order convergence of nuclear many-body calculations in chiral effective field theory.