Ab Initio Description of Light Nuclei via No-Core Shell Model: Conventional and Less Conventional Approaches

In the last years, several methods have been developed in order to solve the nuclear many-body problem in light nuclei (i.e., starting from realistic two- and three-body interactions). While less accurate than the other approaches, the no-core shell model (NCSM) has the advantage that it can be pushed to medium-mass nuclei. NCSM is built on the successes of the interacting shell model, which provides excellent description for p- and sd-shell nuclei in restricted model spaces using phenomenologically adjusted interactions. However, aside from the fact that all nucleons are kept active in NCSM in order to preserve the translational invariance, the main difference with respect to the traditional approach is that in the NCSM one starts from the bare two- and three-nucleon forces and constructs via a unitary transformation an effective interaction suitable for a diagonalization in a restricted many-body space. In this talk, I will review the NCSM, as well as applications to the description of the low-lying spectrum and other properties of light nuclei. Moreover, I will present a novel approach to the derivation of effective operators, based on the general principles of the effective field theories (EFTs). This new method has the advantage that does not require the use of the unitary transformation, which presents shortcomings that become more evident in the context of the renormalization of long-range operators discussed in this talk. To illustrate the new approach, I will present results for the first $(0^+;0)$ excited state in $^4$He and ground-state energy of $^6$Li.