Four-Nucleon Forces in Ab Initio Nuclear Structure

In recent years, there has been tremendous progress in the construction and application of nuclear inter- actions from chiral effective field theory (EFT). Today, two- and three-nucleon interactions are routinely used in many-body calculations, reaching unprecedented quality in the ab initio description of nuclei. Al- though four-nucleon (4N) forces have been constructed from chiral EFT, they have never been investigated systematically in finite nuclei. This works aims at the inclusion of explicit 4N forces in many-body nuclear structure calculations. We investigate two different interactions, a simple 4N contact interaction and the complete leading order of the chiral 4N interaction. To include these interactions, we develop a partial-wave decomposition (PWD) and represent the 4N interactions in a basis of harmonic oscillator states using Jacobi coordinates. Especially the PWD for the chiral 4N interaction requires significant effort, much more than its three-nucleon coun- terpart, and constitutes the main part of this work. However, the endeavor is worthwhile, as it makes the consistent inclusion of 4N interaction in many-body calculations possible. The inclusion of the 4N contact interaction and its PWD is simpler than in the chiral case. It, neverthe- less, yields valuable insights into the effect of 4N interactions in nuclear structure calculations. Two- and three- body interactions from chiral EFT often predict an overbinding of nuclei, and root-mean-square radii are much smaller than the experimental results. We, therefore, focus on ground-state energies and charge radii with the contact interaction. Our results clearly show that the employed contact interaction is not able to mitigate this effect. It does have a sizable effect on radii, but improving the agreement of charge radii with experiment yields unphysical binding energies. Furthermore, the contact interaction is compared to the effect of neglected many-body contributions, which are induced by transforming the two-and three- body interactions using the similarity renormalization group. These neglected contributions scale strongly with the number of nucleons, and we find the contact interaction to have a far gentler scaling. For the first time, we present ground-state energies calculated using a partial-wave decomposed repre- sentation of the chiral 4N interaction. Although we cannot achieve model-space convergence due to the computational cost of the PWD, our analysis strongly indicates that the order of magnitude of the effect of the 4N force is correctly reflected even in small model spaces. Overall, we find the effect of the chiral 4N interaction to be extremely small in all investigated nuclei, yielding contributions below 1% of the binding energy in all cases and even smaller effects in light nuclei. We conclude that, in the foreseeable future, the chiral 4N interaction has no relevance for ab initio descriptions of nuclei based on typical chiral interactions