Three-Nucleon Forces Through Normal-Ordered Approximations

Abstract

Three-body forces have long been known to play an important role in nuclear physics. However, fully including such interactions in ab-initio methods is computationally expensive and not feasible for larger nuclei. As an alternative, approximations based on normal-ordering with respect to a Fermi state of the nucleus can be used. In this framework part of the three-body interaction can be expressed as lower order interactions, which can be included without increasing the computational complexity. This thesis provides a full derivation of the normal-ordered two-body (NO2B) approximation for closed-shell nuclei. In addition, a simple implementation of this method is described. This is then used to calculate ground states of helium-4 in small model spaces, which are compared to the corresponding calculations with full three-body forces. The results show a relative error of less than 1.5%, in line with earlier studies.