Normal ordering of three-nucleon interactions for ab initio calculations of heavy nuclei

Three-nucleon (3N) interactions are key for an accurate solution of the nuclear many-body problem. However, fully taking into account 3N forces constitutes a computational challenge and hence approximate treatments are commonly employed. The method of normal ordering has proven to be a powerful tool that allows to systematically include 3N interactions in an efficient way, but traditional normal-ordering frameworks require the representation of 3N interactions in a large single-particle basis, typically necessitating a truncation of 3N matrix elements. While this truncation has only a minor impact for light and medium-mass nuclei, its effects become sizable for heavier systems and hence limit the scope of ab initio calculations. In this work, we present a novel normal-ordering framework that allows to circumvent this limitation by performing the normal ordering directly in a Jacobi basis. We discuss in detail the new framework, benchmark it against established results, and present calculations for ground-state energies and charge radii of heavy nuclei, such as 132Sn and 208Pb.

Automated summary

Three-nucleon (3N) interactions are essential for accurately solving the nuclear many-body problem, but accurately considering these forces is computationally challenging, so approximate treatments are often used. The method of normal ordering provides a powerful tool for including 3N interactions systematically and efficiently, but traditional frameworks require a large single-particle basis, often leading to truncation of 3N matrix elements. This limitation is overcome by a novel normal-ordering framework performed directly in a Jacobi basis, allowing for calculations of ground-state energies and charge radii of heavy nuclei.