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

TL;DR

This paper introduces a new normal-ordering framework for three-nucleon interactions that enables more accurate ab initio calculations of heavy nuclei by avoiding basis truncation limitations.

Contribution

A novel normal-ordering method in a Jacobi basis that improves the treatment of 3N interactions in heavy nuclei calculations.

Findings

Accurate ground-state energies for heavy nuclei like $^{132}$Sn and $^{208}$Pb.

Benchmarking shows improved results over traditional methods.

Framework effectively handles 3N interactions without large basis truncations.

Abstract

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 \textit{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 $^{132}$Sn and $^{208}$Pb.