3H and 3He calculations without angular momentum decomposition

TL;DR

This paper presents a novel three-dimensional formalism for calculating the bound states of three nucleons without angular momentum decomposition, including Coulomb effects, and compares results for helium-3 and triton.

Contribution

It introduces the first 3D calculations of helium-3 with Coulomb interaction and provides matrix elements relevant for beta decay, using NNLO nuclear forces.

Findings

3D results for $^{3}$He and $^{3}$H are compared, including Coulomb effects.

Matrix elements for beta decay operators are computed.

The approach avoids angular momentum decomposition, simplifying calculations.

Abstract

Results for the three nucleon (3N) bound state carried out using the "three dimensional" (3D) formalism are presented. In this approach calculations are performed without the use of angular momentum decomposition and instead rely directly on the 3D degrees of freedom of the nucleons. In this paper, for the first time, 3D results for $^{3}$He bound state with the inclusion of the screened Coulomb potential are compared to $^{3}$H calculations. Additionally, using these results, matrix elements of simple current operators related to the description of beta decay of the triton are given. All computations are carried out using the first generation of NNLO two nucleon (2N) and 3N forces from the Bochum - Bonn group.