# Calculation of Relativistic Nucleon-Nucleon Potentials in Three-Dimensions

## TL;DR

This paper develops a three-dimensional method to calculate relativistic nucleon-nucleon potentials, accurately relating relativistic and non-relativistic interactions through integral equations and numerical solutions.

## Contribution

It introduces a novel three-dimensional approach for deriving relativistic nucleon-nucleon potentials from non-relativistic ones, using integral equations and iterative numerical methods.

## Key findings

- Relativistic potentials preserve two-nucleon observables with high accuracy.
- The method effectively relates relativistic and non-relativistic interactions.
- Numerical tests confirm the approach's validity.

## Abstract

In this paper, we have applied a three-dimensional approach for calculation of the relativistic nucleon-nucleon potential. The quadratic operator relation between the non-relativistic and the relativistic nucleon-nucleon interactions is formulated as a function of relative two-nucleon momentum vectors, which leads to a three-dimensional integral equation. The integral equation is solved by the iteration method, and the matrix elements of the relativistic potential are calculated from non-relativistic ones. Spin-independent Malfliet-Tjon potential is employed in the numerical calculations, and the numerical tests indicate that the two-nucleon observables calculated by the relativistic potential are preserved with high accuracy.