Relativistic nucleon\u2013nucleon potentials in a spin-dependent three-dimensional approach

M R Hadizadeh,F Nazari,M Radin

doi:10.1038/s41598-021-96924-1

Abstract

The matrix elements of relativistic nucleon–nucleon (NN) potentials are calculated directly from the nonrelativistic potentials as a function of relative NN momentum vectors, without a partial wave decomposition. To this aim, the quadratic operator relation between the relativistic and nonrelativistic NN potentials is formulated in momentum-helicity basis states. It leads to a single integral equation for the two-nucleon (2N) spin-singlet state, and four coupled integral equations for two-nucleon spin-triplet states, which are solved by an iterative method. Our numerical analysis indicates that the relativistic NN potential obtained using CD-Bonn potential reproduces the deuteron binding energy and neutron-proton elastic scattering differential and total cross-sections with high accuracy.

Highlights

The matrix elements of relativistic nucleon–nucleon (NN) potentials are calculated directly from the nonrelativistic potentials as a function of relative NN momentum vectors, without a partial wave decomposition
The input relativistic NN potentials can be obtained from the nonrelativistic potentials by solving a quadratic equation, using an iterative scheme proposed by Kamada and Glöckle[9]
In the “Relativistic NN potentials in a momentum helicity representation” section, we present the 3D formalism for the relationship between relativistic and nonrelativistic NN potentials

Summary

Introduction

The matrix elements of relativistic nucleon–nucleon (NN) potentials are calculated directly from the nonrelativistic potentials as a function of relative NN momentum vectors, without a partial wave decomposition. The single and coupled integral equations are solved using the mentioned iterative scheme, and the matrix elements of relativistic NN potentials are obtained from CD-Bonn p otential[12].

Results

Conclusion