Eur. Phys. J. A (2017) 53: 18
https://doi.org/10.1140/epja/i2017-12209-6

Regular Article - Theoretical Physics

Calculation of relativistic nucleon-nucleon potentials in three dimensions

¹ Institute of Nuclear and Particle Physics and Department of Physics and Astronomy, Ohio University, 45701, Athens, OH, USA
² College of Science and Engineering, Central State University, 45384, Wilberforce, OH, USA
³ Department of Physics, K. N. Toosi University of Technology, P.O.Box 16315-1618, Tehran, Iran

^* e-mail: radin@kntu.ac.ir

Received: 29 November 2016
Accepted: 19 January 2017
Published online: 6 February 2017

Abstract

In this paper, we have applied a three-dimensional approach for the 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. The 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.