Calculation of phases of np- scattering for potentials Reid93 and Argonne v18 on the phase-function method

TL;DR

This paper applies the phase-functions method with various numerical techniques to calculate neutron-proton scattering phase shifts for Reid93 and Argonne v18 potentials, confirming the method's accuracy and potential for broader applications.

Contribution

It demonstrates the effectiveness of Runge-Kutta methods in solving phase equations for nucleon-nucleon scattering with modern potentials.

Findings

Numerical phase shifts agree with previous results.

Runge-Kutta methods are suitable for phase shift calculations.

The approach can be extended to mixed-channel scattering.

Abstract

A known phase-functions method has been considered for calculation of a single-channel nucleon-nucleon scattering. The phase shifts of np- scattering turn out for modern realistic phenomenological nucleon-nucleon potentials Reid93 but Argonne v18. Influence of choice of numeral method is explored on the decision of phase equation. For the decision of phase equation as differential equation of 1th order numeral methods are used: Euler method and Runge-Kutta methods 2-, 3-, 4- and 5th orders of exactness. Numerically calculated phase shifts of np- scattering for potentials Reid93 and Argonne v18 are in good agreement with the results obtained with the other methods of original works. Based on the known phases of scattering one can obtain the full amplitude, the full cross-section and the partial scattering amplitude accordingly. The used Runge-Kutta methods can be applied for finding of phases shifts of the mixed channels of nucleon-nucleon scattering.