Asymptotics of phase and wave functions

TL;DR

This paper investigates the asymptotic behavior of wave and phase functions in nucleon-nucleon scattering, considering various potential singularities and providing numerical calculations for specific states using the Argonne v18 potential.

Contribution

It analyzes the asymptotics of wave functions near the origin for different potential types and computes phase and wave functions for specific nucleon-nucleon states.

Findings

Wave functions have complex asymptotics influenced by potential behavior near zero.

Numerical calculations for Argonne v18 potential match theoretical asymptotic predictions.

Different states exhibit distinct asymptotic behaviors based on potential singularity.

Abstract

For single and twochannel nucleon-nucleon scattering the asymptotic form of the phase function for r->0 were taken into account for the asymptotic behavior of the wave function. Asymptotics of the wave function will not r^(l+1), and will have a more complex view and be also determined by the behavior of the potential near the origin. Have examined the cases for nonsingular (weakly singular) and strongly singular potentials. Were the numerical calculations of phase, amplitude and wave functions for the nucleon-nucleon potential Argonne v18. Considered 1S0-, 3P0-, 3P1- states of the np- system.