Improved convergence of scattering calculations in the oscillator representation

TL;DR

This paper introduces a hybrid oscillator and grid representation for solving the Schrödinger equation in scattering problems, significantly improving convergence over existing methods like JM-ECS.

Contribution

A novel hybrid approach coupling oscillator eigenstates with finite difference grids using a high-order asymptotic formula for better convergence in scattering calculations.

Findings

Significant convergence improvement over JM-ECS method.

Effective in various physics scattering problems.

Uses a large number of oscillator states for accuracy.

Abstract

The Schr\"odinger equation for two and tree-body problems is solved for scattering states in a hybrid representation where solutions are expanded in the eigenstates of the harmonic oscillator in the interaction region and on a finite difference grid in the near-- and far--field. The two representations are coupled through a high--order asymptotic formula that takes into account the function values and the third derivative in the classical turning points. For various examples the convergence is analyzed for various physics problems that use an expansion in a large number of oscillator states. The results show significant improvement over the JM-ECS method [Bidasyuk et al, Phys. Rev. C 82, 064603 (2010)].