Calculation of the Two-body T-matrix in Configuration Space

TL;DR

This paper extends a spectral integral method to compute the two-body T-matrix in configuration space, maintaining efficiency and accuracy for simple and complex potentials, including those with large repulsive cores.

Contribution

The paper generalizes the spectral integral method to calculate the two-body T-matrix, addressing its increased complexity and demonstrating high accuracy for different potential types.

Findings

Achieves 7 significant figures accuracy for exponential potentials.

Accuracy decreases to 4 figures for large-core potentials, but improves with more support points.

Method maintains efficiency despite increased complexity of T-matrix calculation.

Abstract

A spectral integral method (IEM) for solving the two-body Schroedinger equation in configuration space is generalized to the calculation of the corresponding T-matrix. It is found that the desirable features of the IEM, such as the economy of mesh-points for a given required accuracy, are carried over also to the solution of the T-matrix. However the algorithm is considerably more complex, because the T-matrix is a function of two variables r and r', rather than only one variable r, and has a slope discontinuity at r=r'. For a simple exponential potential an accuracy of 7 significant figures is achieved, with the number N of Chebyshev support points in each partition equal to 17. For a potential with a large repulsive core, such as the potential between two He atoms, the accuracy decreases to 4 significant figures, but is restored to 7 if N is increased to 65.