Calculation of the two-body scattering K-matrix in configuration space by an adaptive spectral method

Abstract

A spectral integral method (IEM) for solving the two-body, one-variable Lippmann–Schwinger equation for the wavefunction in configuration space is generalized to the case of the two-variable scattering K-matrix. The main difficulty is that in this case the driving term of the integral equation is discontinuous. 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 this case even though the result is also discontinuous. The main innovation is a judicious choice of the partitions in coordinate space, plus a new recursion relation forward and backward to the point of discontinuity. For a simple exponential potential an accuracy of 7 significant figures is achieved for the K-matrix, 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, an accuracy of 7 significant figures requires that N is increased to 65 support points per partition.