Noniterative Solutions of Integral Equations for Scattering. IV. Preliminary Calculations for Coupled Open Channels and Coupled Eigenvalue Problems

Abstract

The homogeneous integral solution formalism developed by Sams and Kouri is illustrated for coupled open channel scattering calculations and coupled eigenvalue calculations. This method for scattering calculations compares favorably, both in accuracy and in computation time required, with the Lester-Bernstein close coupling solution of the differential equations for scattering and the Johnson-Secrest amplitude density method. Preliminary results for coupled eigenvalue integral equations are also encouraging. A simple technique for applying the quantization condition in searching for the eigenvalues of coupled integral equations is presented, and is employed in the calculations reported. Example results are given for 16, 23, and 30 coupled scattering channels and for 1, 2, and 3, coupled integral eigenvalue equations.

Recursive generation of individual S-matrix elements: application to inelastic collisions

“…This model system contains a reasonable number of rotationally coupled states and will be seen to require a large number of grid points to obtain an accurate S-matrix element, so that it provides a good test of the viability of the approach. In addition, it has also been used previously to test several different approaches (Sams andKouri 1970, Johnson et a1 1967).…”

Comparison of numerical methods for solving the second-order differential equations of molecular scattering theory

“…The few comparisons which have been made [1][2][3][4] usually involved only two or a few methods. Sometimes the calculations were done on different computers, and possibly worst of all, the tests were done on simple model problems.…”