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

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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.