A stable linear reference potential algorithm for solution of the quantum close-coupled equations in molecular scattering theory

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Abstract
We show how the linear reference potential method for solution of the close-coupled equations, which arise in inelastic scattering theory, can be reformulated in terms of an ‘‘imbedding-type’’ propagator. Explicit expressions are given for the blocks of the propagator matrix in terms of Airy functions. By representing these functions in terms of moduli and phases, in both classically allowed and classically forbidden regions, one can evaluate the propagator without any numerical difficulty. The resulting algorithm is tested on a highly pathological problem—the rotationally inelastic scattering of a polar molecule by a spherical ion at extremely low kinetic energy—and found to be completely stable.