We have developed a variable-spacing finite-difference algorithm that rapidly propagates the general solution of Schrödinger’s equation to large distances (whereupon it can be matched to asymptotic solutions, including the ionization channel, to extract the desired scattering quantities). The present algorithm, when compared to Poet’s corresponding fixed-spacing algorithm [R. Poet, J. Phys. B 13, 2995 (1980); S. Jones and A. T. Stelbovics, Phys. Rev. Lett. 84, 1878 (2000)], reduces storage by 98% and computation time by 99.98%. The method is applied to the Temkin-Poet electron-hydrogen model collision problem. Complete results (elastic, inelastic, and ionization) are obtained for low (17.6 eV), intermediate (27.2, 40.8, and 54.4 eV), and high (150 eV) impact energies.

• Received 22 May 2002

DOI:https://doi.org/10.1103/PhysRevA.66.032717