It is well known that the Glauber approximation for scattering amplitudes is obtained by applying the eikonal approximation to the Fourier transform of the transition operator. The eikonal approximation can also be applied to the coupled equations of scattering obtained by the expansion of the state function in terms of a suitable set of functions. The scattering amplitude can thus be obtained by solving the set of eikonal coupled equations. The latter approach is analyzed for a special class of channel-coupling potentials. The first-order approximation to the derived eikonal coupled equations is the eikonal Born approximation. Numerical illustrations in this approximation are given for the 1s-2s and 1s-2p excitations of hydrogen atoms by electron and positron impact. The results are compared with those obtained in the Glauber eikonal approximation and with experimental measurements.
R. T. Ling et al., "Eikonal Approximation for Coupled Equations for Multichannel Scattering," Physical Review A, vol. 6, no. 2, pp. 650-658, American Physical Society (APS), Aug 1972.
The definitive version is available at https://doi.org/10.1103/PhysRevA.6.650
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© 1972 American Physical Society (APS), All rights reserved.