Abstract
The semi-classical solution of the three turning point scattering problem for a real potential is generalized to apply to scattering by a complex local optical potential. The new formula reduces to known results, which use the most external turning point only, in cases where there is very strong absorption inside the Coulomb barrier. In general there are two main corrections to the conventional formula: (i) the contribution to the S-matrix of the wave reflected at the Coulomb barrier is modified by the tunnel effect, (ii) the S-matrix has a contribution from a wave which passes inside the barrier and re-emerges. Interplay of these two contributions produce important interference effects in optical model angular distributions. Examples show that both corrections are important for α-scattering at intermediate energies. Some cases of heavy ion scattering have also been investigated. The corrections given in this paper were found to be unimportant in an example studied by Koeling and Malfliet, but noticeable in a case studied by Knoll and Schaeffer. Agreement between quantal calculations and the semi-classical results are excellent.
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