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In an extension of previous work on the theory of statistical cross sections model calculations have been performed in the presence of weakly absorbing channels, a case which is of particular interest in applied work involving neutron capture or neutron scattering at low energies. Improved formulas for calculating the elastic enhancement factor and compound nucleus cross sections are presented. In our model calculations we find that the factorization condition for cross sections is not satisfied in cases where a few strongly and many weakly absorbing channels are mixed. However, even in these extreme cases, the formulas provide a good description of the computer-generated cross sections involving at least one strong channel. In addition, the structure of the formula for the elastic enhancement factor has been chosen so as to reproduce all known limiting values and to describe cases where many weakly absorbing channels contribute.

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