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A modified derivation of the Wiener-Hopf solution of Milne's problem is given in a form suitable for application to problems in the theory of neutron diffusion.

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A general formula is developed for the probability of nuclear processes with particular consideration of resonance ()2). The dependence of the cross section on the energy of the incident particle can be divided into two parts: Firstly, the dependence over energy regions small compared to nuclear energies, and secondly that over large energy regions, of the order of a million volts or more. The first dependence is completely given by the resonance formula; 'The width would be smaller for charged particles of "medium" energy, i.e. , such energy that the penetrability of the Coulomb potential barrier is small compared to unity but still large enough to make the disintegration observable. We shall come back to this case in $10.