It is possible to apply statistical methods to the calculation of nuclear processes provided that the energies involved are large in comparison with the lowest excitation energies of nuclei. Expressions are obtained for the emission probability of neutrons or charged particles by highly excited heavy nuclei. These expressions are built up in a similar way to the formula for the probability of evaporation of a particle from a body at low temperatures. In applying it to the impact of high energy neutrons on heavy nuclei, the mean energy loss per impact turns out to be $E[1\ensuremath{-}2{(\frac{a}{E})}^{\frac{1}{2}}]$ where $E$ is the energy of the incident neutrons and $a$ is dependent on the nuclear structure; we can put approximately $a\ensuremath{\sim}0.05\ensuremath{-}0.2$ MV. The energy distribution of the scattered neutrons is approximately a Maxwellian one with a mean energy of $2{(\mathrm{aE})}^{\frac{1}{2}}$.