Momentum‐Transfer Theorem for Inelastic Processes

Recently it has been shown that for potential scattering, the well‐known optical theorem—relating the total cross section to the imaginary part of the forward scattering amplitude—can be generalized to yield a ``momentum‐transfer cross‐section theorem.'' The present paper further generalizes the previous potential scattering result. Specifically, it appears that the momentum‐transfer cross‐section theorem is valid also for many‐particle systems, wherein inelastic processes occur. Although this last assertion probably holds quite generally, a proof is given only for the collisions of electrons with atomic hydrogen. The proof takes into account electron indistinguishability, as well as the possibility that the incident electron ionizes the atom, but assumes the forces are not spin‐dependent.