Excitation of "atoms" by fast particles in the high-momentum-transfer limit

Several years ago Potapov showed that in the high-momentum-transfer limit the leading contribution to the differential cross section for excitation of hydrogen atoms by fast electrons comes from the second-Born term, and not the first-Born term, if the proton is treated as infinitely massive. In this paper further insight into the origin of this remarkable result is provided. I discuss, in the high-momentum-transfer limit, the excitation of an "atom" composed of two particles of arbitrary masses $m_1$ and $m_2$. In the case that $m_1=\infty$, a simple heuristic derivation of the second-Born differential cross section is given. For $m_1$ finite it is found that there are two competing mechanisms for producing excitation; one corresponds to the first-Born and the other to the second-Born term. Both the first- and second-Born terms have a "near singularity" at the "critical" mass $m_1=\infty$; these near singularities radically alter the asymptotic dependence of the matrix elements on the momentum transfer and cause the second-Born term to dominate over the first-Born term at the critical mass. Away from the critical mass, however, the second-Born term may not dominate over the first-Born term.