Within the nonrelativistic approximation the authors discuss three different mechanisms for the capture of a light particle from a bare heavy nucleus by another bare heavy nucleus which is incident with a very high relative velocity. The emphasis is on physical interpretation. For each mechanism a "physical" (i.e., more readily comprehensible) derivation is given of the asymptotic form of the total cross section, and a comparison is made of the relative importance of the different mechanisms in the case of electron capture from hydrogenlike "atoms." (Electron capture is normally referred to as charge transfer). The first mechanism is knock-on capture, where the two nuclei have equal masses and simply switch places. The second mechanism is radiative capture, which occurs with the emission of a photon. The third mechanism, which is perhaps the most interesting one, is double scattering, first suggested within the framework of classical mechanics by Thomas in 1927. In this mechanism the light particle undergoes two collisions, the first with the incident nucleus, and the second with the target nucleus; the light particle finally has almost the same velocity as the incident nucleus and therefore has a reasonable probability of being captured. The capture process in the asymptotic domain is a fascinating one theoretically since radiative capture can dominate over nonradiative capture; what is perhaps more remarkable is that for nonradiative capture integrated over the forward direction the second Born contribution dominates over the first in the asymptotic limit. For the capture of an electron bound in a high Rydberg state, capture via the knock-on the double scattering mechanisms are describable classically (Thomas' result becomes exact!) and (near the forward direction) the second Born(Born again) term dominates over the first at much lower energy. (Changing only the notation and the kinematics, the results can be used to study mass transfer processes in which one of a massive gravitationally pound pair of astrophysical objects is captured by a third massive object). A number of results for capture into a true bound state can be readily carried over to "capture to the continuum," with the electron emerging with a small positive energy relative to the incident nucleus. An understanding of the asymptotic form of the capture cross section is of considerable interest in its own right; it may also be helpful in understanding the dynamics of the capture process in the medium velocity range where applications are important. At medium velocities electron capture is of interest in many areas of physics such as astrophysics, chemical physics, plasma physics, and atomic physics; it is also of practical interest, having applications in laser and fusion research.

DOI:https://doi.org/10.1103/RevModPhys.51.369