I. INTRODUCTION It has long been known that at high energies, particle capture (also called particle or mass transfer or exchange) is dominated by classical kinematics. As a fundamental three- body process it has been much studied in both experiment and theory [1–4]. In 1927 L.H. Thomas [5] did a theoretical analysis of the experiments of Rutherford, and especially G.H. Henderson [6], in which energetic alpha particles captured an electron as they passed through several different media, emerging as He + ions. We denote the generic process 1 + (2 , 3) → (1 , 2) + 3 , and “high energy” means that the energy of the incident particle 1 is large compared with the binding energy of particle 2 to either the initial nucleus 3 or the final nucleus 1. Thus, without loss of significance we can consider the transferred particle 2 to be initially at rest with respect to the nucleus 3, and we define “capture” to mean that 2 emerges from the collision with zero velocity with respect to the scattered incident particle 1, i.e. they move off with identical speeds and directions. The nature of the interactions between the particles, generally Coulombic, is not important in our considerations, so we consider only hard contact collisions. Conservation of overall energy and momentum forbids the capture process to take place with only a single collision (except in the case where 1 and 3 have exactly the same mass and 1 collides head-on with 3). In the case Thomas considered, there are two collisions: In the first, particle 1 (the alpha particle) collides with the bound particle 2 (the electron). This collision brings the electron from rest to the speed needed for capture, but its direction is wrong. The electron then collides essentially elastically with the nucleus 3 to which it was bound, changing its direction to parallel that of the recoiling particle 1. The scattering angle of particle 1 is called the “Thomas angle” and is given by ( m$_{2}$/m$_{1}$ ) sin 60 $^{◦}$. In the most studied case, protons on hydrogen, this is 0.472 mrad. We call this scenario “Thomas process A.” Logically (but not necessarily physically) two other double collision processes are con- ceivable. In scenario “Thomas process B” the first collision between 1 and 2 brings particle 2 to the necessary final speed. Particle 1 then collides with particle 3 and has its direction changed to enable capture of 2. In scenario “Thomas process C” the first collision is between particles 1 and 3. Recoiling particle 3 then collides with particle 2. These three possibilities are shown schematically in Fig. 1. Note that in all three cases, the kinematics are fixed 2