[en] An idealized model of nonreactive collinear C--B+A collisions has been developed for the calculation of the number of impacts and amount of vibration--translation energy exchange at each impact as functions of the mass distribution and the initial collision energy. The maximum number of impacts that a single collision can have is n*=90 degree/phi, where phi= tan/sup -1/ [m/sub B/(m/sub A/ + m/sub B/ + m/sub C/)/m/sub A/m/sub C]/sup ¹/₂/; for nonintegral values of 90 degree/phi, n* = [90 degree/phi, where the square brackets denote the algebraically largest integer which just exceeds the nonintegral value 90 degree/phi. The model is applied to the collinear collisions H--F+F, F--H+F, Cl--H+Cl, Br--H+Br, I--H+Cl, and several other hypothetical systems with particular emphasis on the dependence of energy exchange on the number of impacts. Comparison with exact trajectory calculations at high collision energies shows a diminished inelasticity as the result of repeated encounters between A and B in a single collision