Low Velocity Inelastic Collisions

The probability that a low velocity collision be inelastic is shown to depend in a relatively simple manner upon three factors: the magnitude of the change in total internal energy, ΔE; the matrix element, with respect to the initial and final states, of the interaction energy at the closest distance of approach, W12; and the "time of collision," τ, a function of the relative velocity and of the sharpness of the collision. An approximation to this probability is P=[2πW12/h τ (1+ε1βε2)e-ε3β]2 where β=2πτΔE/h and ε1, ε2, ε3 are nearly unity, their precise values depending upon the characteristics of the particular collision.