Collision Trajectories for Inverse Power Intermolecular Potentials

If −cr−n is the intermolecular potential for separation r, b the classical collision parameter, μ the reduced mass, g the relative velocity before collision, and χ the angle of deflection of the relative velocity due to collision, it is found that χ=− ∑ t=1∞Γ(12nt+12)Γ(12)t!Γ(12nt−t+1)[2cμg2bn]t,the series converging only for b > b0, where μg2b0n = ½nn/2(n − 2)1−n/2, this being true both for c positive (attractive potentials) and c negative (repulsive potential). This result makes it possible to calculate, by analytic integrations, the contributions to the elementary collision integrals from the range b > b0. It also simplifies greatly the calculation of the collision integrals for both attractive and repulsive inverse power potentials which can be evaluated entirely by analytic means, for n > 2.