If −cr−nis the intermolecular potential for separationr, bthe classical collision parameter, &mgr; the reduced mass,gthe relative velocity before collision, and &khgr; the angle of deflection of the relative velocity due to collision, it is found that&khgr;=−t=1∞&Ggr;(12nt+12)&Ggr;(12)t!&Ggr;(12nt−t+1)2c&mgr;g2bnt,the series converging only forb>b0, where &mgr;g2b0n= ½nn/2(n− 2)1−n/2, this being true both forcpositive (attractive potentials) andcnegative (repulsive potential). This result makes it possible to calculate, by analytic integrations, the contributions to the elementary collision integrals from the rangeb>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, forn> 2.