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Extra resources for A system of physical chemistry. Kinetics
The anisotropy in the potential that is expected from the different molecular orientations during the collision is evidently not too pronounced, however, since otherwise the secondary rainbow structure would not be observable. The superimposed fine structure, on the other hand, is washed out by the anisotropy and by the occurrence of inelastic processes. If a realistic estimate is made for rm, a Morse potential can be used to obtain agreement between calculated + and experimental rainbow structures.
Scattering of Identical Particles E. Semiclassical Inversion Procedures References 553 557 557 559 569 570 571 572 572 573 575 593 595 601 601 602 617 621 622 625 I. Introduction From the analysis of transport properties in gases it is well known that the elastic scattering of atoms and molecules may be described, to a large extent, by classical mechanics alone [see, for example, Hirschfelder (1954)]. Molecular beam investigations, however, show that a number of important features of the scattering behavior require a quantum mechanical treatment (Pauly and Toennies, 1965, 1968; Bernstein, 1966; Bernstein and Muckermann, 1967; Beck, 1970; Massey et al, 1971).
Table I gives a survey of the reduced notation used in the following sections. II. Particle Scattering in Classical Mechanics* A. BASIC FORMULAS FOR SPHERICALLY SYMMETRIC POTENTIALS The two-particle collision problem is formally reduced to a one-particle problem by a transformation to the center-of-mass system. If r ( and p t are the position and momentum of particle / (i= 1, 2) before the collision and r/ and p / are the position and momentum after the collision, we introduce the position and momentum of the center of mass (r 0 , p 0) and the position of one particle with respect to the other and the momentum of the relative motion (r, p) as r 0 = (m^ + m2 r 2 ) / M , p 0 = p1 + r = rx - r 2 , ρ=(πι2/Μ p2 )p, - (mJM )p 2 where M is the total mass m1 + m2.