Calculation of Chemical Reaction Probabilities from Elastic Scattering Data

Abstract

We discuss the validity of the expression $$P_R{\text{(E,b)=1−[σ}}_{\mathrm{obs}}{\mathrm{(E,\chi )/\sigma }}_0\mathrm{(E,\chi )]}$$ previously used in reactive systems of the kind A+BC→AB+C to evaluate the probability of reaction P_R for given relative kinetic energy E and impact parameter b. The nonreactive differential scattering cross section σ_obs(E, χ) is derived from measurements as a function of the relative scattering angle χ and the elastic scattering cross section σ₀(E, χ) is obtained from an exp−6 potential made to fit the observed scattering in angular regions apparently unaffected by reaction, as the rainbow region in some examples. By using an optical model and assuming the validity of a semiclassical description, we show that this expression holds whenever $${\mathrm{|\; dP}}_R{\text{/db |≪2k(π−χ)[1−P}}_R\mathrm{(E,b)];\hspace{0.17em}\hspace{0.17em}E=}\frac{1}{2}{\mathrm{\mu k}}^2{\hslash }^2.$$ The simple expression for the probability of reaction is also shown to be approximately valid in a first‐order distorted wave approximation and random phase approximation for σ₀(E, χ).