On the Evaluation of Rate Coefficients from Limited Cross‐Section Data

An analysis is presented of the error involved in calculating rate coefficients from cross‐section data in a limited energy range. For reactive cross sections of the form σ(E) = a(E—E*)n exp[—b(E—E*)], where E is the relative kinetic energy and E* is the threshold energy, it is shown that an upper bound on the error can readily be derived in terms of the parameters n, b, and E′—E*, where E′ is the largest kinetic energy for which σ(E) has been determined. For cross sections which can be represented by a polynomial of degree N in the range E* to E′, the m‐point Laguerre integration formula yields exact results for the rate coefficient for m≥½(N+2), and also provides the criterion for the required energy range E* to E′.