Analytic Representation of Cross-Section Data

Abstract

In many applications we use cross sections for electronic and atomic collisions as input data in certain calculations. To take a simple example, we evaluate the rate for a thermal chemical reaction by averaging the product of the pertinent cross section and the collision speed over the Maxwell distribution. The procedure is easy and transparent, if the cross section as a function of the collision speed is given in an analytical expression. The merit of analytic expressions is greater when an application requires the use of cross sections in more complicated calculations. For instance, in studies of electron transport phenomena, we may numerically solve a Boltzmann or Fokker-Planck equation, which involves cross section as coefficients; alternatively, we may carry out a Monte Carlo simulation. Either method requires using cross-section values repeatedly, and therefore analytic expressions for the cross sections involved are helpful. 91 refs., 7 figs., 1 tab.