A Semiempirical Expression for the First Townsend Coefficient of Molecular Gases

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Abstract
The general utility of an approximate expression for the first Townsend coefficient of a gas, derived several years ago by Druyvesteyn and Penning, has been tested by introducing into the theoretical treatment somewhat more realistic assumptions regarding the relevant scattering cross sections of the gas molecule. It has been demonstrated by numerical calculations that the functional dependence of the Townsend α upon the electric field and the gas pressure is, within certain limits, insensitive to the assumed energy dependence of the elastic and inelastic cross sections. The functional form of the inelastic cross section does, however, influence the way in which the ionization energy of the gas molecule enters in the exponential part of the expression.