A new formulation of the electron multiplication factor in proportional counters

Staring from the kinetic theory of electrons in gases, a near semimicroscopic model of the electron multiplication through Townsend avalanches is developed. It allows to predict with much accuracy the gas electron multiplication factor in binary gas mixtures-filled proportional counters. The new formulation permits also to unify the previous formulae of William's and Sara and that of Diethorn. Moreover, it shows that the formulae of Diethorn and that of Zastawny are in fact only simple mathematical approximations straightforwardly derived from a more general model such as the one herein presented. Validation tests of this formula carried out on the basis of experimental gas gain measurements, showed a very good consistency. Generalization of the proposed formulation to other detection structures based on the same principle is finally discussed. (authors)