A semi-microscopic derivation of gas gain formula for proportional counters

Using the microscopic definition of the Townsend coefficient and based on theoretical considerations related to the physical behaviour of electrons in gases in conjunction with a set of empirical results, a semi-microscopic formula of α/N, the first Townsend coefficient to gas density ratio, is developed in the form α/N=KS exp[−(S0/S)1+m], where S=E/N is the electric field strength to gas density ratio, and K, S0 and m (0≤m≤1) characterize the gaseous medium. It is shown that when m=0 the α/N formula reduces to the product of the analytical forms suggested by Diethorn as well as Williams and Sara. Moreover, it is shown that Diethorn and Zastawny formulae are simply deduced, respectively, as the first- and the second-order expansions of the combined formula. Applicability of the obtained gas gain formula for different sets of experimental gas gain data bring out a good consistency of the proposed gas amplification model.