Development of a semi-empirical expression for light gain factors in gas scintillation proportional counters

An attempt is made to develop a semi-empirical expression for light gain factors in single wire anode (SWA) gas scintillation proportional counters (GSPC) as a function of various other counter parameters like operating voltage, anode and cathode radii, filling gas mixture and its pressure. Experimental data of charge gain and light gain factors has been taken from four GSPCs having anode diameters ranging from 25 μm to 1.7 mm and operated with Ar or Ar + 2.5% N2 mixture. First the quality of our experimental data has been investigated by fitting the values of charge gain factors from one of the four GSPCs to four different semi-empirical expressions selected from the literature which have been developed for charge gain factors in ordinary ionization proportional counters and which are suitable for experimental verification. Subsequently, assuming appropriate functional forms of electron excitation and ionization coefficients and using derived or assumed values of some other unknown parameters, the relevant integrals have been evaluated. Then the assumed values of unknown parameters are adjusted in such a way that the calculated values of light gain factors are comparable to the experimental values. Thus a correlation between the light gain factors and other counter parameters is established. The values of the effective electron excitation coefficients as a function of electric field strength per unit pressure in Ar + 2.5% N2 from these GSPCs having considerably different electric field gradients have also been estimated.