Temperature scaling of the coefficient for ionic recombination in an ambient gas

On introducing natural units (the reduced mass of the ion pair for mass, e2/k theta for length and k theta for energy, theta being the temperature) the physical similitude of the recombination process becomes apparent. It is hence shown that the dependence of the recombination coefficient alpha on theta and on the ambient gas number density n(Z) must be such that a plot of ( theta / theta s)3/2 alpha against ( theta s/ theta )tn(Z) is rigorously theta independent where t=3/2 for a purely polarisation interaction and t=1 for a simple hard sphere interaction and where theta s is some standard temperature. This enables results at one temperature to be deduced from results at another for the same species of ions in the same gas.