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Correlations between cross sections and threshold energies for positronium formation

Strong correlations between the cross sections and threshold energies for positronium formation in positron-impact single ionization of noble gases are shown to exist over a wide energy range. These correlations also extend to higher degrees of ionization, and they can be used as an empirical tool for predicting such cross sections within the relevant Ore gaps. Similar correlations are shown to exist for the exothermic positronium formation process in positron-impact single ionization of the alkali atoms. All the single ionization data are consistent with the hypothesis that the magnitude of the positronium formation cross section is determined by the modulus of the difference between the kinetic energies of the incident positron and the emerging positronium. An explanation is given for the qualitative difference between the alkali atoms and the noble gases in the magnitude of the ratio of the cross sections for positronium formation into the ground and first excited states.