Correlations between Cross Sections and Threshold Energies for Positronium Formation and Direct Ionization

Abstract

The correlation between the cross section for positronium formation and its threshold energy E _ps is studied for positron impact on the alkali atoms and the noble gases. Similar correlations are found between the direct ionization cross section and the target ionization energy E _i in electron, positron and proton impact on the noble gases. Specifically, for a given family of atoms, all these cross sections are well represented by a simple formula, σ = A exp(−B¦ E _th¦), where σ is the cross section for each process and E _th is the relevant threshold energy. The coefficients A and B are functions of the excess energy of the projectile, different for each process and projectile, but independent of the target atom. The generality of this formula for positronium formation and for different ionization processes suggests a common underlying mechanism.