Correlations between cross sections and threshold energies for positronium formation

Abstract

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.

Local Epitaxial Growth of (103) One-Axis-Oriented SrBi2Ta2O9 Thin Films Prepared at Low Deposition Temperature by Metalorganic Chemical Vapor Deposition and Their Electrical Properties

“…The present scaling formula might also appear similar to the correlations that have been found in the inert gases between the threshold energy and several ionization cross sections (Van Reeth et al 2000. These correlations have been expressed…”

“…In figure 2, the results are illustrated using the experimental results for H (Jones et al 1993), He and Ar (Moxom et al 1996), Ne, Kr and Xe (Kara et al 1997). The uncertainties concerning the absolute magnitude of the ionization cross sections of the inert gases by positron-and electron-impact (see Van Reeth et al 2002, Sorokin et al 1998 are irrelevant to the present discussion as the data are scaled to their peak value. Ne, Ar, Kr and Xe have the same general shape 3 whilst He and H data are found to be narrower and shifted towards lower values of E/E th .…”

Correlations between ionization cross sections and threshold energies in electron-, positron-, proton- and antiproton-atom collisions

“…very well, where A and B are energy-dependent parameters, the same for all atoms belonging to a given column of the periodic table. A slightly modified form of this equation also provides a remarkably good fit to low-energy Ps formation cross sections in double and triple ionization, with the data for all three degrees of ionization extending over almost six orders of magnitude (see figure 2 of [2]). The investigations presented in [1] were restricted to the 6.8 eV wide energy interval between the thresholds for Ps formation and for direct ionization, within which ionization can only occur through Ps formation.…”

“…These correlations, extending from near threshold to high projectile energies, are similar to those previously observed for positronium formation, namely σ = A exp(−BE th ), where σ is the cross section for each process, E th is the relevant threshold energy and A and B are functions of the excess energy of the projectile. The generality of this form for the four projectiles is suggestive of a common underlying fundamental aspect of the collisions.Recent investigations of positronium (Ps) formation in positron-atom collisions have revealed a strong correlation between the Ps formation cross section σ Ps and the corresponding threshold energy E Ps = (E i − 6.8) eV (E i being the single-ionization threshold of the target and 6.8 eV the binding energy of Ps) [1,2]. The data for Ps formation in single ionization for both the noble gases and the alkalis were shown to fit the relation…”

“…Recent investigations of positronium (Ps) formation in positron-atom collisions have revealed a strong correlation between the Ps formation cross section σ Ps and the corresponding threshold energy E Ps = (E i − 6.8) eV (E i being the single-ionization threshold of the target and 6.8 eV the binding energy of Ps) [1,2]. The data for Ps formation in single ionization for both the noble gases and the alkalis were shown to fit the relation…”