P. Van Reeth

Elastic scattering and positronium formation in low-energy positron-helium collisions

Ab initio variational calculations are made of the elastic scattering and positronium formation cross sections for positron-helium scattering below the first excitation threshold of the target. Three variants of the Kohn variational method are used with very flexible trial wavefunctions and a very accurate helium wavefunction. The elastic scattering and positronium formation cross sections are believed to have converged to within 5% and 10%, respectively. The calculated positronium formation cross section displays a similar energy dependence to that of recent experimental results but with a 25% difference in magnitude. However, the theoretical total cross section, both above and below the positronium formation threshold, agrees with the experimental measurements to within 10%. Threshold effects in the s-wave cross sections manifest themselves as a significant feature in the total cross section. Similarities with the corresponding results for positron-hydrogen scattering are discussed.

Annihilation in low-energy positron - helium scattering

Elaborate wavefunctions representing low-energy positron - helium elastic scattering, which were obtained in the course of calculating accurate values of the scattering phase shifts, are used to determine the electron - positron annihilation rate and the Doppler-broadened annihilation -ray spectrum. This spectrum is also measured using room-temperature positrons in a Penning trap and a non-Gaussian lineshape is observed for the first time. Excellent agreement is obtained between the theoretical spectrum and the present results.

The energy dependence of the annihilation rate in positron - atom scattering

Detailed theoretical studies of annihilation in low-energy positron - atom scattering reveal a very pronounced enhancement of the annihilation rate in the vicinity of the positronium formation threshold, providing qualitative confirmation of the predictions of a recent model in which the enhancement is attributed to virtual positronium formation. The present investigations relate specifically to atomic hydrogen but similar results have also been obtained for helium. From investigations of annihilation at energies above the positronium formation threshold, we conclude that no clear distinction can be made between direct annihilation and annihilation following positronium formation.

On the normalization of the positron-impact direct ionization cross-section in the noble gases

Abstract Difficulties in the normalization of the positron-impact direct ionization cross-sections due to differences among the various data for electron impact ionization are discussed. Consequently, the cross-sections of Kara et al. (J. Phys. B 30 (1997) 3933) and of Moxom et al. (Can. J. Phys. 74 (1996) 367) have been renormalized using more recent and accurate data for electron impact ionization from Sorokin et al. (Phys. Rev. A. 58 (1998) 2900; 61 (2000) 022723). The new normalization for Ne, Kr and Xe lowers the cross-sections by 19%, 8% and 14% respectively, while that for Ar increases the cross-section by 2%.

Energy dependence of the total ionization and positronium formation cross-sections in e+-Xe collisions

Abstract Detailed precise measurements of the energy dependence of the total ionization cross-sections for Xe by positron impact have been performed from around threshold up to 120 eV. In contrast with a theoretical prediction, no structure in the vicinity of 80 eV has been found in neither the total ionization nor the Ps formation cross-sections for Xe.

Positronium formation in low energy s-wave positron-helium scattering

A two channel version of the Kohn variational method is used with very flexible trial wavefunctions and elaborate helium target wavefunctions to obtain accurate values of the s-wave elastic and positronium-formation cross sections for positron-helium scattering in the Ore gap. The positronium-formation cross section displays a similar behaviour to that found in positron-hydrogen scattering, with a rapid rise from threshold followed by a slowly rising plateau at the higher energies. The small magnitude of this cross section is consistent with the findings of a recent analysis of the experimental results. Investigations are also made of the behaviour of the elastic-scattering cross section near to the positronium-formation threshold.

Empirical scaling of positron- and electron-impact ionization cross sections

A simple empirical formula has been found which factors out the gross target dependence of single ionization cross sections by positron and electron impact. The formula can be used to estimate cross sections for an atom if the cross section maxima for any other two atoms in the same column of the periodic table are known. Further investigation is required to understand the basic physical mechanism underlying the degree of accuracy of such a factorization.

Theoretical studies of threshold features in the cross-sections for low-energy e+–H and e+–He scattering

Abstract The Kohn variational method is used to investigate structure in the elastic scattering and positronium formation cross-sections close to the positronium formation threshold for low energy positron scattering by hydrogen and helium. The results agree with Wigners threshold law, but show that its validity only extends over a very restricted energy range. A great similarity is found in the s-wave contribution to the positronium formation cross-section for the two systems in both energy dependence and magnitude, and a significant feature is found in the total cross-section for positron–helium scattering at the positronium formation threshold.

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.

Annihilation in low energy positron–helium scattering

Abstract Elaborate wave functions representing low energy positron–helium elastic scattering, which were obtained in the course of calculating accurate values of the scattering phase shifts, are used here to determine the energy distribution of the γ-rays arising from electron–positron annihilation. The results are found to be in excellent agreement with recent experimental measurements. The energy dependence of the electron–positron annihilation rate parameter, Zeff, is also investigated. It experiences a very sharp rise as the positronium formation threshold is approached, qualitatively in agreement with recent predictions concerning the importance of virtual positronium formation in the annihilation process near the threshold.