Physica Scripta

On the Energy Dependence of Annihilation Cross-Sections for Positrons in Collision with Atoms and Molecules

Peter Van Reeth, Gaetana Laricchia, J W Humberston

Published Jan 1, 2005• 19 citations

Abstract

The very large annihilation rates observed at room temperature in positron collisions with certain molecules have instigated the development of several models of positron annihilation based on the role of virtual processes, Feshbach resonances and bound states. One of the outcomes of these models has been the interest they have generated in investigations of the energy dependence of the annihilation cross-section in the vicinity of inelastic thresholds. The aim of this article is to provide a review of these recent studies and to highlight outstanding questions.

DOI: 10.1238/physica.regular.071a000c9

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Physica Scripta

On the Energy Dependence of Annihilation Cross-Sections for Positrons in Collision with Atoms and Molecules

Peter Van Reeth, Gaetana Laricchia, J W Humberston

Published Jan 1, 2005• 19 citations

Publisher

Abstract

DOI: 10.1238/physica.regular.071a000c9

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s

-wave scattering length can be analyzed and where signatures of virtual state formation appear for all the three systems considered (

{\mathrm{C}}_{2}{\mathrm{H}}_{2}

{\mathrm{C}}_{2}{\mathrm{H}}_{4}

, and

{\mathrm{C}}_{2}{\mathrm{H}}_{6}

). Furthermore, the present calculations show that the stretching of the CH bonds in all molecules causes the moving of the existing virtual state closer to threshold and further makes it become a bound state whenever highly distorted molecules are involved. The effects of these changes are further seen to cause a marked enhancing of the corresponding annihilation parameters

{Z}_{\mathit{eff}}

at low collision energies, in line with what is experimentally observed for such gases. The significance of such model calculations is discussed in some detail.

The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at

2.2

eV). The low-energy phase shifts for the elastic scattering of positrons from cadmium were derived from the bound and pseudostate energies of a very large basis configuration-interaction calculation of the

{e}^{+}

-Cd system. The

s

-wave binding energy is estimated to be $126\ifmmode\pm\else\textpm\fi{}42$ meV, with a scattering length of ${A}_{\mathrm{scat}}=(14.2\ifmmode\pm\else\textpm\fi{}2.1)$

{a}_{0}

, while the threshold annihilation parameter,

{Z}_{\mathrm{eff}}

, was $93.9\ifmmode\pm\else\textpm\fi{}26.5$. The

p

-wave phase shift exhibits a weak shape resonance that results in a peak

{Z}_{\mathrm{eff}}

of $91\ifmmode\pm\else\textpm\fi{}17$ at a collision energy of about $490\ifmmode\pm\else\textpm\fi{}50$ meV.

{Z}_{\mathrm{eff}}(k)

even if the magnitude is incorrect. Analysis of the

{Z}_{\mathrm{eff}}

versus temperature data of Kurz et al. [Phys. Rev. Lett. 77, 2929 (1996)] suggests scattering lengths of $\ensuremath{-}5.6\ifmmode\pm\else\textpm\fi{}{1.0a}_{0},$ $\ensuremath{-}10.3\ifmmode\pm\else\textpm\fi{}{2.0a}_{0},$ and $\ensuremath{-}56\ifmmode\pm\else\textpm\fi{}{15a}_{0}$ for Ar, Kr, and Xe, respectively. Existing bound-state calculations can be used to fix the values of the semi-empirical parameters for a number of metal vapors, resulting in predicted

{Z}_{\mathrm{eff}}

of 119, 36, and 94 for Be, Mg, and Cu at threshold. In addition to the calculations, expressions relating the threshold form of

{Z}_{\mathrm{eff}}(k)

to the complex scattering length are presented.