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Physical Review A

Enhanced positron annihilation in small gaseous hydrocarbons: Threshold effects from symmetric C−H bond deformations

Tamio Nishimura, Franco Antonio Gianturco

Published Aug 12, 2005• 28 citations

Abstract

The present results report a computational analysis of the effects of symmetric bond stretching during positron scattering from polyatomic hydrocarbon molecules in the gas phase. The collisions are considered at very low energies where the behavior of the $s$-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.

DOI: 10.1103/physreva.72.022706

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The present results report a computational analysis of the effects of symmetric bond stretching during positron scattering from polyatomic hydrocarbon molecules in the gas phase. The collisions are considered at very low energies where the behavior of the

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.

Quantum calculations are carried out to evaluate the scattering length A 0 for low-energy positron collisions with gaseous acetylene molecules which are being "distorted" in their ν 5 vibrational mode during the scattering. As the molecular structure undergoes increasingly larger distortions of that bending mode, the clear signature of a metastable state (change of sign for A 0 ) appears at bending deformation of about 16° from the linear geometry. The effects of such state on the size of the annihilation parameters of the title molecule are evaluated and the implications for larger polyatomics are discussed.

An overview is presented of recent studies of the interaction of low-energy positrons with atoms and molecules using a trap-based positron beam. The beam is tunable from ~100 meV to many electron volts, with a typical energy resolution of 25 meV (FWHM). A variety of scattering processes are investigated using the properties of positron orbits in a spatially varying magnetic field. Recent scattering measurements are reviewed, and new data for electronic excitation, ionization, and positronium formation in noble gases are presented. In a separate set of experiments, positron annihilation below the threshold for positronium formation is studied in molecules as a function of positron energy. The data show large Feshbach resonances in the range of energies of the molecular vibrations. Within the framework of this model, these results provide the first experimental evidence that positrons bind to hydrocarbon molecules.

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.

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.

The lifetime of positrons contained in an electrostatic trap is studied when small quantities of alkanes (i.e., hydrocarbon molecules of the form

{\mathrm{C}}_{\mathrm{n}}

{\mathrm{H}}_{2\mathrm{n}+2}

) are added. As n is increased from 4 to 16, the annihilation rate per molecule is found to increase by a factor of 300 and then to level off. These data are interpreted as evidence for the existence of long-lived resonances and bound states of positrons and neutral molecules, and a model of the formation process is discussed.

A two-parameter semiempirical theory of positron scattering and annihilation is developed and used to investigate the behavior of positrons interacting with the rare gases and metal vapors. The two-parameter theory is able to do a reasonable job of reproducing existing cross section and annihilation data for the rare gases. A model-potential calculation that correctly predicts the behavior of the phase shifts will also predict the energy dependence of

{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.