Effect of positron–atom interactions on the annihilation gamma spectra of molecules

Abstract

Calculations of γ -spectra for positron annihilation on a selection of molecules, including methane and its fluoro-substitutes, ethane, propane, butane and benzene are presented. The annihilation γ -spectra characterise the momentum distribution of the electron-positron pair at the instant of annihilation. The contribution to the γ -spectra from individual molecular orbitals is obtained from electron momentum densities calculated using modern computational quantum chemistry density functional theory tools. The calculation, in its simplest form, effectively treats the low-energy (thermalised, room-temperature) positron as a plane wave and gives annihilation γ -spectra that are about 40% broader than experiment, although the main chemical trends are reproduced. We show that this effective 'narrowing' of the experimental spectra is due to the action of the molecular potential on the positron, chiefly, due to the positron repulsion from the nuclei. It leads to a suppression of the contribution of small positron-nuclear separations where the electron momentum is large. To investigate the effect of the nuclear repulsion, as well as that of short-range electron-positron and positron-molecule correlations, a linear combination of atomic orbital description of the molecular orbitals is employed. It facilitates the incorporation of correction factors which can be calculated from atomic manybody theory and account for the repulsion and correlations. Their inclusion in the 4 2 calculation gives γ -spectrum linewidths that are in much better agreement with experiment. Furthermore, it is shown that the effective distortion of the electron momentum density, when it is observed through positron annihilation γ -spectra, can be approximated by a relatively simple scaling factor. annihilation on a range of molecules including hydrogen, methane and its fluoro-substitutes, ethane, propane, butane and benzene.The first measurement of the Doppler-broadened γ -spectrum for positron annihilation on molecules was made in 1986 by Brown and Leventhal in low-density hydrogen gas [27]. In the early 1990s the confinement of thermalized positrons in a Penning trap allowed Tang et al [28] to measure γ -spectra for a range of molecules, including hydrocarbons and perfluorocarbons. This work was built upon by Iwata et al [3] who measured γ -spectra for positron annihilation on a large range of atoms and molecules in the gas phase. Despite this extensive set of experimental results, there is a paucity of theoretical calculations of the annihilation γ -spectra in molecules. Theoretical predictions of the γ -spectra do exist for the molecular ion H + 2 , for which (numerical) Coulomb-Born and configuration-interaction Kohn variational calculations have been performed [29], and for the small molecules H 2 and N 2 [30,31]. However, the application of these sophisticated methods to larger molecules is considerably more difficult. More than thirty years ago Chuang and Hogg [32] analysed the annihilation γ -spectra for hexane and decane. However, their ca...

Plasma and trap-based techniques for science with positrons

“…49, similar experiments were able to distinguish annihilation from inner-shell electrons from the dominant contribution of that from the valence shell that agreed well with contemporary theoretical calculations (Iwata et al, 1997a). Recent theoretical studies aim to provide a more complete understanding of the contribution of the positron wave function to the spectra from molecules (Green et al, 2012).…”

On the Nature of the Positronic Bond

“…Beyond the academic curiosity, the annihilation process is the basis of the Positron Emission Tomography as a powerful medicinal imaging technique . Accordingly, a large body of experimental, and theoretical and computational, studies have been conducted recently on polyatomic and diatomic, positronic species in order to trace the sticking site of the positron. These studies reveal that in general the positronic density is very diffuse and is not centered between bonds but behind the most electronegative atom of the molecule (the cases with two or more atoms with equal electronegativity are more complicated) .…”

Positron scattering and annihilation on noble-gas atoms

“…The complete evaluation of the ladder-diagram series was implemented in the positron-hydrogen study [17] which used B-spline basis sets to discretize the positron and electron continua. This approach has since been applied to positron binding to the halogen negative ions [27], to positron scattering and annihilation on hydrogen-like ions [28], to the calculation of gamma-ray spectra for positron annihilation on the core and valence electrons in atoms [9,29] and in molecules [30]. Another many-body theory technique that allows one to sum the dominant series of diagrams to all orders is the linearized coupled-cluster method which was used to calculate positron-atom bound states for a large number of atoms [31,32].…”