Positron Binding and Annihilation in Alkane Molecules

A model-potential approach has been developed to study positron interactions with molecules. Binding energies and annihilation rates are calculated for positron bound states with a range of alkane molecules, including rings and isomers. The calculated binding energies are in good agreement with experimental data, and the existence of a second bound state for $n$-alkanes (${\mathrm{C}}_n{\mathrm{H}}_{2n+2}$) with $n\ge 12$ is predicted in accord with experiment. The annihilation rate for the ground positron bound state scales linearly with the square root of the binding energy.

Figure 1

Positron binding energies for $n$-alkane molecules ${\mathrm{C}}_n{\mathrm{H}}_{2n+2}$. Black crosses, experiment [41]; blue circles, present calculation; orange triangles, zero-range potential model [42].

Figure 2

Contour plots of the first (upper panel) and second (lower panel) bound positron states for dodecane ${\mathrm{C}}_{12}{\mathrm{H}}_{26}$. The contour for which the magnitude of the wave function is largest is indicated. The change in the magnitude of the wave function between neighboring contours is $\mathrm{\Delta }=0.0015$.

Figure 3

Electron-positron contact density for $n$-alkane molecules ${\mathrm{C}}_n{\mathrm{H}}_{2n+2}$. Panel (a) shows the contact density in terms of $n$, while panel (b) shows it as a function of $\sqrt{{ϵ}_b}$. Black symbols, independent-particle approximation; blue symbols, with enhancement factors and renormalization. Circles, first bound state; squares, second bound state. In (b), thin black and blue dashed lines are fits of the respective first-bound-state data, and the thick red dashed line is a fit of the calculated contact densities for positron-atom bound states [1].