Physisorption of Positronium on Quartz Surfaces

Whether positronium (Ps) can be physisorbed on a material surface is of great fundamental interest, since it can lead to new insight regarding quantum sticking and is a necessary first step to try to obtain a ${\mathrm{Ps}}_2$ molecule on a material host. Experiments in the past have produced evidence for physisorbed Ps on a quartz surface, but firm theoretical support for such a conclusion was lacking. We present a first-principles density-functional calculation of the key parameters determining the interaction potential between Ps and an $\alpha$-quartz surface. We show that there is indeed a bound state with an energy of $0.14\mathrm{eV}$, a value which agrees very well with the experimental estimate of $\sim 0.15\mathrm{eV}$. Further, a brief energy analysis invoking the Langmuir-Hinshelwood mechanism for the reaction of physisorbed atoms shows that the formation and desorption of a ${\mathrm{Ps}}_2$ molecule in that picture is consistent with the above results.

Figure 1

Imaginary part of the dielectric function of $\alpha$-quartz for a polarization vector perpendicular to the $c$ axis. The continuous line shows the total function, arising from interband and exciton excitations. To illustrate the excitonic effects, the dotted line shows the interband contribution only.

Figure 2

Behavior of the electron density at the surface of a $\alpha$-quartz slab exposing a (011) surface, illustrated by a logarithmic plot of the electron density averaged over the section of the unit cell, as a function of the coordinate $z$ perpendicular to the slab.

Figure 3

Plot of the Ps ground state probability density (solid curve) and of its sole excited state (dotted curve). The inset shows the interaction potential. The potential saturates once it reaches the Ps work function value (1 eV).