Positronium physisorption at quartz surfaces

The possibility of having positronium (Ps) physisorbed at 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 Ps$_2$ molecule on a material host. Experimental evidence for physisorbed Ps at the surface of quartz was reported some years ago,\footnote{Sferlazzo, Berko, Canter, Phys. Rev. B {\bf 3}, 6067 (1985).} but firm theoretical support for such a conclusion was lacking. With the FLAPW method\footnote{Wimmer, Krakauer, Weinert, Freeman, Phys. Rev. B {\bf 24}, 864 (1981).} we calculated the electronic structure and dielectric function of $\alpha$-quartz and obtained the interaction potential with a Ps atom on its surface. We show that there is indeed a bound state with an energy of $\sim0.19$ eV, which is reasonably close to the experimental estimates of $0.14$ - $0.17$ eV. A brief energy analysis in terms of the Langmuir-Hinshelwood mechanism further shows that the formation of a Ps$_2$ molecule at quartz surface would be possible.