Self-trapping of ortho-positronium in dense fluid helium

Abstract

Previous theoretical work by the author, on electron self-trapping, is extended to positronium in helium. Results are obtained for several values of the positronium-helium $s$-wave scattering length ($a$), in order to determine the validity of published analyses of data on the dependence of the ortho-positronium annihilation rate on the average density and temperature of its fluid helium host. It is concluded that the recently reported value of $^{1}Z_{\mathrm{eff}}=0.129\ifmmode\pm\else\textpm\fi{}0.006$ is not contaminated by self-trapping effects or models, while the value reported for $a=0.77\ifmmode\pm\else\textpm\fi{}0.04$ \AA{} results from an invalid analysis. It is suggested that a value for $a$ in the neighborhood of 0.8 \AA{} may be reasonably inferred from available experimental data and the calculations presented here, but that the precision of this determination is not very high.