Orthopositronium decay in gaseous, liquid, and solid helium

Abstract

Orthopositronium annihilation rates in liquid and solid helium up to 140 atm and in the liquid along the vapor-pressure curve up to the critical temperature have been measured and are analyzed in terms of the cavity model with a pressure-dependent radius. Two interdependent parameters of the model are the effective number of singlet annihilation electrons per helium atom ${}_{}{}^1{}_{}{}^{}Z_{\mathrm{eff}}^{}{}_{}{}^{}$ for orthopositronium decay in helium gas and the orthopositronium—helium-atom scattering length $a_s$. Measurements of $o-\mathrm{P}\mathrm{s}$ in low-density helium gas at 77 K yielded ${}_{}{}^1{}_{}{}^{}Z_{\mathrm{eff}}^{}{}_{}{}^{}=0.116\mathrm{}\pm 0.004$ which is reasonably consistent with recently reported measurements at 300 K. With a low-density limit of ${}_{}{}^1{}_{}{}^{}Z_{\mathrm{eff}}^{}{}_{}{}^{}=0.125\mathrm{}$, our pressure-dependent data are fit very well with an $a_s\simeq 1.15 a_B$, while we do not obtain a good fit to the vapor-pressure measurements with the approximations used in the analysis. Sensitivity to the details of the model limits the accuracy of this result as a determination of $a_s$. We have also observed a nonlinearity in the $o-\mathrm{P}\mathrm{s}$ annihilation rate in He gas, and we have found $Z_{\mathrm{eff}}$ for free-positron decay to be 3.86 ± 0.04 in the gas.