Positronium Bubbles in Liquid and Solid Helium-4

A theoretical investigation of positronium atoms localized within bubbles, in condensed helium, has been carried out in order to compare it with recent experiments. The theory explores the size of the bubbles and the implications of the localization which are relevant to experiments on the angular correlation of the two annihilation photons. Pressure dependence is explored in a range from the vapor pressure to 170 atm at temperatures of 1.7 and 4.2°K. Theoretical predictions at thermal equilibrium yield excellent agreement with experiment except for two small, though notable, features. Agreement between theory and experiment can be made complete by noting that some annihilations will occur during the formation of a bubble and if it is assumed that the region adjacent to the bubble may not have quite enough time to come into thermal equilibrium with the bulk helium before the singlet positronium annihilates ($\tau \sim {10}^{-10\mathrm{}}$ sec). Further, the degree of nonthermalization must increase between 1.7 and 4.2°K. Theoretically, nonthermalization effects are indeed expected to be more evident when the thermal conductivity is low [$\kappa \left(4.2\mathrm{}°\mathrm{K}\right)\simeq {10}^{-2\mathrm{}}\kappa \left(1.7\mathrm{}°\mathrm{K}\right)$ in the solid at 140 atm]; this suggests further experiments to test the hypothesis.