Delayed emission of cold positronium from mesoporous materials

Abstract

It is well known that ortho-positronium (ortho-Ps) atoms are emitted with high efficiency from various porous materials following the implantation of positrons. Since the ortho-Ps lifetime in a mesoporous material may be a substantial fraction of the ortho-Ps vacuum lifetime ($142$ ns), the time dependence of Ps emission may have to be considered when conducting certain types of experiments, such as time of flight measurements or pulsed ortho-Ps-laser interactions, when using this kind of target as a positronium source. By taking into account the positron implantation profile and subsequent Ps diffusion and decay in a mesoporous film we calculate the time dependent ortho-Ps emission rate $\ensuremath{\Gamma}$($t$), which in turn allows us to establish the total annihilation rate, arising from the decay of ortho-Ps both inside and outside the sample. Using time-delayed laser spectroscopy and single-shot lifetime measurements we have directly probed the rate at which Ps is emitted into vacuum from a target with $~$3-nm diameter pores and have observed delayed ortho-Ps emission that is consistent with our model. From the ortho-Ps decay spectrum we find that, whereas a simple two-component lifetime fit gives a short lifetime of $25.3$$\ifmmode\pm\else\textpm\fi{}$$0.3$ ns, an analysis that properly takes into account the emission rate yields an ortho-Ps lifetime inside the porous material of $32.3$$\ifmmode\pm\else\textpm\fi{}$$1.2$ ns, demonstrating that the ortho-Ps escape rate into vacuum can significantly modify the apparent lifetime of ortho-Ps inside a mesoporous material. Our measurements yield a Ps diffusion coefficient $D$ $=$ $0.07$ $\ifmmode\pm\else\textpm\fi{}$ $0.01$ cm${}^{2}$ ${\mathrm{s}}^{\ensuremath{-}1}$, which is consistent with a tunneling limited diffusion process.