Delayed emission of cold positronium from mesoporous materials

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 Γ(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±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±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 ± 0.01 cm² s^-1, which is consistent with a tunneling limited diffusion process.