Resolution of the Orthopositronium-Lifetime Puzzle

The long-standing discrepancy [G. S. Adkins, R. N. Fell, and J. Sapirstein, Ann. Phys. (N.Y.) 295, 136 (2002)] between the theoretical calculations of the orthopositronium ($o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$) annihilation decay rate (${\lambda }_{\mathrm{T}}=1/\mathrm{\text{lifetime}}$) and some of the experimental measurements has been resolved. A focused beam of positrons incident on a special nanoporous silica film produces near-thermal energy $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$ in vacuum that is slow enough to be virtually free of perturbing interactions. The fitted decay rate requires only a 500 ppm correction for nonthermal $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$ effects. The new value of ${\lambda }_{\mathrm{T}}=7.0404(10)(8)\mu {\mathrm{s}}^{-1}$ is in excellent agreement with theory.

Figure 1

The $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$ formation and confinement region. The time-tagged positron beam is focused through apertures of 4 and 3 mm, respectively, and then deflected into a porous silica film where $\sim 30\%$ form $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$. After many collisions in the interconnected 3.3 nm pores, most of the $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$ that escapes the film is nearly thermalized and, hence, too slow to escape from the cavity or annihilate in wall collisions.

Figure 2

The energy distribution of $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$ emitted from a typical porous silica film. Note that higher energy positrons implanted more deeply (solid circles) in the film produce more thermalized $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$ with fewer events in the epithermal tail.

Figure 3

The fitted decay rate as a function of the start time of the fit for two of the positron implantation energies used in this measurement. The decay rate for the full spectrum (of all $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$ decays) has a higher decay rate at lower beam energy due to the increased relative intensity of the backscattering component. The corrected spectra have an appropriately normalized pure backscattering spectrum subtracted.

Figure 4

The fitted decay rates at $t=250\mathrm{n}\mathrm{s}$ for a range of Ps implantation energies, plotted as a function of backscattered Ps over thermal $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$ ($I_{\mathrm{B}\mathrm{S}}/I_{o\mathrm{\text{−}}\mathrm{P}\mathrm{s}}$). A linear fit to the full spectrum decay rates is made to remove the effect of the backscattered $o\mathrm{\text{−}}\mathrm{P}\mathrm{s}$. The decay time spectra are also corrected directly for backscattering by subtracting an appropriately scaled backscattering spectrum from the full spectrum.