Single-shot positron annihilation lifetime spectroscopy (SSPALS) is an extremely useful tool for experiments involving the positronium atom (Ps). I examine some of the methods that are typically employed to analyze lifetime spectra, and use a Monte-Carlo simulation to explore the advantages and limitations these have in laser spectroscopy experiments, such as resonance-enhanced multiphoton ionization (REMPI) or the production of Rydberg Ps.Positronium (Ps) [1] is the bound state of an electron and a positron. In vacuum, the components of the particle-antiparticle pair will ultimately annihilate with each other. The mean lifetime against self-annihilation is 125 ps for the n = 1 singlet spin state (1 1 S 0 , para-Ps) [2,3] or 142 ns for the n = 1 triplet spin states (1 3 S 1 , ortho-Ps) [4,5]. Annihilation of p-Ps usually results in two 511 keV gamma-ray photons, whereas o-Ps predominately decays into three with a combined energy of 1.022 MeV [6]. A scintillator coupled to a photomultiplier tube (PMT) can be used to efficiently detect gamma rays with subns timing resolution [7]. This facilitates precision positron annihilation lifetime spectroscopy (PALS) [8, 9] -a simple but powerful technique that was instrumental in the discovery of positronium by Deutsch in 1951 [10].The gross atomic structure of Ps [11] can be described by the Bohr model for hydrogen but with a reduced mass of µ Ps = m e /2; the corresponding energy levels are then given by E n = −6.8/n 2 (eV). Optical excitation from the ground state can be achieved using a pulsed laser synchronized to a time-bunched Ps source (∆t 10 ns) [12][13][14][15][16][17][18]. The annihilation and fluorescence decay rates of the excited states range widely [19,20] and laser excitation to these can have a marked effect on the overall lifetime. But to measure a PALS spectrum each annihilation event must be resolvable in the time domain, which is generally not possible with ns Ps sources. In this case, single-shot positron annihilation lifetime spectroscopy (SSPALS) [21] can be implemented instead. Here, the output of a fast gamma-ray detector constitutes the lifetime spectrum. This is a valid approximation if the Ps formation time and the decay time of the detector are both sufficiently short. PbWO 4 has a scintillation decay time of κ ∼ 10 ns, which is well suited to resolving o-Ps decay (τ = 142 ns). The Cerenkov radiator PbF 2 can be used to improve timing resolution [22] but Email address: a.deller@ucl.ac.uk (Adam Deller) it has a lower light output. For some applications, a slower material with a higher light output, such as LYSO (κ ∼ 40 ns), might be chosen to improve detection efficiency and the signalto-noise ratio [23].Pulsed Ps sources, with time widths of a few ns, can be obtained by implanting time-focused positron beams [24,25] into Ps-converter materials, such as mesoporous SiO 2 [26]. The interconnected network of pores provides a path to vacuum along which Ps atoms cool via inelastic collisions [14,27]. The overall efficiency for emission of o-Ps from...