## Positronium formation detected using annihilation radiation energy spectroscopy

When a positron and an electron annihilate directly, instead of forming a Ps atom, all of their energy is converted into two gamma ray photons, each with 511 keV (the rest mass energy of the electron/positron). However, if an electron and a positron form a Ps atom the annihilation can occur either into two or three photons, depending on the spin state of the Ps atom. The longer-lived Ps state is called ortho-positronium (o-Ps), and in this system the electron and positron spins point in the same direction, so the total spin of the atom is 1. This means that o-Ps has to decay into an odd number of gamma rays in order to conserve angular momentum. Usually this means three photons, as single photon decay can only happen if there is a third body present (this has been observed). The three photon energies are spread out over a large range (but they always add up to 2 x 511 keV). The short-lived Ps state is called para-positronium (p-Ps) and this usually decays into two photons. It is possible for a three photon state to have zero angular momentum, so singlet decay into three photons is not ruled out by momentum considerations, but this mode is suppressed and to a good approximation p-Ps decays into two gamma rays with well-defined energies (i.e., 511 keV). This means that p-Ps decays look very similar to direct electron-positron decays. It also means that we can detect the presence of o-Ps by looking at the energy spectrum of annihilation radiation, as is shown in the graph below.

We are able to measure gamma ray energies using a detector; in this case NaI(TI), or thallium doped sodium iodide. The data shown above were taken with a positron beam fired into a piece of untreated metal, from which we expect hardly any Ps to be made, and also in a silica film, which we know converts about 30% of the incident positrons into the Ps atoms. When the beam hits the metal many events at energies close to 511 keV are detected, since most positrons will annihilate directly into two 511 keV photons.
The production of Ps can be seen when we compare the two curves (red and black lines) shown in the figure. These spectra are normalised to have the same total area, so the excess of counts in the valley region (i.e., energies between about 300 and 500 keV), and the reduction of counts in the photopeak (at 511 keV) is exactly what you would expect if you made positronium: the decay into three photons means there are more photons with energies less than 511 keV.