Positronium is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom, specifically an onium. The system is unstable: the two particles annihilate each other to predominantly produce two or three gamma-rays, depending on the relative spin states. The energy levels of the two particles are similar to that of the hydrogen atom. However, because of the reduced mass, the frequencies of the spectral lines are less than half of those for the corresponding hydrogen lines.
States
The mass of positronium is 1.022 MeV, which is twice the electron mass minus the binding energy of a few eV. The ground state of positronium, like that of hydrogen, has two possible configurations depending on the relative orientations of the spins of the electron and the positron. The singlet state,, with antiparallel spins is known as para-positronium. It has a mean lifetime of 0.125 ns and decays preferentially into two gamma rays with energy of each. By detecting these photons the position at which the decay occurred can be determined. This process is used in positron-emission tomography. Para-positronium can decay into any even number of photons, but the probability quickly decreases with the number: the branching ratio for decay into 4 photons is. Para-positronium lifetime in vacuum is approximately The triplet state, 3S1, with parallel spins is known as ortho-positronium. It has a mean lifetime of, and the leading decay is three gammas. Other modes of decay are negligible; for instance, the five-photons mode has branching ratio of ≈. Ortho-positronium lifetime in vacuum can be calculated approximately as: However more accurate calculations with corrections to O yield a value of 7.040 μs−1 for the decay rate, corresponding to a lifetime of. Positronium in the 2S state is metastable having a lifetime of against annihilation. The positronium created in such an excited state will quickly cascade down to the ground state, where annihilation will occur more quickly.
Measurements
Measurements of these lifetimes and energy levels have been used in precision tests of quantum electrodynamics, confirming quantum electrodynamics predictions to high precision. Annihilation can proceed via a number of channels, each producing gamma rays with total energy of , usually 2 or 3, with up to 5 gamma ray photons recorded from a single annihilation. The annihilation into a neutrino–antineutrino pair is also possible, but the probability is predicted to be negligible. The branching ratio for o-Ps decay for this channel is and in predictions based on the Standard Model, but it can be increased by non-standard neutrino properties, like relatively high magnetic moment. The experimental upper limits on branching ratio for this decay are < for p-Ps and < for o-Ps.
Energy levels
While precise calculation of positronium energy levels uses the Bethe–Salpeter equation or the Breit equation, the similarity between positronium and hydrogen allows a rough estimate. In this approximation, the energy levels are different because of a different effective mass, m*, in the energy equation : where: Thus, for positronium, its reduced mass only differs from the electron by a factor of 2. This causes the energy levels to also roughly be half of what they are for the hydrogen atom. So finally, the energy levels of positronium are given by The lowest energy level of positronium is −6.8 electronvolts . The next level is. The negative sign is a convention that implies a bound state. Positronium can also be considered by a particular form of the two-body Dirac equation; Two particles with a Coulomb interaction can be exactly separated in the center-of-momentum frame and the resulting ground-state energy has been obtained very accurately using finite element methods of J. Shertzer and confirmed more recently. The Dirac equation whose Hamiltonian comprises two Dirac particles and a static Coulomb potential is not relativistically invariant. But if one adds the terms, where, then the result is relativistically invariant. Only the leading term is included. The contribution is the Breit term; workers rarely go to because at one has the Lamb shift, which requires quantum electrodynamics.
History
predicted the existence of positronium in a 1934 article published in Astronomische Nachrichten, in which he called it the "electrum". Other sources credit Carl Anderson as having predicted its existence in 1932 while at Caltech. It was experimentally discovered by Martin Deutsch at MIT in 1951 and became known as positronium. Many subsequent experiments have precisely measured its properties and verified predictions of quantum electrodynamics. There was a discrepancy known as the ortho-positronium lifetime puzzle that persisted for some time, but was eventually resolved with further calculations and measurements. Measurements were in error because of the lifetime measurement of unthermalised positronium, which was only produced at a small rate. This had yielded lifetimes that were too long. Also calculations using relativistic quantum electrodynamics are difficult to perform, so they had been done to only the first order. Corrections that involved higher orders were then calculated in a non-relativistic quantum electrodynamics.
Exotic compounds
Molecular bonding was predicted for positronium. Molecules of positronium hydride can be made. Positronium can also form a cyanide and can form bonds with halogens or lithium. The first observation of di-positronium molecules—molecules consisting of two positronium atoms—was reported on 12 September 2007 by David Cassidy and Allen Mills from University of California, Riverside.
