The binding of a proton and an electron to form the Hydrogen atom is probably the most studied phenomenon in physics – starting with the Bohr atom in 1913 and the advent of quantum mechanics. Further progress in understanding the Hydrogen atom resulted from Schroedinger’s equation in 1926 and from Dirac’s relativistic equation in 1928 (shown here on the plaque in Westminster Abbey). Finally, in the 1940’s, Richard Feynman based his relativistic quantum electrodynamics on the Dirac equation allowing for an even more accurate description of the Hydrogen atom.
A positron is the antiparticle to the electron and positronium has a positron bound to the electron. It would be surprising in the extreme if there were unknown solutions to the Dirac equation for positronium. Yet, as shown on this site, there are indeed two solutions to the Dirac equation for positronium: one is the normal atomic solution in which the electron and positron are bound at atomic distances (Bohr) and another is the ‘resonance’ solution in which they are bound at nuclear distances (Fermi). The resonance occurs because the positron and electron motion can become highly synchronized when moving near the speed of light. This resonance allows the relatively weak electric and magnetic force between the electron and positron to bind them at nuclear distances (without the need for the ‘strong’ force). Unlike the positronium atom, this positronium ‘resitron’ can neither emit nor absorb light – it is ‘dark.’ Further, it has an energy much less than the atom and so it is more stable. Still, it is very difficult to transform from the atomic form to the resonance form of positronium. Most matter in the universe is indeed ‘dark.’ Can the ‘resitron,’ if it exists, be the missing dark matter.