Defect theory of positronium and nontrivial QED relations

An effective theory of the excited states positronium is derived and some its consequences are explored. At large physical separation, binding electron positron assumed to be described completely by QED, whereas all short-ranged phenomena, including those within beyond can accounted for with energy-dependent quantum defects. This has at least two practical applications. First, it provides an accurate economical, yet largely QED-independent, means fit spectrum in order predict compare outcome experiments. Second, matching this that predicted QED reveals nontrivial relationships exist bound-state QED; higher contributions may obtained from lower contributions. These relations verified up $m{\ensuremath{\alpha}}^{6}$, predictions made $m{\ensuremath{\alpha}}^{7}$ $m{\ensuremath{\alpha}}^{8}$ corrections. extensions other hydrogenic systems provide a useful complement QED.