It is shown that there are anomalous bound-state solutions to the two-body Dirac equation for an electron and a positron interacting via an electromagnetic potential. These anomalous solutions have quantized coordinates at nuclear distances (fermi) and are orthogonal to the usual atomic positronium bound states as shown by a simple extension of the Bethe-Salpeter equation. It is shown that the anomalous states have many properties which correspond to those of neutrinos.

• Received 23 July 2022
• Revised 3 April 2023
• Accepted 12 April 2023

DOI:https://doi.org/10.1103/PhysRevA.107.042816