Proportionally off-mass-shell equation for unequal mass systems

Abstract

A new two-body relativistic equation is presented. The major advantage of the proposed equation over existing equations in the literature is that this equation automatically adjusts itself for different mass systems. Besides unitarity and covariance, this equation gives a physically meaningful prescription of how the particles go off-mass-shell in the intermediate states. It allows the particles to go off-mass-shell proportionally to their masses so that when one of the masses becomes infinite, it automatically becomes a one-body equation for the lighter particle and for equal mass systems, it reduces to the Todorov equation. Because of the off-mass-shell prescription for the intermediate states, it will be useful for systems with a wide variety of masses such as mesons, positronium, muonium, pionium, the deuteron and light hadronic atoms.