Nonappearance of Dehnen-Shahin resonances in the positronium continuum

Abstract

The Dehnen-Shahin relativistic equations for the positronium are found to have no resonant solutions in both the 1S 0 and the 3P 0 positronium continua. A certain pole singularity appearing in the 1S 0 potential gives rise to resonances, but only if the electromagnetic interaction strength is increased 160-fold or more. These resonances are found to have zero width. However, the same singularity, even in a weak potential, gives unacceptable nonphysical bound states near zero energy. The strange similarity of Spence-Vary 3P 0 resonances to resonances in an infinite square-well potential is noted.