Dirac resonance energies for central potentials with different Lorentz-type potential couplings

Abstract

The amplitude-phase method is applied to relativistic Dirac-particle resonances related to electron–atom collisions. Complex-energy resonance poles of the S matrix in central potentials of differing Lorentz couplings are studied near the non-relativistic limit. It is confirmed that an equal mixture of a Lorentz vector-type potential (with a single time component) and a Lorentz scalar-type potential of the same radial shape makes the interaction essentially spin independent, as if spin does not couple to orbital angular momentum. Hence, resonance poles of the S matrix depend simply on the orbital angular momentum and the radial quantum number in a similar way as in the Schrödinger limit and in the Klein–Gordon equation. In a Lorentz-vector potential model, there is a splitting of pole positions, but the splitting may be surprisingly small, as demonstrated for one of the potentials considered. The numerical method used automatically assigns a vibrational (radial) quantum number to the resonance state, which is usually a characteristic feature of semiclassical methods.