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Article

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

Authors: Thylwe, K.-E.
Document Type: Article
Pubstate: Published
Journal: Physica Scripta
Volume: 81   035007
Year: 2010

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 (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 Schr\"{o}dinger 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 usually is a characteristic feature of semiclassical methods.