High-order expansion of the energy eigenvalues of a relativistic Coulomb equation

Journal Article · Mon May 01 04:00:00 EDT 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1034· OSTI ID:165246

Le Yaouanc, A; Oliver, L; Raynal, J ^[1]

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1. Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris XI, Batiment 211, 91405 Orsay cedex (France)

It is shown that the Herbst equation, i.e., a Coulomb potential wave equation including a free relativistic kinetic energy, presents a rather nontrivial series expansion of its eigenvalues in powers of {alpha}. In fact, in contrast to Klein--Gordon and Dirac equations, it presents not only odd powers of {alpha} but also nonanalytic ln {alpha} terms. The first orders ({alpha}{sup 4}, {alpha}{sup 5}) are obtainable by a standard perturbation method on the Sommerfeld correction. A much more effective and systematic method is proposed to get higher orders ({alpha}{sup 7}). To appreciate the resulting expansion, we compare it to the known results coming from other approaches to relativistic bound states, namely Klein--Gordon and Dirac equations in an external field and for the two-body problem, the Breit and Sucher-type equations, and the positronium QED result. {copyright} 1995 Academic Press, Inc.

• OSTI ID: 165246
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 239; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUND STATE
COULOMB FIELD
DIRAC EQUATION
EIGENVALUES
ENERGY LEVELS
KLEIN-GORDON EQUATION
PERTURBATION THEORY
POSITRONIUM
QUANTUM ELECTRODYNAMICS
SERIES EXPANSION