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