What is it about?
A general analysis of the two-body Dirac equation is presented for the case of equal masses interacting via a static Coulomb potential. Radial equations are derived and their analytical structure is discussed. Standard analytical and perturbative methods have failed to provide solutions to the radial equations due to the presence of the singularity on the negative radial axis at roughly the distance of the classical electron radius. The exact radial equations are solved using finite-element analysis, and the low-lying bound states are obtained to an accuracy of one part in 10^18. The effect of the singularity is clearly seen in the structure of the finite-element radial components.
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Why is it important?
This paper is important. It lead to the discovery of Anomalous states of Positronium by Chris W. Patterson. See Wikipedia link on Positronium.
Perspectives
A thorough investigation of higher-order relativis-tic corrections is in progress and we anticipate that theFEM algorithm can resolve the question of the existence of bound states for these relativistic Hamiltonians.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: Accurate finite-element solutions of the two-body Dirac equation, Physical Review A, April 1992, American Physical Society (APS),
DOI: 10.1103/physreva.45.4393.
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