Accurate finiteelement solutions of the twobody Dirac equation
Abstract
A general analysis of the twobody 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 finiteelement analysis, and the lowlying 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 finiteelement radial components.
 Publication:

Physical Review A
 Pub Date:
 April 1992
 DOI:
 10.1103/PhysRevA.45.4393
 Bibcode:
 1992PhRvA..45.4393S
 Keywords:

 31.20.Di;
 11.10.Qr;
 02.60.+y