1206.5408 (John H. Connell)

Sommerfeld Fine-Structure Formula for Two-Body Atoms    [PDF]

John H. Connell

For relativistic atomic two-body systems such as the hydrogen atom, positronium, and muon-proton bound states, a two-body relativistic wave equation and its two-body Sommerfeld fine-structure formula are given. The wave equation gives the energies to order alpha^4 correctly. In addition its Sommerfeld formula predicts, for every bound state and every mass ratio: (a) The coefficient of the alpha^6/N^6 energy term; (b) the coefficient of the alpha^6/N^4 energy term as a multiple of the square of the coefficient of the alpha^4/N^3 energy term. Here N is the Bohr quantum number. These predictions are verified in positronium by previous calculations which used second-order perturbation theory. One parameter in the two-body Sommerfeld formula remains unknown at present, so other alpha^6 energy terms remain unpredicted.

View original: http://arxiv.org/abs/1206.5408