Direct relativistic formulation of the hyper fine interaction in simple atoms. 3

We apply a previously developed procedure for obtaining approximate solutions for the Dirac equation for the electron to the formulation of the hyperfine interaction in spherically symmetric atoms. Expressions are obtained to order α 2 , α being the usual fine structure constant. The hydrogen 1S state is solved and seen to be correct to order α 2 . This result is taken to be a positive test of the procedure. Further, one sees that the first order equations are solvable, the form of the solutions, and that all the required contributions are finite. Also, in terms of numerical work the time required will not be appreciably greater than needed for a nonrelativistic calculation. This leads to the conclusion that one has a practical and valid method of solving relativistic problems to order α 2 .