Mass Corrections to the Hyperfine Structure in Hydrogen

In a previous paper, a covariant wave equation for bound states was used to calculate corrections to fine structure. The techniques developed in that paper are extended here to the study of hyperfine structure (hfs) in the hydrogen atom. An expression is derived for corrections of relative order ($\frac{\alpha m}{M}$) to the hfs splitting of any $S$-state of hydrogen, arising from the finite mass of the nucleus. The proton is considered as a point particle with an anomalous magnetic moment of the Pauli type in addition to its Dirac moment. It is shown that the corrections obtained with an unmodified Pauli moment diverge logarithmically, and a cut-off in momentum space is introduced. Numerical results are given for the limit of large cut-off momentum. It is shown that the leading terms, which involve $log\left(\frac{M}{m}\right)$ as a factor, can also be obtained from a modified form of three-dimensional perturbation theory.