Reformulation of the theory of the mass shift

The conventional division of the mass shift in atomic spectra into normal and specific mass shift is shown to lead to cancellation between the two terms in heavy atoms. It is suggested that the evaluation of the NMS in terms of the binding energy of a level is potentially unreliable, and certainly complicates unnecessarily the relativistic corrections to the mass shift. A mass shift Hamiltonian is derived, including relativistic corrections to order 1/c 2 , and the physical significance of the terms discussed. The Hamiltonian is given in two equivalent forms, for use with non-relativistic and relativistic wavefunctions. The implications for parametric analysis of isotope shifts are discussed.