Isotope shift and hyperfine structure for a valence s electron

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Abstract
The authors show that it is valid to use the value of the non-relativistic quantity mod psi (0) mod 2 obtained from a measurement of hyperfine structure (HFS) in the interpretation of field isotope shifts (FS) using conventional theory, in so far as both effects are directly due to a valence s electron interacting with the nucleus. They calculate directly from the Dirac equation the ratio R=FSHFS/ for a simple nuclear model, assuming the potential close to the nucleus to be Coulombic. They discuss the approximations involved, and obtain numerical results for a range of nuclei. Since they are evaluating a ratio they avoid the need to normalise the Dirac wavefunction, the step which leads to the introduction of mod psi (0) mod 2 in the usual treatment. However, this step gives rise to no error in the value of R obtained from the conventional expressions since the normalisation has been carried out in the same way in the two cases. This conclusion is supported by the agreement of the new values of R with those derived from published calculations. Their values of R also agree to within about 1% with those they have obtained using wavefunctions derived from a relativistic self-consistent field program, showing the validity of the Coulomb approximation.

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