A reformulation of the theory of field isotope shift in atoms

The theory of the field isotope shift (FS) in atomic spectra is discussed critically and the results are presented in a form which is more straightforward than the expressions traditionally used to interpret experimental data. First-order perturbation theory is applied within the single-particle framework to the case of an s or p1/2 electron outside closed shells. Parameters to take account of many-body effects are subsequently included. The nuclear and electronic dependences of the FS are separately discussed. In a generalisation of the work of Seltzer (1986), it is shown that the former can be represented as a series of even charge moments: the coefficients of the first three terms for an s electron are given. The difference between the series for an s and a p1/2 electron is shown to be generally insignificant. The electronic dependence enters through the (relativistic) probability density N of the electron at the origin; for the case of an s electron. They relate N to the magnetic hyperfine splitting factor alpha s. A table which allows N to be found from a measurement of alpha s is given. Second-order field shifts are of the order of 10-3-10-4 of the first-order shifts for a two-neutron change.