Numerical values for the one-electron integrals of interest in the analysis of atomic hyperfine structure have been calculated by using screened relativistic wave functions. Ratios of these integrals, representing the relativistic correction factors of Casimir, are given to replace the older values which neglected shielding effects. The most marked changes occur in the studies of the octopole interaction and hfs anomalies in $p$-states. The calculated one-electron magnetic dipole integral, when compared with the experimental ratio, dipole hfs/nuclear moment, makes it possible to deduce the magnitude of atomic polarization (Sternheimer) effects. In the doublet $p$-states that were studied, the polarization terms seem to be almost entirely of the sort discussed in an earlier paper: excitation of $s$-electrons. In a general discussion of polarization calculations we give some explanation of the large correction factors for the fine structure, dipole and quadrupole hyperfine structure that were calculated by Sternheimer (the radial redistribution of charge terms). It is also suggested that large polarization corrections may be needed for the octopole interaction.

• Received 31 August 1956

DOI:https://doi.org/10.1103/PhysRev.105.173