Relativistic effects on the core-polarization contribution to the hyperfine interaction in transition-metal and rare-earth atoms and ions

Relativistic effects on the exchange core-polarization (ECP) contribution to the hyperfine constant are analysed. In contrast to the situation for the isomer shift it is not possible to apply a constant relativistic scaling factor for the various shells of the same atom or ion. The origin of this behaviour of the ECP hyperfine effect is examined for a number of systems. It is shown that it is a consequence of the fact that the ECP contribution to the hyperfine constants involves the densities of the s shells at the nucleus as in isomer shift, as well as the exchange interaction of these shells with the unpaired spin electrons (d or f), these two mechanisms are influenced very differently by relativistic effects.