Relativistic effects on transition probabilities in the Mg isoelectronic sequence

Abstract

The dipole oscillator strengths ($f$) for some transitions within the ground complex of the magnesium isoelectronic sequence up to nobelium ($Z=102\mathrm{}$) are calculated using the relativistic wave functions obtained by the parametric-potential method. The length and velocity formulations are used for the transition operator. For the resonance lines, the trend along the sequence differs strongly from the predictions of the nonrelativistic $Z$-dependent theory of many-electron atoms. This behavior is explained in the framework of the relativistic $Z$-dependent theory, which introduces a double power-series expansion in $Z^{-1\mathrm{}}$ (for correlation) and $Z^2{\alpha }^2$ (for relativistic effects). The $f$ value for the first resonance transition increases for low values of $Z$, as the departure from the Russell-Saunders coupling becomes more important, and decreases at high values of $Z$ owing to the contraction of the orbitals toward the nucleus. The $f$ value for the second resonance transition does not fall off for large $Z$, since the frequency of the transition increases approximately as $Z^4$ for high values of $Z$, owing to the relativistic corrections (spin-orbit, Darwin, and $p^4$ terms). The length and velocity formulations are discussed, with particular emphasis on how relativistic contributions to the transition energies or to the transition matrix elements occur. Corrections coming from the finite size of the nucleus, the Breit interaction, and the Lamb shift are introduced; although they are significant, they do not alter the general shape of the curves giving the $Z$ dependence of the $f$ values. On the contrary, retardation effects remain unimportant over the entire range of $Z$.