The $\alpha$-dependence of transition frequencies for ions Si II, Cr II, Fe II, Ni II, and Zn II

Abstract

We performed accurate calculation of $\alpha$-dependence ($\alpha=e^2/hc$) of the transition frequencies for ions, which are used in a search for the variation of the fine structure constant $\alpha$ in space-time. We use Dirac-Hartree-Fock method as a zero approximation and then the many-body perturbation theory and configuration interaction methods to improve the results. An important problem of level pseudocrossing (as functions of $\alpha$) is considered. Near the crossing point the derivative of frequencies over $\alpha$ varies strongly (including change of the sign). This makes it very sensitive to the position of the crossing point. We proposed a semiempirical solution of the problem which allows to obtain accurate results.