Heavy alkali atoms in jellium

We report one-electron calculations of the soft-x-ray outer-shell absorption and emission in K, Rb, and Cs. The absorbing ion is placed at the center of a metal consisting of a valence band of electrons and a uniform positive background which has a spherical cavity removed from around the ion. Self-consistent solutions for states with and without a core hole are found using the density-functional approach. In our solution the core electrons bound to the central ion and the valence electrons are allowed to relax into the self-consistent solution. We find self-consistent potentials, charge densities, threshold energies, and cross sections for the soft-x-ray transitions. Moreover, we calcualte the exponents $\alpha$, ${\alpha }_0$, and ${\alpha }_1$ essential to the threshold theory of Mahan, Nozières, and de Dominicis. We point out that the anomalous behavior of ${\alpha }_0$ for K, Rb, and Cs, where it decreases for increasing $r_s$ rather than increases as it does for other metals, can be explained if one takes into account the effects of the structure and size of the core hole, as well as the screening when determining ${\alpha }_0$ for a series of metals.