Accurate characterization of charged impurity centers is of importance for electronic devices and materials. The role of valley-spin degeneracy on the screening of an attractive ion by the mobile carriers is assessed within a range of systems from spin-polarized single valley to six valley. The screening is treated using the self-consistent local-field correction of Singwi, Tosi, Land, and Sjolander, known as STLS. The bound electron wave function is formulated in the form of an integral equation. Friedel oscillations are seen to be influential especially in two dimensions that cannot be adequately accounted for by the hydrogenic Variational approaches. Our results show appreciable differences at certain densities with respect tb simplified techniques, resulting mainly in the enhancement of the impurity binding energies. The calculated Mott constants are provided where available. The main conclusion of the paper is the substantial dependence of the charged-impurity binding energy on the valley-spin degeneracy in the presence of screening.