The shell structure of atoms and ions in momentum space

The radial momentum distributions for the ground states of the first 92 atoms from hydrogen to uranium, and of singly positive ions from helium to barium and from lutetium to radium, constructed from nonrelativistic SCF wave functions, are investigated. These distributions display a number of maxima that, as is shown, depend strongly on the electronic structure and can be assigned each to a particular shell—the first maximum corresponding to the outermost shell. Four maxima is the most that appear for each atom or ion studied implying that in some cases only the outermost shells are evident. This result is similar to the fact that for some atomic systems in position space, only the innermost shells lead to maxima in the radial density. As a general conclusion, if both momentum and position space radial electronic densities are considered, then all shells become evident for the atomic cases studied.