For the model of closed electron shells in a bare Coulomb potential energy −Z/r, the mth moment of the momentum p for 𝒩 closed shells is calculated as which is valid in the range −3<m<5. For the reduced range −3<m<3, it is shown that (i) can be written in terms of an integral over a finite domain, which is then interpreted as an r-space representation of the moments of momentum. For an arbitrary number 𝒩 of closed shells, the total kinetic energy T can then be written exactly in the form where and μ is determined by normalization of ρsemiclassical to the total number of electrons N. The quantity ck(N) in Eq. (ii) depends on N through Other moments 〈p〉 and 〈p−1〉 are briefly discussed, as well as the relevance of these bare Coulomb field results to the true situation in atomic ions with screened Coulomb potentials and especially to moments of the Compton profile.