Comparison of methods for calculating atomic shielding factors

A new method for determining atomic shielding factors to use in hydrogenlike wave functions which gives "exact" Compton profiles in close agreement with experiment was recently developed by the present authors. These shielding factors Z*(0) are determined by imposing the requirement for each atomic orbital that the "impulse" hydrogenic Compton-profile value at its center, $q=0$, match the Hartree-Fock Compton-profile value. We now compare the use of Z*(0) hydrogenic values in the calculation of the moments $〈r〉$, 〈r²〉, and 〈r⁴〉 with values of these moments obtained using Slater, Clementi, Burns, and binding-energy-matched Z*'s used in hydrogenic wave functions for K-, L-, and M-shell orbitals for rare-gas atoms up through xenon. Relative accuracy is determined by comparison to Hartree-Fock results for these moments. It is found that for $1s$, $2p$, and $3d$ states, our Z*(0) values give the most consistently accurate results. A table of recommended Z* values is given for all atoms and states considered.