It is shown that with proper values of the effective charge, the hydrogen-like (HL) wave functions are almost as good as the more sophisticated Hatree-Fock (HF) wave functions in calculations of the double-differential cross section of Compton scattering within the nonrelativistic impulse approximation (IA). Only a single value of the optimized effective charge for a given subshell of an atom is required for an accurate description of Compton spectra in a wide range of experimental conditions under which IA is a good approximation. That is demonstrated by results obtained for the K-shell of several atoms and for higher subshells in germanium. It has been found that a constant value of the optimal effective charge can be used as a criterion for the validity of IA, which is explained within the existing knowledge of IA. Simple analytical expressions for HL-Compton profiles have a compact form and are a much faster way to calculate the cross sections than using extensive tabulations of HF Compton profiles. These features can be useful in very extensive numerical calculations of Compton scattering in radiation physics, biomedicine, industry and in other practical applications
