## Abstract

If P(nl; r) is the (nl) radial wave function in an atom of atomic number N, and P$_{\text{H}}$(nl; r) is the corresponding wave function of hydrogen, then, for a given configuration and for large N N$^{-\frac{1}{2}}$P(nl; r) = P$_{\text{H}}$(nl; Nr) + (1/N) Q(nl; Nr) + O(1/N$^{2}$). The equations for the functions Q(nl; Nr) have been set up and solved for a number of (nl) values and configurations of up to twenty-eight electrons. From the solutions, the limiting values as N $\rightarrow \infty $ of certain screening numbers $\sigma $(nl) have been determined, so that estimation of $\sigma $(nl) for atoms of atomic number higher than any for which calculation of wave functions has been carried out becomes a process of interpolation instead of extrapolation. It is found that for given configuration $\sigma $(nl) is nearly linear in the mean radius $\overline{r}$ over the whole range from N $\rightarrow \infty $ to the neutral atom. For a given value of r/$\overline{r}$(nl), $\overline{r}^{\frac{1}{2}}$P$_{N}$(nl; r) is nearly linear in $\overline{r}$. The $\overline{r}$ derivatives of this function at $\overline{r}$ = 0 can also be evaluated from the Q(nl; Nr) functions.