The limiting behaviour of atomic wave functions for large atomic number

If P(nl; r) is the (nl) radial wave function in an atom of atomic number N, and PH(nl; r) is the corresponding wave function of hydrogen, then, for a given configuration and for large NN-1/2P(nl; r) = PH(nl;Nr)+(1/N) Q(nl;Nr) + O(1/N2) 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 -> oo of certain screening numbers o(nl) have been determined, so that estimation of o(nl) for atoms of atomic number higher than any for which calculation of wave functions frag been carried out becomes a process of interpolation instead of extrapolation. It is found that for given configuration o(nl) is nearly linear in the mean radius r over the whole range from N ->oo to the neutral atom. For a given value of r/r(nl), r1/2PN(nl; r) is nearly linear in r. The r derivatives of this function at r = 0 can also be evaluated from the Q(nl; Nr) functions.