Asymptotic coefficients for atoms and ions

We derive convenient analytical formulas in the effective-range approximati on for the asymptotic coefficient C (kappa) of the radial wave function at infinity and for the average radius of the system. A comparison with the re sults of numerical calculations (done by the Hartree-Fock method) for multi -electron atoms and ions reveals that this approximation has good accuracy for valence s-electrons in all atoms from hydrogen to uranium. We calculate the values of the scattering lengths and the effective ranges for electron -atom and electron-ion scattering. We also examine the quasiclassical appro ximation for C (kappa). Finally, we discuss the logarithmic increase in the effective ranges of ns states as n --> infinity. (C) 1999 American Institu te of Physics.