Asymptotic coefficients for atoms and ions

We derive convenient analytical formulas in the effective-range approximation for the asymptotic coefficient C _κ of the radial wave function at infinity and for the average radius of the system. A comparison with the results 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 approximation for C _κ. Finally, we discuss the logarithmic increase in the effective ranges of ns states as n→∞. Zh. éksp. Teor. Fiz. 115, 521–541 (February 1999)