Abstract
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→∞.
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