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.