Analytical expressions for the n-order momenta of charge distribution for ions

Abstract

In this work a family of four analytic expressions for the n-order momenta of the charge distribution for ions, 〈rn〉, depending on three, two, or one parameters will be presented. These expressions are derived through the use of electronic charge densities obtained from a family of four analytical potentials. The parameters in the expressions were obtained for ions in the ground state from helium to uranium isoelectronic sequences. The use of these parameters allows to find analytical expressions for the 〈rn〉 as functions of the nuclear charge, Z, only. Finally, the results obtained are compared with results computed by different methods.