n-shell Thomas-Fermi model: Coulomb atom

A simple expression for the electron density of then-shell of the Coulomb atom with the nuclear charge Zρ _n(r)=Z ³ π ^?2 n ^?3(2Z ^?1 r ^?1?n ^?2)^1/2 is found in the semi-classical approximation. It is used for the asymptotic estimation of averages 〈r ^a 〉 (?2<a<∞). An explicit dependence of the leading oscillatory contribution to 〈r ^a 〉 due to angular moments on the electron number is also obtained.