Compact expressions for the radial electronic density functions for the 2S states of three-electron systems

Abstract

The radial electronic density function D0(r) has been evaluated in closed form for the 2S states of three-electron systems that are described by Hylleraas-type wave functions. The density function D0(r) can be reduced to the form: D0(r)=𝒥I=17 𝒥K=0gI 𝒜IKrKe−αIr. Numerical values of the expansion coefficients 𝒜IK, summation limits gI and exponents αI are determined for the ground states of the following members of the Li I isoelectronic series: Li, Be+, B2+, C3+, N4+, O5+, F6+, and Ne7+. A discussion is given on the constraints that must be imposed on the choice of the basis set for the Hylleraas wave function, in order that D0(r) be reducible to the aforementioned compact analytic form. Expectation values for several moments 〈rn 〉 are calculated using D0(r). The electron–nuclear cusp condition is evaluated for the wave functions used to determine D0(r) for each member of the Li I sequence examined in this investigation.