Scaling in the S and P states of the helium isoelectronic sequence

Mean values of r ₁ ^r and r _r ¹² for the ground and several excited states of the helium isoelectronic sequence are used to demonstrate that a simple scaling which superimposes the distribution function f(r ₁₂) as a function of the atomic number leads to a similar result for the electron density distribution D(r₁). On the basis of a screening interpretation of the scaling parameter , it is concluded that screening is greater in the singlet than the triplet state of a particular configuration, that screening is greater in the P states than the corresponding S states, and that the screening approaches the limiting value of 1 for the highly excited states. The perturbation expansions of Scherr and Knight are used to determine the limiting value of when Z and the relationship between the scaling parameter and the scale factor, chosen so that a trial wave function satisfies the virial theorem, is discussed. A brief discussion of the scaling of the Coulomb hole is presented.