Spherically and system-averaged pair density functional theory

In a couple of recent papers Gori-Giorgi and Savin [Phys. Rev. A 71, 032513 (2005)] proposed a theory that provides simple radial equations to generate the spherically and system averaged pair density. In a recent density matrix functional theory [A. Nagy, Phys. Rev. A 66, 022505 (2002)] it was shown that the problem of an arbitrary system can be reduced to a two-particle problem. Based on this theory, via a double adiabatic connection, it is rigorously derived that the square root of the ground-state spherically and system averaged pair density is the solution of a simple radial equation, that is, contrary to the theory of Gori-Giorgi and Savin only a single equation has to be considered.