On the s-wave model of two-electron atoms

One of the simplest s-wave models of a two-electron atom, in which the electron-electron repulsion is replaced by the lowest order term in a one-centre expansion about the nucleus, is investigated. The comparison of the corresponding Schroedinger equation with that of the real two-electron atom for S-states leads to a simple analytical property for the variational ground-state energy of the s-wave model. As a consequence, it is demonstrated that the solution to the s-wave model recently proposed by Howard and March (2005 Phys. Rev. A 71 042501) cannot be the exact ground-state wavefunction as claimed