On thes-wave model of two-electron atoms

Abstract

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 Schrödinger 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.

Approaching the s-wave model ground state energy of He-like atomic ions: results from a model Hamiltonian

“…is the corresponding ground-state energy. If we take ξ = Z and λ = 1 of a two electron atomic ion, Ψ[Z, 1] is a very poor approximate solution for the real system with a mean value of the real Hamiltonian much above the Hartree-Fock energy [6,7]. So, here we attempt the search of optimal ξ and λ for an external confinement due to a nucleus with charge Z by minimizing the functional…”

“…Howard and March [4] and Amovilli and March [5] discussed in detail, respectively, the properties of the corresponding oneparticle density and density matrix. Nevertheless, the ground-state wave function of the AHM model constitutes a rather poor approximation to the exact solution of the real two-electron system [6,7].…”

Simple relationships between the ionization energies of one-, two- and three-electron ions of consecutive elements

“…A solution for the helium atom and two-electron ions has been sought for (Howard and March 2005) but not found (Ancarani 2006, Serra 2006, Tanner et al 2000. The situation is the same with more complicated systems such as the lithium atom and three-electron ions.…”