An exact coupled cluster theory for Moshinsky and Hookean two-electron model atoms with spin-compensated ground states

The Moshinsky (M) and Hookean (H) models of two-electron atoms replace the electron–nuclear interaction by harmonic forces. The difference between them resides in the interparticle interaction, the H model retaining e2/r12 as in helium, whereas the M atom is entirely harmonic. Using a ‘coupled cluster’ representation that Ψ=exp(X̂)Φ, X̂ is shown to be the sum of a one-body operator X̂1 and a two-body contribution X̂2. For Φ taken as a product of Gaussian functions, the one-body operator X̂1 is of length scaling form. In the M model, X̂2 is proportional to r122 whereas in the H model it is given explicitly as an infinite series in powers of r12. Finally, some comments are added about the He-like ions in the limit of large atomic number.