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 e(2)/r(12) as in helium, whereas the M atom is entirely harmonic. Using a 'coupled cluster' representation that = exp((X) over cap)Phi, (X) over cap is shown to be the sum of a one-body operator (X) over cap (1) and a two-body contribution (X) over cap (2). For Phi taken as a product of Gaussian functions, the one-body operator (X) over cap (1), is of length scaling form. In the M model, (X) over cap (2) is proportional to r(12)(2), whereas in the H model it is given explicitly as an infinite series in powers of r(12). Finally, some comments are added about the He-like ions in the limit of large atomic number. (C) 2003 Elsevier B.V. All rights reserved.