In very recent work, Amovilli and March have considered the Hookean atom with four electrons. In particular, they demonstrated the cross-over from a triplet P-g ground state at large harmonic force constant k to a quintet S-u configuration for weak confinement, by means primarily of diffusion quantum Monte Carlo simulation. Here, we focus on such a quintet state for again four spin half fermions but now interacting via a harmonic pair force -K r(ij). The spatial quintet Psi is then available, with its eigenvalue. Progress on calculating low-order spinless density matrices is recorded. Finally, this prompts us to examine the Amovilli-March results when extrapolated to small k not equal 0. We display as k --> 0(+) approximate results for the four-electron Hookean atom model, including fitted analytic forms for kinetic and Coulomb energy as a function of k as k --> 0(+). (C) 2012 Elsevier B. V. All rights reserved.