Four electrons interacting pairwise in the limit of infinitesimal confining potentials: Especially the quintet spin state

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 Pg ground state at large harmonic force constant k to a quintet Su 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 rij. The spatial quintet Ψ 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 ≠ 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+.