Correlated kinetic energy density functional of ground states of harmonically confined two-electron atoms for arbitrary interparticle interaction

Utilizing the earlier work of Holas et al (2003 Phys. Lett. A 310 451) and the more recent contribution of Akbari et al (2009 Phys. Rev. A 80 032509), we construct an integral equation for the relative motion (RM) contribution tRM(r) to the correlated kinetic energy density for modelling two-electron atoms with harmonic confinement but arbitrary interparticle interaction. It is stressed that tRM = tRM[f(G)], where f(G) is the atomic scattering factor: the Fourier transform of the density ρ(r). As a simple illustrative example of this functional relation for the correlated kinetic energy density, the harmonic Moshinsky case is investigated, the scattering factor then having a Gaussian form. (paper)