Three electrons in a harmonic oscillator potential: Pairs versus single particles

Abstract

The three-dimensional Schrödinger equation for three electrons in a parabolic confinement potential (with strength measured by the frequency ω) can be decoupled into three pair problems, provided the expectation value of the center of mass vector R is small compared with the average distance between the electrons. This should be fulfilled at the strong correlation limit (small ω), where the electron system tends to crystallize. The remaining part of the Hamiltonian, which is not included in the independent pair model, is taken into account in perturbation theory. The complementary treatment of the weak correlation limit (large ω) considers noninteracting electrons as a zeroth-order approximation and includes the electron–electron interaction in perturbation theory. It turns out that both approaches match satisfactorily for intermediate ω. Our results are compared with those obtained with the Hartree–Fock, configuration interaction, multiconfigurational complete active space, and stochastic variational method approaches and the data from a Wigner crystal treatment in a harmonic approximation.