Correlation energies of quantum dot electrons with harmonic model interactions

The correlation energies of quantum dot electrons with harmonic model interactions in a large magnetic field are studied by comparing the Hartree-Fock (HF) ground state energies with the exact values. The results for GaAs quantum dots show that the correlation corrections to the ground state energies are very small, only 0.1-0.8% for N = 2-7 electrons. The changes of the correlation energies with the electron-electron interaction strength Omega(2) are also studied. It is shown that the correlation energies increase rapidly with Omega(2) for larger N, but are limited by the condition Omega(2) < omega(0)(2)/N for a stable dot. The comparison of the HF and the exact energies, varying with the total angular momentum, reveals that the correlation energies take their minima at the so-called 'magic' angular momenta that exist in the cases of Coulomb interactions.