Correlations in quantum dots

The lowest excitations of a repulsively interacting few particle system are investigated within correlated “pocket state” basis functions. For long range interaction and non-isotropic confining potentials the method becomes exact, in the limit of large mean inter-particle distancesr _s. The multiplet structure of the many-electron energy levels is explained and the ratios δ between the lowest excitation energies, which are related to the electron spin, are determined quantitatively using group theoretical means. The δ are independent of the detailed form of the inter-particle repulsion and of sufficiently larger _s. The obtained δ-values are confirmed by available numerical data. The method is applied to 1D and 2D quantum dots.