Electron-electron interactions between orbital pairs in quantum dots

We derive a simple model for the estimates of the orbital-pair interaction in self-assembled dots and show that many-body interactions between all orb ital pairs for a few electrons are determined in a first approximation by t he classical Coulomb interaction between the first two electrons. The estim ated values are within 35% of the accurate results derived from local densi ty functional theory. We extend the model to electrostatically defined plan ar quantum dots and find a better agreement (20%). This is a result of the weakening of the individual orbital-pair interactions with the number of el ectrons in the dot caused by the screening of the confining potential.