Interacting Electrons in Parabolic Quantum Dots: Energy Levels, Addition Energies, and Charge Distributions

We investigate the properties of interacting electrons in a parabolic confinement. To this end we numerically diagonalize the Hamiltonian using the Hartree-Fock based diagonalization method which is related to the configuration interaction approach. We study different types of interactions, Coulomb as well as short range. In addition to the ground state energy we calculate the spatial charge distribution and compare the results to those of the classical calculation. We find that a sufficiently strong screened Coulomb interaction produces energy level bunching for classical as well as for quantum-mechanical dots. Bunching in the quantum-mechanical system occurs due to an interplay of kinetic and interaction energy, moreover, it is observed well before reaching the limit of a Wigner crystal. It also turns out that the shell structure of classical and quantum mechanical spatial charge distributions is quite similar