  We show that the addition spectra of semiconductor quantum dots in the
presence of magnetic field can be studied through a theoretical scheme that
allows an accurate and practical treatment of the single particle states and
electron-electron interaction up to large numbers of electrons. The calculated
addition spectra exhibit the typical structures of Hund-like shell filling, and
account for recent experimental findings. A full three dimensional description
of Coulomb interaction is found to be essential for predicting the conductance
characteristics of few-electron semiconductor structures.
