  A theoretical study of single electron capacitance spectroscopy in quantum
dots is presented. Exact diagonalizations and the unrestricted Hartree-Fock
approximation have been used to shed light over some of the unresolved aspects.
The addition spectra of up to 15 electrons is obtained and compared with the
experiment. We show evidence for understanding the decrease of the single
electron tunneling rates in terms of the behavior of the spectral weight
function. (To appear in Phys. Rev. B (Rapid Comm.))
