We report exact diagonalization studies of inelastic light scattering in few-electron quantum dots under the strong confinement regime characteristic of self-assembled dots. We apply the orthodox (second-order) theory for scattering due to electronic
excitations, leaving for the future the consideration of higher-order effects in the formalism (phonons, for example), which seem relevant in the theoretical description of available experiments. Our numerical results stress the dominance of monopole peaks in Raman spectra and the breakdown of selection rules in open-shell dots. The dependence of these spectra on the number of electrons in the dot and the incident photon energy is explicitly shown. Qualitative comparisons are made with recent experimental results.
In a two-dimensional parabolic quantum dot charged with $N$ electrons, Thomas-Fermi theory states that the ground-state energy satisfies the following non-trivial relation: $E_{gs}/(hbaromega)approx N^{3/2} f_{gs}(N^{1/4}beta)$, where the coupling co
nstant, $beta$, is the ratio between Coulomb and oscillator ($hbaromega$) characteristic energies, and $f_{gs}$ is a universal function. We perform extensive Configuration Interaction calculations in order to verify that the exact energies of relatively large quantum dots approximately satisfy the above relation. In addition, we show that the number of energy levels for intraband and interband (excitonic and biexcitonic) excitations of the dot follows a simple exponential dependence on the excitation energy, whose exponent, $1/Theta$, satisfies also an approximate scaling relation {it a la} Thomas-Fermi, $Theta/(hbaromega)approx N^{-gamma} g(N^{1/4}beta)$. We provide an analytic expression for $f_{gs}$, based on two-point Pade approximants, and two-parameter fits for the $g$ functions.
