We probe the electronic shell structure of quasiatomic systems, realized in GaAs-AlGaAs quantum dots, by resonant Raman spectroscopy. We observe a series of discrete spin-density excitations, whose energies are very close to single-particle level spacings in a quantum dot. The combined information from experiments at different wave vectors in the lateral direction and from investigations with applied magnetic fields reveals a distinct set of Raman allowed transitions (Δn,Δm), where changes Δn and Δm are changes in radial and angular momentum quantum numbers, respectively.