Collective excitations in quantum dots

We investigate different types of collective excitations in a quantum dot containing finite number of electrons at zero magnetic field. To estimate the excitation energies analytically we follow the energy weighted sum-rule approach. We consider the most general multipole excitation with angular momentum l, and the breathing mode excitation (monopole excitation) of a large quantum dot, for three different types of effective electron–electron interaction. These are the logarithmic interaction, the short-range pseudopotential and the Coulomb interaction. The ground-state density of the many-body system is calculated within Thomas–Fermi approximation. The analytical results for the collective excitation energies and their dependence on the system size and other external parameters are discussed in detail.