Research on the differential cross-section areas for the Raman scattering in quantum wires without phonons
Abstract
We research the problem solving for quantum wire of cylindrical ring geometry with the length L and radius R in the vacuum, we gain the states and energies of conduction and valence electrons. Using the obtained results to calculate the differential cross-section areas in Raman scattering by considering (here, the assumption that is, in the first state, the valence band is completely occupied and the conduction band is completely empty and the energy of the incoming photon is ; the final state consists of an electron in the conduction band and a hole in the valence band and the energy of the emitted photon is ). By utilizing Hamiltonian to describe interactions of electrons with an electromagnetic field, and investigating two capable processes in electronic Raman scattering, we can calculate their transition amplitudes. From that, we get transition velocity of the processes and finally obtain the formula of differential cross-section areas. Numerical calculations with the GaAs quantum wire show that the positions of the peaks of cross-section areas don’t depend on the frequency of the incident photons, they only depend on the difference of the energy levels. Remarkably, the size of the quantum wire affects the intensity of the peaks of cross-section areas in the opposite direction.