Selection rules for Raman scattering from eigenmodes of spherical nanoparticles

The elastic vibrations of spherical nanoparticles have been widely studied by Raman scattering. However, there exist more than one set of selection rules for Raman scattering from these vibrations. For instance, Kanehisa has stated that only torsional modes with angular momentum l = 2 are Raman-active, while Tanaka et al. proposed that spheroidal modes of even l and torsional modes of odd l are Raman-active. These contradict selection rules of Duval which states that only spheroidal modes of l = 0 or 2 are Raman-active. Our present calculations based on a macroscopic model show that all torsional modes have vanishing intensity in the Raman spectrum.