Application of perturbation theory to finding vibrational frequencies of a spheroid
Phys. Rev. B 113, 035412 – Published 8 January, 2026
DOI: https://doi.org/10.1103/qvbw-yd7z
Abstract
We apply perturbation theory of boundary conditions, originally developed by A.B. Migdal and independently by S.A. Moszkowski for deformed atomic nuclei, to finding eigenfrequencies of Raman-active spheroidal modes of a spheroid from those of a sphere and compare the outcomes with the results of numerical calculations for CdSe and silver nanoparticles. The modes are characterized by the total angular momentum and are fivefold degenerate for a sphere but split into three distinct modes, characterized by the absolute value of the total angular-momentum projection onto the spheroidal axis, in the case of a spheroid. The perturbation method works well in the case of the rigid boundary conditions, with the displacement field set to zero at the boundary, and accurately predicts the splittings when the spheroidal shape is close to a sphere, but fails in the case of the stress-free boundary conditions.
