The connection between elastic scattering cross sections and acoustic vibrations of an embedded nanoparticle

TL;DR

This paper explores how acoustic vibrational frequencies of an embedded nanoparticle relate to its elastic scattering cross sections, providing new methods to predict mode frequencies and analyzing wave interactions.

Contribution

It introduces a novel connection between scattering cross sections and vibrational modes, along with an alternative prediction method using a large shell approximation.

Findings

Vibrational frequencies correspond to poles of the scattering cross section.

Pole locations remain unchanged for nonplanar incident waves.

A shell approximation effectively predicts mode frequencies.

Abstract

Arbitrary waves incident on a solid embedded nanoparticle are studied. The acoustic vibrational frequencies are shown to correspond to the poles of the scattering cross section in the complex frequency plane. The location of the poles is unchanged even if the incident wave is nonplanar. A second approach approximating the infinite matrix as a very large shell surrounding the nanoparticle provides an alternate way of predicting the mode frequencies. The wave function of the vibration is also provided.