Electron elastic scattering off $A$@C$_{60}$: The role of atomic polarization under confinement

TL;DR

This paper investigates how atomic polarization influences electron elastic scattering off endohedral fullerenes, specifically A@C60, highlighting the effects of confinement and dynamical polarization on scattering processes.

Contribution

It introduces a model for C60 confinement and solves the Dyson equation to analyze the impact of atomic polarization on electron scattering in endohedral fullerenes.

Findings

Atomic polarization significantly affects scattering off A@C60.

Confinement modifies the polarization impact compared to free atoms.

The role of polarization in endohedral scattering differs markedly from free-atom scattering.

Abstract

The present paper explores possible features of electron elastic scattering off endohedral fullerenes $A$@C$_{60}$. It focuses on how dynamical polarization of the encapsulated atom $A$ by an incident electron might alter scattering off $A$@C$_{60}$ compared to the static-atom-$A$ case, as well as how the C$_{60}$ confinement modifies the impact of atomic polarization on electron scattering compared to the free-atom case. The aim is to provide researchers with a "relative frame of reference" for understanding which part of the scattering processes could be due to electron scattering off the encapsulated atom and which due to scattering off the C$_{60}$ cage. To meet the goal, the C$_{60}$ cage is modeled by an attractive spherical potential of a certain inner radius, thickness, and depth which is a model used frequently in a great variety of fullerene studies to date. Then, the Dyson equation for the self-energy part of the Green's function of an incident electron moving in the combined field of an encapsulated atom $A$ and C$_{60}$ is solved in order to account for the impact of dynamical polarization of the encaged atom upon $e + A@{\rm C_{60}}$ scattering. The Ba@C$_{60}$ endohedral is chosen as the case study. The impact is found to be significant, and its utterly different role compared to that in $e + Ba$ scattering is unraveled.