Thomas-Fermi Theory of the Hyperfine Constants of Endohedral Fullerene Atoms

TL;DR

This paper introduces a modified Thomas-Fermi model to accurately predict hyperfine constants of endohedral fullerenes, aligning well with experimental data and offering insights for quantum computing applications.

Contribution

A novel modified Thomas-Fermi approach that accounts for fullerene effects on hyperfine constants, providing quantitative predictions and understanding of size and charge influences.

Findings

Quantitative agreement with experimental data for N@C60 and N@C70.

Fullerene radius has a greater impact than charge on hyperfine constants.

Predictions for hyperfine constants of larger fullerenes C60 to C500.

Abstract

We present a modified Thomas-Fermi theory that describes the increase of the hyperfine coupling constants of endohedrally enclosed atoms. We use the March boundary conditions corresponding to a positively charged spherical shell surrounding the nuclear potential to represent the effect of the fullerene shell. We obtain quantitative agreement with experimental data for N@C$_{60}$ and N@C$_{70}$, and find that fullerene radius dominates over the fullerene charge in its effect on the hyperfine coupling constants. We also present predictions for the hyperfine coupling constants of the endohedral nitrogen fullerenes between C$_{60}$ and C$_{500}$, and discuss the implications for proposed quantum computing schemes.