# The Electron Bubble and the \(He_{60}\) Fullerene: A First-Principles Approach

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## Abstract

Helium has a light atomic mass and, as a closed shell element, shows minimal interaction with other particles of the environment. Such properties favor the capture of an electron by liquid helium, leading to the formation of an electron bubble. The helium bubbles are of theoretical importance since different levels of quantum mechanical models can be tested for the correct prediction of a single quantum particle trapped in a cage. In this work, we propose a first-principles model of the electron bubble that takes, for the first time, the electronic structure of the cage into consideration. The model consists of a fullerene-type cage made of *He* atoms with an additional electron. The solution of the many-body Schroedinger equation is then performed using density functional theory, with a small and an extra-large atomic basis set. Several major improvements over the model of a particle in a rigid or soft spherical potential are assessed in this way, such as the localization and delocalization of the electron in the helium bubble, the transition of the electron to the continuum, the polarization of the *He* atoms building the wall, the ionic state of the electron bubble, besides the determination of relations of the volume-pressure type.

## Keywords

Electron bubble Confinement of an electron Electronic properties Localized–delocalized states Density functional theory## Notes

### Acknowledgements

The authors express gratitude to DGTIC-UNAM for the supercomputing facilities, and the computing staff of the Institute of Physics, UNAM, for their valuable support. RS acknowledges financial support from IF-UNAM, under project PIIF-03, and project IN-111-918 from PAPIIT-DGAPA to perform this research.

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