Particle in a box: From textbook to real life example

M. Aouanea , J. Armstronga, M. Walkeyb, G. Hoffmanb, G. R. Bacanub, R. J. Whitbyb, M. H. Levittb and S. Rolsc,

a ISIS Pulsed Neutron and Muon Source, Didcot, Oxfordshire, UK
b School of Chemistry, University of Southampton, Southampton, UK
c Institut Laue-Langevin, Grenoble, France

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Endofullerene molecules, denoted as A@C60, consist of small atomic or molecular entities trapped inside a highly symmetric C60 cage. The molecular surgery method, consisting of opening an orifice in the fullerene cage, allows the introduction of light molecules and atoms. The simplest form of endofullerenes and subject of this highlight is the atomic endofullerene 3He@C60.
Atomic endofullerenes offer a real-life manifestation of the ‘particle in a spherical well’, with a single atom enclosed inside a nearly spherical cavity. Through performing inelastic neutron scattering (INS) experiments at cryogenic temperatures, we can probe the translational dynamics of the confined 3He atom, and directly recreate a system where the eigenvalues and eigenstates can be analytically calculated by solving the Schrödinger equation. By simulating the INS spectrum and comparing it to the experimental data (figure), we gain insights into the shape of the potential energy surface inside the cage.
This work was part of M. Aouane’s thesis work, a collaboration between ILL, ISIS and the University of Southampton, and was awarded the yearly SFN thesis prize during the 2023 Journées de la Diffusion Neutronique.

Figure: measured and calculated inelastic neutron scattering (energy, wave-vector) maps. Ei is the incident neutron energy.

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