Quantum states of three 3He atoms confined in a C60 fullerene

We employ a Non-Coulombic Non-Orthogonal Configuration Interaction (NC-NOCI) approach to study the confinement of three fermionic helium atoms, 3He, inside a C60 fullerene, with the aim of elucidating how encapsulation affects their spatial distribution and energy-level structure. To interpret the NC-NOCI results, we use a reference Hamiltonian that separates translational, rotational, and vibrational degrees of freedom, which allows us to distinguish (via symmetry arguments) the system's spin isomers, corresponding to doublet and quartet states. The results indicate that, under confinement, the 3He atoms behave collectively as an oblate symmetric rotor consistent with the global Ih symmetry of the 3He3@C60 endohedral fullerene. The NC-NOCI calculations show that the doublet state lies lower in energy than the quartet; moreover, the effect of the C60 cage is not strong enough to force the fermionic helium atoms to form a shell structure. This can be attributed to the very small energy differences between spin-isomer states, on the order of 2 cm-1.