A nuclear configuration interaction approach to study nuclear spin effects: an application to ortho- and para-³ He₂...

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two ³ He atoms encapsulated in C₆₀ . At the Hartree-Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree-Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-³ He₂ @C₆₀ ) and triplet (ortho-³ He₂ @C₆₀ ) nuclear spin configurations, respectively. The ortho-³ He₂ @C₆₀ ground state is 5.69 cm^-1 higher in energy than the para-³ He₂ @C₆₀ ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C₆₀ embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of ³ He₂ @C₆₀ .