Nuclear spin symmetry-breaking and spin polarization in rotational energy level clusters

Abstract: We present the first quantum mechanical study of hyperfine effects in the rotational cluster states of a symmetric triatomic molecule H$_2$S. Rotational clusters arise from spontaneous symmetry breaking induced by high-angular-momentum rotational motions in certain rigid molecules, resulting in dynamic enantiomorphism driven by kinetic distortion effects. Hyperfine interactions in the cluster states lead to collision-free breaking of nuclear spin symmetry, with the magnitude of nuclear spin ortho-para mixing significantly exceeding that in other states with same or lower angular momentum. The ortho-para mixing induces nuclear spin polarization in the laboratory frame and gives rise to two sets of enantiomers, that have different energies and oppositely oriented nuclear spin projections. Although hyperfine interactions preserve parity, they lift the degeneracy of opposite-parity cluster states. This phenomenon, previously observed experimentally, is explained as a result of tunneling between rotating enantiomers, facilitated by the Pauli exclusion principle.