Long-lived nuclear spin states have a relaxation time much longer than the longitudinal relaxation time T1. Long-lived states extend significantly the time scales that may be probed with magnetic resonance, with possible applications to transport and binding studies, and to hyperpolarised imaging. Rapidly rotating methyl groups in solution may support a long-lived state, consisting of a population imbalance between states of different spin exchange symmetries. Here, we expand the formalism for describing the behaviour of long-lived nuclear spin states in methyl groups, with special attention to the hyperpolarisation effects observed in 13CH3 groups upon rapidly converting a material with low-barrier methyl rotation from the cryogenic solid state to a room-temperature solution [M. Icker and S. Berger, J. Magn. Reson. 219, 1 (2012)]. We analyse the relaxation properties of methyl long-lived states using semi-classical relaxation theory. Numerical simulations are supplemented with a spherical-tensor analysis, which captures the essential properties of methyl long-lived states.
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