By treating the hindered methyl group rotation in solids quantum-mechanically the proton spin lattice relaxation at low temperatures is calculated in first and second order. For low hindering barriers (smaller than 1 kcal/mole) significant differences from the usual relaxation theory are obtained. The inverse correlation time 1/τ0 is essentially given by the rate of non magnetic transitions between the zeroth and first torsional state; and as a consequence the apparent activation energy at low temperatures is given by the difference between these levels. For a given To the relaxation is by a factor ω0/Λ0 (Λ0 is the tunneling frequency) less effective than in the classical case. Good agreement between earlier measurements and this theory is obtained by considering at low efficiency factors also the magnetic interaction between the methylprotons and the surrounding protons. In this way the experimentally observed two relaxation maxima and the ω0-dependence can be explained too.
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J. Haupt (1971) studied this question.