Theory of nuclear spin conversion in the phase of solid CH4

Calculations of the T(I = 1) to A(I = 2) spin isomer conversion rate for solid CH 4 in the partially ordered β phase are performed for mechanisms involving both inter- and intramolecular dipole–dipole interactions. In each case energy is conserved by means of phonon emission. The intermolecular mechanism leads to a conversion rate of about 1%/h for the free rotor molecules and about 0.002 to 0.010%/h (for 0 < T < 4.2) for the ordered molecules. Here the difference in ordered and disordered molecule conversion rates results mainly from the fact that the T-A splitting is much smaller for ordered molecules and that the efficiency of the phonon emission process scales like the cube of this energy. The closely related calculation for an ordered molecule with a neighboring O 2 impurity gives conversion rates of roughly 25%/min. The most effective intrinsic mechanism for free rotor molecules is the hybrid process in which the intramolecular dipole–dipole interaction mixes the nuclear spin states and the intermolecular octupole–octupole interaction causes transitions between rotational states and conserves energy by coupling to the lattice. The rate for this mechanism is 33 to 59% per hour, depending on the value used for the octupole moment, in reasonable agreement with experiment. For ordered molecules the rate is much slower and temperature dependent. At 4.2 K the calculated conversion time is 50 to 100 h.