Nuclear magnetic resonance line shapes of methyl-like quantum rotors in low-temperature solids

Dissipative dynamics of a tunneling, methyl-like rotor, whose spatial coord inate is weakly coupled to a thermal bath, are described using the reduced density matrix (RDM) approach. It is found that, owing to selection rules i mposed on thermally induced transitions by the symmetrization postulate, th ere are two sorts of coherences between the rotor eigenstates that live lon g enough to be observed on the nuclear magnetic resonance (NMR) time scale. One comprises degenerate pairs of Kramers sublevels at sequential libratio nal levels of the rotor. The other involves nearly degenerate pairs each of which engages one Kramers sublevel and the remaining sublevel, separated f rom the Kramers doublet by tunneling quantum. These are the coherences whic h are seen in the inelastic neutron scattering (INS) patterns of methyl-lik e rotors. From the RDM equation of motion, augumented with spin-dependent t erms relevant in the presence of an external magnetic field, the NMR line s hape equation is derived. With no loss of information it can be formulated in terms of only the spin degrees of freedom. Its dissipative part includes two rate constants that describe damping of the long-lived tunneling and K ramers coherences, respectively; coherent tunneling is represented in the H amiltonian part by an apparent spin-spin coupling. These rate constants are the widths of the inelastic and quasielastic lines, respectively, in the I NS spectra of methyl-like rotors; the apparent coupling constant is the shi ft of the inelastic line. This seems to be the first full exposition of the parallelism between INS and NMR images of tunneling rotors. Rationalizatio n of previous findings involving a CD3 rotor was achieved by use of a simpl e model of rotor-bath couplings, combined with inferences from numerical si mulations of NMR line shapes. (C) 1999 American Institute of Physics. [S002 1-9606(99)02025-5].