INELASTIC-NEUTRON-SCATTERING STUDY OF METHYL TUNNELING AND THE QUANTUM SINE-GORDON BREATHER IN ISOTOPIC MIXTURES OF 4-METHYL-PYRIDINE AT LOW-TEMPERATURE

The inelastic-neutron-scattering spectra in the 500-eV region of a series of mixtures of totally hydrogenated and totally deuterated 4-methyl-pyridine molecules (4MP-h7 and 4MP-d7, respectively) with relative concentrations in 4MP-h7 of 100, 85, 65, 50, 26, 20, and 5 % are presented at various temperatures: 2.5, 4.5, 6.5, 8.5, 11 and 15 K. In pure 4MP-h7 at 2.5 K, the spectrum shows three partially resolved bands at 468, 510, and 535 eV. These frequencies are unaffected by temperature up to 15 K where the bands become rather weak. At 2.5 K, the main peak shows a continuous frequency shift with increasing concentration in 4MP-d7 down to 360 eV (5% 4MP-h7) indicating collective motions of the methyl groups. This frequency shift is very sensitive to temperature and vanishes above 10 K. These unusual aspects of the methyl-group dynamics are quantitatively represented by the quantum sine-Gordon equation describing a one-dimensional infinite chain of coupled methyl groups. Accordingly, the weak side bands at 468 and 535 eV are assigned to in-phase and out-of-phase tunneling transitions, respectively. The main peak at 510 eV in pure 4MP-h7 is due to the excitation of the first quantized traveling state of the breather mode. Isotopic dilution effects are understood in terms of breathers trapped in clusters of 4MP-h7 molecules surrounded by 4MP-d7 molecules which act as reflective walls. Temperature effects are due to the thermal excitation of breather-roton states in relationship with the zero-point energy difference for 4MP-h7 and 4MP-d7 clusters. Finally, some previous spectroscopic data are reconsidered on the basis of the quantum sine-Gordon theory. © 1990 The American Physical Society.