Inelastic-neutron-scattering study of the sine-Gordon breather interactions in isotopic mixtures of 4-methyl-pyridine

The inelastic-neutron-scattering spectrum of totally hydrogenated 4-methyl-pyridine (4MP-h₇) at 0.5 K reveals three bands whose widths are limited to the resolution function of the spectrometer: 9 μeV. Within the quantum sine-Gordon theory, these bands are assigned to in-phase (537 μeV) and out-of-phase (470 μeV) tunneling transitions and to the traveling transition of the breather mode (516 μeV). The spectra of isotopic mixtures with the totally deuterated analogue (4MP-d₇), containing 85%, 65%, and 50% of 4MP-h₇, respectively, were obtained at 1.8 K with the same resolution. The frequency of the breather traveling state is progressively shifted downwards to 506 μeV. The frequency shift is represented with the breather mode in clusters of hydrogenated molecules. Simultaneously, an additional band is observed between 490 and 497 μeV whose intensity is proportional to the amount of deuterated molecules. This band is attributed to the breather-mode interaction with isolated deuterated molecules. The breather wave form and the effective potential for the impurity are calculated. For the sample containing 50% of each isotopomer, new bands at 478 and 464 μeV are attributed to the breather mode in rather small hydrogenated clusters with deuterated clusters as reflective boundaries.