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

Abstract

The inelastic-neutron-scattering spectrum of totally hydrogenated 4-methyl-pyridine $(4\mathrm{MP}{\ensuremath{-}h}_{7})$ at 0.5 K reveals three bands whose widths are limited to the resolution function of the spectrometer: 9 \ensuremath{\mu}eV. Within the quantum sine-Gordon theory, these bands are assigned to in-phase (537 \ensuremath{\mu}eV) and out-of-phase (470 \ensuremath{\mu}eV) tunneling transitions and to the traveling transition of the breather mode (516 \ensuremath{\mu}eV). The spectra of isotopic mixtures with the totally deuterated analogue $(4\mathrm{MP}{\ensuremath{-}d}_{7}),$ containing 85%, 65%, and 50% of $4\mathrm{MP}{\ensuremath{-}h}_{7},$ respectively, were obtained at 1.8 K with the same resolution. The frequency of the breather traveling state is progressively shifted downwards to 506 \ensuremath{\mu}eV. The frequency shift is represented with the breather mode in clusters of hydrogenated molecules. Simultaneously, an additional band is observed between 490 and 497 \ensuremath{\mu}eV 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 \ensuremath{\mu}eV are attributed to the breather mode in rather small hydrogenated clusters with deuterated clusters as reflective boundaries.