  The inelastic scattering of neutrons by nanoparticles due to acoustic
vibrational modes (energy below 10 meV) confined in nanoparticles is calculated
using the Zemach-Glauber formalism. Such vibrational modes are commonly
observed by light scattering techniques (Brillouin or low-frequency Raman
scattering). We also report high resolution inelastic neutron scattering
measurements for anatase TiO2 nanoparticles in a loose powder. Factors enabling
the observation of such vibrations are discussed. These include a narrow
nanoparticle size distribution which minimizes inhomogeneous broadening of the
spectrum and the presence of hydrogen atoms oscillating with the nanoparticle
surfaces which enhances the number of scattered neutrons.
