Using probe molecules with resonant nuclei and nuclear inelastic scattering, we are able to measure the density of states exclusively for collective motions with a correlation length of more than $\sim 20\AA$. Such spectra exhibit an excess of low-energy modes (boson peak). This peak behaves in the same way as that observed by conventional methods. This shows that a significant part of the modes constituting the boson peak is of collective character. At energies above the boson peak, the reduced density of states of the collective motions universally exhibits an exponential decrease.

• Received 12 December 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.245508