Excitations in confined helium

We design models for helium in matrices such as aerogel, Vycor, or Geltech from a manifestly microscopic point of view. For that purpose, we calculate the dynamic structure function of ${}^{4}\mathrm{He}$ on Si substrates and between two Si walls as a function of energy, momentum transfer, and the scattering angle. The angle-averaged results are in good agreement with the neutron scattering data; the remaining differences can be attributed to the simplified model used here for the complex pore structure of the materials. A focus of the present work is the detailed identification of coexisting layer modes and bulklike excitations, and, in the case of thick films, ripplon excitations. Involving essentially two-dimensional motion of atoms, the layer modes are sensitive to the scattering angle.