Do density oscillations exist near the free surface of ⁴He?

Variational calculations are carried out for liquid ⁴He with a free surface. Five classes of wave functions are studied, four of which permit the density profile to exhibit oscillations near the surface. We conclude that it is not possible to determine with certainty whether density oscillations exist by variational methods alone. On the other hand, certain qualitative features of the layered structure and quantitative bounds on the extent of the oscillations can be observed, if the latter indeed exist. These observations lead us to believe that effects of a layered structure on, e.g., evaporation, surface scattering, and properties of adsorbates are probably too weak to be detectable.