Low-energy elementary surface excitations of symmetric films of liquid4He atT=0 K

Abstract

It is known that low-energy elementary excitations of symmetric films of liquid4He atT=0 K are characterized by a momentum ħq parallel to the surface and may be described by bound states. We have evaluated wave functions and energies of these states for both “best” short-ranged and optimal long-ranged correlations. Quantities of physical interest may be expressed in terms of these eigenstates and, in particular, for very small momenta (q<0.2 A−1) they are mainly determined by the contribution due to the lowest-lying one. We propose analytic expressions for the lowest-lying excitations and fluctuations in the long-wavelength limit. It is proved that in this limiting case, the excitation energy ħωLW(q) and the “averaged” static structure functionSLW(q) should go linearly to zero asq→0, whereas the “averaged” direct correlationX LW Dg (q) should diverge at the origin as 1/q. It is shown that numerical solutions exhibit the expected long-wavelength behavior provided that optimal correlations are used. All these results are displayed in a series of figures and are discussed in detail.