Elastic scattering of 4He atoms at the surface of liquid helium

Elastic scattering of He-4 atoms when they approach the surface of He-4 liquid, has been studied. The liquid surface is assumed to be uniform and the density profile is the same along and perpendicular to the surface. The incident He-4 atom will interact with a large number of He-4 atoms in the liquid near the surface of liquid He-4. Hence, the effective interaction of the incident particle will be due to many-body forces. The many-body forces are represented by the t-matrix. In the equation for potential energy per atom in the bulk liquid, the pair potential was replaced by the t-matrix. The Gaussian potential used in calculating the expectation value of the t-matrix is equivalent to the Lennard-Jonnes potential. The results give quantitative agreement with the corresponding experimental values for He-4 for the various values of chi(2). The potential energy per atom in the bulk liquid obtained in this calculation is -20.130 K. The experimental energy of interaction is -20.81K, which implies that the formula derived by us for the potential energy per atom in the bulk liquid works well.