Abstract
A wave function previously used to represent an excitation (phonon or roton) in liquid helium, inserted into a variational principle for the energy, gave an energy-momentum curve having the qualitative shape suggested by Landau; but the value computed for the minimum energy of a roton was 19.1°K, while thermodynamic data require K. A new wave function is proposed here. The new value computed for is 11.5°K. Qualitatively, the wave function suggests that the roton is a kind of quantum-mechanical analog of a microscopic vortex ring, of diameter about equal to the atomic spacing. A forward motion of single atoms through the center of the ring is accompanied by a dipole distribution of returning flow far from the ring.
In the computation both the two-atom and three-atom correlation functions appear. The former is known from x-rays, while for the latter the Kirkwood approximation of a product of three two-atom correlation functions is used. A method is developed to estimate and correct for most of the error caused by this approximation, so that the residual uncertainty due to this source is negligible.
- Received 27 February 1956
DOI:https://doi.org/10.1103/PhysRev.102.1189
©1956 American Physical Society