Energy Spectrum of the Excitations in Liquid Helium

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 $\Delta$ of a roton was 19.1°K, while thermodynamic data require $\Delta =9.6\mathrm{}°$K. A new wave function is proposed here. The new value computed for $\Delta$ 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.