Superfluid Film of Helium near the Lambda-Point

On the basis of Usui's phenomenological theory it is found that a superfluid film of helium undergoes a phase transition of the first kind when the temperature is raised up to Tλ and that the superfluid critical velocity υsc multiplied by the healing length ξ is a monotonically increasing and saturating function of the scaled film thickness d/ξ, not depending on the temperature explicitly. These results are qualitatively different from those of Ginzburg and Pitaevskii's theory, although the difference is small for the additional surface tension.