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Superfluid Parameters of Thin $^4$He Films
New Physics: Sae Mulli 2017; 67: 12~16
Published online January 31, 2017;
© 2017 New Physics: Sae Mulli.

Sang-Tack NAM*

Department of Physics and Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, Korea
Correspondence to:
Received June 11, 2016; Revised October 30, 2016; Accepted November 2, 2016.
cc This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The properties related to the third sound of liquid helium are argued using the equation for the conservation of mass on a slab of film, the heat-flow equation, the hydrodynamical equation of motion of the incompressible superfluid component, and each traveling wave solution. We represented the third-sound velocity of thin superfluid $^4$He films on glass substrates and on polished CaF$_2$ single-crystal substrates by using the Atkins model and obtained $\bar{\rho}_s/\rho$ and $\bar{\rho}_sd/T$ for the thin superfluid $^4$He films by using the measured third-sound speed, the van der Waals constant, and the thickness of the film. We found that the superfluid parameters $\bar{\rho}_s/\rho$ and $\bar{\rho}_sd/T$ decreased both on glass and polished CaF$_2$ single-crystal substrates as the temperature was increased at temperatures below the critical temperature when the thicknesses of the films were constant. Also, the parameters $\bar{\rho}_s/\rho$ and $\bar{\rho}_sd/T$ increased both on glass and polished CaF$_2$ single-crystal substrates as the thickness of the films increased when the temperature was constant below the critical temperature.
PACS numbers:, 67.25.dt
Keywords: Superfluid $^4$He films, Atkins model, Superfluid parameter

January 2017, 67 (1)