On the Surface Tension of Liquid Helium II

Abstract

The "intrinsic" surface tension of liquid He II, arising from the structural energy of the free surface, is calculated on the basis of Gross and Pitaevski's imperfect-gas model. The resulting expression, when supplemented by the contribution arising from the presence of quantized surface modes of vibration, gives a value of 0.28 erg ${\mathrm{cm}}^{-2\mathrm{}}$ for the surface tension of liquid helium in the limit T → 0°K. This value compares well with the experimental estimate of 0.37 erg ${\mathrm{cm}}^{-2\mathrm{}}$. It is also demonstrated that the so-called boundary effects, which arise from a better enumeration of the density of states in a bounded statistical system, do not make a significant contribution to the temperature dependence of the surface tension. The dominant contribution is again the one due to the quantized surface modes.