Curvature effects on the surface thickness and tension at the free interface of $^4$He systems

TL;DR

This study investigates how curvature influences the surface thickness and tension at the free interface of superfluid helium-4, using density functional calculations for different geometries and comparing with experimental data.

Contribution

It provides a unified analysis of surface properties of superfluid helium-4 across various geometries, highlighting the independence of surface thickness from shape at large sizes and comparing theoretical and experimental results.

Findings

Surface thickness W is geometry-independent for large systems.

Finite range approaches align better with experimental data.

Surface tension and related observables show overshoot behavior before reaching asymptotic values.

Abstract

The thickness $W$ and the surface energy $\sigma_A$ at the free interface of superfluid $^4$He are studied. Results of calculations carried out by using density functionals for cylindrical and spherical systems are presented in a unified way, including a comparison with the behavior of planar slabs. It is found that for large species $W$ is independent of the geometry. The obtained values of $W$ are compared with prior theoretical results and experimental data. Experimental data favor results evaluated by adopting finite range approaches. The behavior of $\sigma_A$ and $W \sigma_A$ exhibit overshoots similar to that found previously for the central density, the trend of these observables towards their asymptotic values is examined.