Thickness Scaling of the Convective Conductance of ⁴He Films

We report results of analysis of the convective conductance, K_f, of pure ⁴He films of thickness from 11.7 to 156Å, and critical temperature, T_c,, from 1.281 to 2.155 K. The data show a narrowing of the critical region with thickness as T_c approaches Tλ. In our analysis we have corrected for the small change of film thickness with temperature, and explored the consequences of using different values for the background conductance and a possible temperature dependence of the vortex diffusion constant, D. In all circumstances we find a strong thickness dependence of the parameters D/a² and b, with a the vortex core parameter and b a constant describing the divergence of the correlation length. The shift of T_c, with thickness, which does not follow simple scaling predictions, can be partly understood in terms of φ theory with the addition of the van der Waals interaction.