Effects of surface-normal motion for adsorbedHe4films

We investigate the effects of motion normal to the substrate on condensed phases of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorbed on graphite. We find that normal motion has small effects on the ground-state energy and critical temperature for first-layer adsorbed ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, but that the second layer suffers substantial decreases in both these quantities. Calculated results for $\Delta T_c$ compare favorably with experiment.