Helium diffraction from metal surfaces: Elimination of a class of potentials

For helium diffraction from surfaces, Esbjerg and Nørskov proposed a helium-atom potential proportional to the surface electonic charge density $V\left(\overrightarrow{\mathrm{r}}\right)=\alpha \rho \left(\overrightarrow{\mathrm{r}}\right)$. This potential, however, has been unable to explain the experimental Ni(110) corrugations. We consider possible modifications to this potential, changing the proportionality constant, nonlinearity, and nonlocality (gradient terms). Combining these modifications, we derive a potential of the form $V\left(\overrightarrow{\mathrm{r}}\right)=E\left(\rho \right)+\beta {\nabla }^2\rho$ which accurately describes experiential helium—rare-gas potentials in the diffraction region. However, calculations for Ni(110) show that the modified potential is also unale to explain the helium Ni(110) potential corrugations or helium physisorption well depths.