Journal of Low Temperature Physics, VoL 3, No. 3, 1970 Quantum States of He Atoms Adsorbed on Surfaces of Rare Gas Solids Anthony D. Novaco and Frederick J. Milford Battelle MemorialInstitute Columbus, Ohio (ReceivedJune 4, 1970) Wave functions and energies for band states of helium atoms in the two-dimensional periodic potential at the surface of a semiinfinite rare gas solid have been studied. In the case of Kr and Ar substrates, the atoms are highly localized and, corre- spondingly, the band widths are small. In a third case, namely that of an argon crystal highly compressed to simulate the adsorption site density of the close-packed face of argon, much larger band widths were found. If this is a reasonable simulation, then band effects may be observable. 1. INTRODUCTION Quantum states of light atoms adsorbed on crystal faces must be understood in order to develop a complete picture of physical and/or chemical adsorption. The case of physical adsorption is simpler, and perhaps the simplest of these is a He atom adsorbed on the surface of a rare gas crystal. In this case a great deal is known about the dominant interactions, and the immutability of the atomic systems involved insures essentially "pure" physical adsorption. Experiments on physical adsorption have progressed to the point where reliable and accurate theoretical work may be very useful. From another viewpoint He adsorbed on solid surfaces represents an approxi- mation to a two-dimensional system. It is well known that the superfluid transition of a Bose system is suppressed to 0°K in a two-dimensional system. The way in which this suppression is manifest as a function of thickness and the role of the solid surface have been the objects of many studies. Still another way in which quantum states of He on surfaces are manifest is in low-temperature heat-capacity studies. These play a central role in the motiva- tion of the work being reported here and will be discussed more fully later. It will suffice at this point to observe that calorimeters can be constructed with sufficiently large surface areas to permit the accurate determination of the heat capacity of He films covering as little as 10 ~o of the available surface. All of the phenomena described above pertain to so-called unsaturated He films, that is, to film in equilibrium with unsaturated vapor. Many aspects of 307