Journal of Low Temperature Physics, Vol. 119, Nos.56, 2000 Binding of Two Helium Atoms in Confined Geometries. II. Dimerization on Flat Attractive Substrates S. Kilic, 1 E. Krotscheck, 2 and L. Vranjes 1 1 Faculty of Natural Sciences, University of Split, 21000 Split, Croatia 2 Institut fur Theoretische Physik, Johannes Kepler Universitat, A 4040 Linz, Austria (Received November 11, 1999; accepted January 18, 2000) We study the binding of dimers of helium isotopes in a geometry that corresponds to the adsorption on a flat substrate. By varying the width of the holding potential, we go continuously from a rigorously three-dimensional to a rigorously two-dimensional geometry. It is shown that the binding energy is significantly enhanced when the width of the holding potential is approximately equal to the range of the pair interaction. I. INTRODUCTION We have in a recent paper 1 studied the binding of dimers of helium isotopes in two and three dimensions when their motion is confined by a spherically symmetric external holding potential. The calculation was designed to provide a model for the interaction between helium atoms in solid matrices or on a solid, corrugated substrate. Among others, we devised a formalism that allows to map the problem of two particles with confinement onto the problem of two particles in free space; the effect of confinement appeares as an auxiliary ``confinement potential'' that sup- plements the pair interaction. In this paper, we apply the same technique to examine the problem where two helium atoms are located in an external holding potential that depends only on one coordinate, say z. This system is, for example, the ``seed'' for the condensation of liquid 4 He on a substrate. It is commonly believed that this situation can be modeled by a two-dimensional liquid. Indeed, the two-dimensional equation of state is a reasonable approxima- tion 2 for an atomic monolayer of 4 He, however, many-body calculations have also revealed that the atomic monolayer is more strongly bound than 715 0022-2291000600-0715818.000  2000 Plenum Publishing Corporation