Impurity states in liquid-helium films

Abstract

We study the properties of impurity atoms of $^{3}\mathrm{He}$ and spin-polarized hydrogen isotopes in films of liquid $^{4}\mathrm{He}$ adsorbed to a substrate. We find that a $^{3}\mathrm{He}$ impurity has three or more bound states, two of which we associate with surface states. Hydrogen atoms are very weakly bound and have only one bound state. Depending on the thickness of the film, deuterium impurities may form two surface bound states, or may penetrate to the substrate. For all cases studied, tritium impurities also tend to penetrate to the substrate. We develop the theory of the formation of ``self-bound'' or ``polaron'' states, but we see no evidence that such states can become energetically favorable.