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Physical Review A

Bound State of a He3 Atom in Surface of Liquid He4

Chieh C. Chang, Michael Cohen

Published Dec 1, 1973• 30 citations
Publisher

Abstract

The bound state of a ${\mathrm{He}}^{3}$ atom trapped in the free surface of ${\mathrm{He}}^{4}$ is studied, using a trial function suggested by Lekner. The effective potential which determines the bound-state wave function is calculated from first principles, and results in a binding energy 20% larger than the observed value.

DOI
10.1103/physreva.8.3131

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The Journal of Chemical Physics•Dec 1, 1982•7 citations
The bound state of a He3{\mathrm{He}}^{3}He3 atom trapped in the free surface of He4{\mathrm{He}}^{4}He4 is studied, using a trial function suggested by Lekner. The effective potential which determines the bound-state wave function is calculated from first principles, and results in a binding energy 20% larger than the observed value.
An approximate theory of the motion of a He3{\mathrm{He}}^{3}He3 atom in the vicinity of a superfluid He4{\mathrm{He}}^{4}He4 surface is presented. The theory predicts a bound state of the He3{\mathrm{He}}^{3}He3 atom in the vicinity of the surface, in accord with experimental results. The theoretical value for the energy of this state (measured with respect to the He4{\mathrm{He}}^{4}He4 chemical potential) is within 35% of the experimentally determined value.
The ground states of drops of spin-polarized liquid 3He^{3}\mathrm{He}3He containing 56, 84, and 120 atoms are calculated with the variational Monte Carlo method using wave functions containing pair, triplet, and backflow correlations. The calculated energies of these drops are higher by \ensuremath{\sim}0.2 K per atom than those of drops of unpolarized liquid 3He^{3}\mathrm{He}3He. The results also indicate that the equilibrium density of liquid $^{3}\mathrm{He}_{\mathrm{\ensuremath{\uparrow}}}$ is larger than that of unpolarized 3He^{3}\mathrm{He}3He by \ensuremath{\sim}5%, and that the thickness of its surface is smaller.
The magnitude, sign, and momentum dependence of the effective interaction between He3{\mathrm{He}}^{3}He3 atoms in superfluid He4{\mathrm{He}}^{4}He4 are derived from the experimental data. Calculations of the Fermi-liquid parameters for the normal state of He3{\mathrm{He}}^{3}He3 in solution yield results in agreement with experiment; the temperature for a superfluid transition associated with the He3{\mathrm{He}}^{3}He3 is estimated to be \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ \ifmmode^\circ\else\textdegree\fi{}K.
Quantum Monte Carlo simulations confirm the existence of a bound state of a single He-3 atom at a free superfluid He-4 surface in three dimensions, localized within a ~10-A thick low-density He-4 surface layer, with a binding energy of approximately 4 K with respect to vacuum. As the temperature is raised above ~ 1 K the He-3 atom leaves the surface to dissolve into the superfluid. The situation is entirely different in two dimensions, as the He-3 atom is excluded from the superfluid and no surface bound state exists. Results are also presented for the a He-3 atom binding to nanoscale size He-4 clusters adsorbed on weak substrates, a physical system that may allow for the observation of some of the physics predicted for extended surfaces. It is shown that a He-3 bound state localized at the perimeter of sufficiently small (a few tens of atoms) clusters exists not just on Cs, as previously reported, but on all alkali substrates.
A variational calculation is performed for the (3He)4 system interacting pairwise through the Lennard-Jones He–He potential. Use of an integrodifferential Euler equation is made to determine an optimum wave function, leading to results showing that the existence of this molecule is unlikely. It is confirmed that states of the system with nonzero orbital angular momentum yield lower energies. Also, it appears that the number of 3He atoms needed to form self-bound molecules must be larger than 5.