Physical Review A

Origin of Bound States of He3 Atoms on Free Superfluid He4 Surfaces

William Frederick Saam

Published Sep 1, 1971• 44 citations

Abstract

An approximate theory of the motion of a ${\mathrm{He}}^{3}$ atom in the vicinity of a superfluid ${\mathrm{He}}^{4}$ surface is presented. The theory predicts a bound state of the ${\mathrm{He}}^{3}$ 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 ${\mathrm{He}}^{4}$ chemical potential) is within 35% of the experimentally determined value.

DOI: 10.1103/physreva.4.1278

Related papers

Bound State of a He3 Atom in Surface of Liquid He4

Chieh C. Chang, Michael Cohen

Physical Review ADec 1, 197330 citations

Bound state of a He-3 atom at free He-4 surfaces

Massimo Boninsegni

arXiv:2608.27664Aug 27, 20260 citations

Interactions Between He3 Atoms in Dilute Solutions of He3 in Superfluid He4

J. Bardeen, Gordon Baym, David Pines

Physical Review LettersAug 15, 1966105 citations

Atomic hydrogen on the surface of superfluid helium: the sticking probability and polaronic behavior

Dan S. Zimmerman

Jan 1, 20100 citations

Theory of Dilute Mixtures of He3 in Liquid He4 at Low Temperatures

Victor J. Emery

Physical ReviewAug 5, 196631 citations

Hydrogen in the submillikelvin regime: Sticking probability on superfluid He4

John M. Doyle, Jon C. Sandberg, Ite A. Yu +3 more

Physical Review LettersJul 29, 1991193 citations

Physical Review A

Origin of Bound States of He3 Atoms on Free Superfluid He4 Surfaces

William Frederick Saam

Published Sep 1, 1971• 44 citations

Publisher

Abstract

An approximate theory of the motion of a

{\mathrm{He}}^{3}

atom in the vicinity of a superfluid

{\mathrm{He}}^{4}

surface is presented. The theory predicts a bound state of the

{\mathrm{He}}^{3}

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

{\mathrm{He}}^{4}

chemical potential) is within 35% of the experimentally determined value.

DOI: 10.1103/physreva.4.1278

Related papers

Bound State of a He3 Atom in Surface of Liquid He4

Chieh C. Chang, Michael Cohen

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.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.

Physical Review ADec 1, 197330 citations

Bound state of a He-3 atom at free He-4 surfaces

Massimo Boninsegni

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.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.

arXiv:2608.27664Aug 27, 20260 citations

Interactions Between He3 Atoms in Dilute Solutions of He3 in Superfluid He4

J. Bardeen, Gordon Baym, David Pines

The magnitude, sign, and momentum dependence of the effective interaction between ${\mathrm{He}}^{3}$ atoms in superfluid ${\mathrm{He}}^{4}$ are derived from the experimental data. Calculations of the Fermi-liquid parameters for the normal state of ${\mathrm{He}}^{3}$ in solution yield results in agreement with experiment; the temperature for a superfluid transition associated with the ${\mathrm{He}}^{3}$ is estimated to be \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ \ifmmode^\circ\else\textdegree\fi{}K.The magnitude, sign, and momentum dependence of the effective interaction between ${\mathrm{He}}^{3}$ atoms in superfluid ${\mathrm{He}}^{4}$ are derived from the experimental data. Calculations of the Fermi-liquid parameters for the normal state of ${\mathrm{He}}^{3}$ in solution yield results in agreement with experiment; the temperature for a superfluid transition associated with the ${\mathrm{He}}^{3}$ is estimated to be \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ \ifmmode^\circ\else\textdegree\fi{}K.

Physical Review LettersAug 15, 1966105 citations

Atomic hydrogen on the surface of superfluid helium: the sticking probability and polaronic behavior

Dan S. Zimmerman

A study is made of the interaction between hydrogen atoms and the surface elementary excitations of superfluid "He. Calculations for the sticking probability and for the energy and effective mass of a hydrogen atom bound to the surface are presented. As a first step in the calculations, we formulate the Hamiltonian describing a hydrogen atom interacting with the surface of "He in its ground state together with the interaction coupling to the surface elementary excitations (the ripplons). The derivation is based on the association of the surface ground state with a flat surface and the excited states with a sinusoidally varying height of the surface. The interaction potential is derived by summing a *He-H atom-atom pair potential over helium atoms below the surface. The atom-atom pair potential is chosen so that the derived surface potential is a Morse potential with parameters which are fitted to the effective surface potential derived by Mantz and Edwards for a hydrogen atom interacting with N-1 helium atoms. The energy and angle dependent sticking probability, S(E,θ), and the thermally averaged sticking probability, S(T), are calculated. Results are compared with the experimental value of S(T), S(T)=0.035±0.005, measured for the temperature range 0.18<T<0.27K. The possibility that a hydrogen atom bound above the surface may exhibit polaronic behaviour is investigated. The energy of the hydrogen surface "polaron" and its effective mass are calculated using perturbation theory. The hydrogen atom is found to be weakly coupled to the surface elementary excitations, and therefore the polaronic effects are weak. The contribution to these results from virtual transition to free states is emphasized.A study is made of the interaction between hydrogen atoms and the surface elementary excitations of superfluid "He. Calculations for the sticking probability and for the energy and effective mass of a hydrogen atom bound to the surface are presented. As a first step in the calculations, we formulate the Hamiltonian describing a hydrogen atom interacting with the surface of "He in its ground state together with the interaction coupling to the surface elementary excitations (the ripplons). The derivation is based on the association of the surface ground state with a flat surface and the excited states with a sinusoidally varying height of the surface. The interaction potential is derived by summing a *He-H atom-atom pair potential over helium atoms below the surface. The atom-atom pair potential is chosen so that the derived surface potential is a Morse potential with parameters which are fitted to the effective surface potential derived by Mantz and Edwards for a hydrogen atom interacting with N-1 helium atoms. The energy and angle dependent sticking probability, S(E,θ), and the thermally averaged sticking probability, S(T), are calculated. Results are compared with the experimental value of S(T), S(T)=0.035±0.005, measured for the temperature range 0.18<T<0.27K. The possibility that a hydrogen atom bound above the surface may exhibit polaronic behaviour is investigated. The energy of the hydrogen surface "polaron" and its effective mass are calculated using perturbation theory. The hydrogen atom is found to be weakly coupled to the surface elementary excitations, and therefore the polaronic effects are weak. The contribution to these results from virtual transition to free states is emphasized.

Jan 1, 20100 citations

Theory of Dilute Mixtures of He3 in Liquid He4 at Low Temperatures

Victor J. Emery

Dilute mixtures of ${\mathrm{He}}^{3}$ in liquid ${\mathrm{He}}^{4}$ are regarded as a set of ${\mathrm{He}}^{3}$ atoms intereacting with elementary excitations of the ${\mathrm{He}}^{4}$ . The coupling between the ${\mathrm{He}}^{3}$ and the ${\mathrm{He}}^{4}$ is chosen phenomenologically and it is not weak but, for low temperatures, its main effects may be eliminated by means of two canonical transformations. The equations which determine the transformations describe the motion of a ${\mathrm{He}}^{4}$ excitation in the presence of one or two ${\mathrm{He}}^{3}$ atoms and, in the latter case, they resemble Faddeev's equations in the three-body problem. At low temperatures, there are few ${\mathrm{He}}^{4}$ excitations and many of the properties of the mixture are determined by the effective ${\mathrm{He}}^{3}$ Hamiltonian produced by the transformation. In this respect, the system behaves like a Fermi liquid. The ${\mathrm{He}}^{3}$ - ${\mathrm{He}}^{3}$ potential is essentially momentum-independent and consists of the Van der Waals interaction together with an effectively repulsive potential induced by the ${\mathrm{He}}^{4}$ . It is suggested that a Fermi-liquid analysis is the best way of obtaining information about this potential, and the possible existence of a fermion superfluid phase transition is discussed from that point of view.Dilute mixtures of ${\mathrm{He}}^{3}$ in liquid ${\mathrm{He}}^{4}$ are regarded as a set of ${\mathrm{He}}^{3}$ atoms intereacting with elementary excitations of the ${\mathrm{He}}^{4}$. The coupling between the ${\mathrm{He}}^{3}$ and the ${\mathrm{He}}^{4}$ is chosen phenomenologically and it is not weak but, for low temperatures, its main effects may be eliminated by means of two canonical transformations. The equations which determine the transformations describe the motion of a ${\mathrm{He}}^{4}$ excitation in the presence of one or two ${\mathrm{He}}^{3}$ atoms and, in the latter case, they resemble Faddeev's equations in the three-body problem. At low temperatures, there are few ${\mathrm{He}}^{4}$ excitations and many of the properties of the mixture are determined by the effective ${\mathrm{He}}^{3}$ Hamiltonian produced by the transformation. In this respect, the system behaves like a Fermi liquid. The ${\mathrm{He}}^{3}$-${\mathrm{He}}^{3}$ potential is essentially momentum-independent and consists of the Van der Waals interaction together with an effectively repulsive potential induced by the ${\mathrm{He}}^{4}$. It is suggested that a Fermi-liquid analysis is the best way of obtaining information about this potential, and the possible existence of a fermion superfluid phase transition is discussed from that point of view.

Physical ReviewAug 5, 196631 citations

Hydrogen in the submillikelvin regime: Sticking probability on superfluid He4

John M. Doyle, Jon C. Sandberg, Ite A. Yu +3 more

We have measured the sticking probability of atomic hydrogen on a superfluid $^{4}\mathrm{He}$ surface for atom energies between 100 \ensuremath{\mu}K and 1 mK. The sticking probability shows little variation with energy over this interval, and is close to the value 0.2. The studies were carried out using a magnetic trap that produced a density of 8\ifmmode\times\else\texttimes\fi{} ${10}^{13}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ at a temperature of 100 \ensuremath{\mu}K.We have measured the sticking probability of atomic hydrogen on a superfluid $^{4}\mathrm{He}$ surface for atom energies between 100 \ensuremath{\mu}K and 1 mK. The sticking probability shows little variation with energy over this interval, and is close to the value 0.2. The studies were carried out using a magnetic trap that produced a density of 8\ifmmode\times\else\texttimes\fi{}${10}^{13}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ at a temperature of 100 \ensuremath{\mu}K.

Physical Review LettersJul 29, 1991193 citations

An approximate theory of the motion of a

{\mathrm{He}}^{3}

atom in the vicinity of a superfluid

{\mathrm{He}}^{4}

surface is presented. The theory predicts a bound state of the

{\mathrm{He}}^{3}

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

{\mathrm{He}}^{4}

chemical potential) is within 35% of the experimentally determined value.

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.

The magnitude, sign, and momentum dependence of the effective interaction between

{\mathrm{He}}^{3}

atoms in superfluid

{\mathrm{He}}^{4}

are derived from the experimental data. Calculations of the Fermi-liquid parameters for the normal state of

{\mathrm{He}}^{3}

in solution yield results in agreement with experiment; the temperature for a superfluid transition associated with the

{\mathrm{He}}^{3}

is estimated to be \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ \ifmmode^\circ\else\textdegree\fi{}K.

Dilute mixtures of

{\mathrm{He}}^{3}

in liquid

{\mathrm{He}}^{4}

are regarded as a set of

{\mathrm{He}}^{3}

atoms intereacting with elementary excitations of the

{\mathrm{He}}^{4}

. The coupling between the

{\mathrm{He}}^{3}

and the

{\mathrm{He}}^{4}

is chosen phenomenologically and it is not weak but, for low temperatures, its main effects may be eliminated by means of two canonical transformations. The equations which determine the transformations describe the motion of a

{\mathrm{He}}^{4}

excitation in the presence of one or two

{\mathrm{He}}^{3}

atoms and, in the latter case, they resemble Faddeev's equations in the three-body problem. At low temperatures, there are few

{\mathrm{He}}^{4}

excitations and many of the properties of the mixture are determined by the effective

{\mathrm{He}}^{3}

Hamiltonian produced by the transformation. In this respect, the system behaves like a Fermi liquid. The

{\mathrm{He}}^{3}

{\mathrm{He}}^{3}

potential is essentially momentum-independent and consists of the Van der Waals interaction together with an effectively repulsive potential induced by the

{\mathrm{He}}^{4}

. It is suggested that a Fermi-liquid analysis is the best way of obtaining information about this potential, and the possible existence of a fermion superfluid phase transition is discussed from that point of view.

We have measured the sticking probability of atomic hydrogen on a superfluid

^{4}\mathrm{He}

surface for atom energies between 100 \ensuremath{\mu}K and 1 mK. The sticking probability shows little variation with energy over this interval, and is close to the value 0.2. The studies were carried out using a magnetic trap that produced a density of 8\ifmmode\times\else\texttimes\fi{}

{10}^{13}

${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ at a temperature of 100 \ensuremath{\mu}K.