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

Dan S. Zimmerman

Published Jan 1, 2010• 0 citations

Abstract

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.

DOI: 10.14288/1.0085060

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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.

The probability of sticking of spin-polarised atomic hydrogen, H down arrow , on the superfluid helium surface as a function of temperature from 73 to 526 mK has been identified to arise from its interaction with third-sound ripplons. When the number density of the spin-polarised hydrogen atoms in the bulk helium becomes equal to that of the third-sound ripplons, the rate of sticking of H down arrow on the surface of the superfluid helium becomes a linear function of temperature. The predicted linearity is in accord with the experimental measurements.

Experimental investigations of spin-polarized hydrogen H\ensuremath{\downarrow} are carried out in a sample cell lined with a helium film whose purpose is to shield the H\ensuremath{\downarrow} atoms from magnetic impurities in the walls. The purpose of the He buffer is to minimize spin flips which cause recombination into the

{\mathrm{H}}_{2}

molecular ground state and degradation of the sample. In this paper, we focus our attention on the H\ensuremath{\downarrow}-

^{4}\mathrm{He}

film system and investigate the consequences of allowing the adsorbed H\ensuremath{\downarrow} atom to interact with a dynamic He surface. The coupling between the H\ensuremath{\downarrow} atom and the modes of the film raises the possibility that the atom will find it energetically favorable to be localized in the plane parallel to the surface of the film, i.e., to form a H\ensuremath{\downarrow} polaron. Using a simple model for the atom-film interaction, we show that polaron production can be important. We estimate the order of magnitude for the parallel binding energy and find that it can be comparable to the experimentally measured binding energy. We call attention to the important characteristics of the particle-film system that influence the size and nature of the polaron; e.g., the effect of evolution of the film from

^{4}\mathrm{He}

to

^{3}\mathrm{He}

and the consequences of the mobility of the surface modes. Where polaron effects are important the parallel binding problem and the perpendicular binding problem are strongly interdependent and cannot be factored. We then use a simple perturbation theory argument to calculate the polaron effective mass. We finally calculate the ripplon-mediated H\ensuremath{\downarrow}-H\ensuremath{\downarrow} interaction and show that it is short ranged and attractive.

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.

The binding energy of a hydrogen atom to the surface of liquid 4He has been calculated to be at least 0.6K by Mantz and Edwards. This means that the properties of adsorbed spin-polarized hydrogen (H↑), a 2D Bose fluid, may soon be observed experimentally. Since 4He is used as a neutral coating for vessels to contain H↑ gas, adsorption onto the 4He surface may enhance the rate of recombination into H2 molecules. For given temperature and density in the gas, the amount of H↑ adsorbed depends strongly on the H↑-H↑ interaction on the 4He surface. We estimate the interaction in a simple approximation, and find that it limits the surface density to not more than 1014 cm-2. Nevertheless this density should be sufficient for a 2D superfluid transition to be observed, under conditions close to those achieved experimentally.

Spin-polarized, atomic hydrogen at temperatures below 1K shows promise of becoming the first physically realizable example of a degenerate, weakly interacting Bose gas. Because of the hyperfine structure of the hydrogen atom the Bose condensed state is expected to exhibit novel magnetic properties such as spin wave excitations of the superfluid and possibly a coherent precessing, spontaneous magnetization. This paper discusses a variety of theoretical problems which arise in the study of atomic hydrogen gas. Theories are presented for spin relaxation of the hyperfine levels and for the recombination of H-atoms into H2 molecules. The problem of the binding of H atoms to a surface of superfluid 4He is reviewed together with the theory of surface superfluidity in the hydrogen film proposed by Edwards and Mantz. Finally we consider the problem of superfluidity in the bulk atomic hydrogen gas. We describe the theory of Siggia and Ruckenstein of double Bose condensation into the two lowest hyperfine states and speculate about the possible observable consequences of this phenomenon.