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Physical Review Letters

Hydrogen in the submillikelvin regime: Sticking probability on superfluid He4

John M. Doyle, Jon C. Sandberg, Ite A. Yu, Claudio Lenz Cesar, Daniel Kleppner, Thomas J. Greytak

Published Jul 29, 1991• 193 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.67.603

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We have measured the sticking probability of atomic hydrogen on a superfluid 4He^{4}\mathrm{He}4He 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{}1013{10}^{13}1013 cm\ensuremath−3{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}cm\ensuremath−3 at a temperature of 100 \ensuremath{\mu}K.
We present the results of experiments measuring the film thickness dependence of the sticking probability for H on superfluid {sup 4}He for H atom temperatures of 0.3-5.0 mK. Data is presented for 3 nm to 1 mm thick films on a silver sinter substrate. For the 0.3 mK H atoms, the sticking probability varies from 0.4 for a film 3 nm thick to 6 x 10{sup -3} for films thicker than 100 nm. In the case of the thick films the temperature dependence of the sticking probability is consistent with the observation of pure quantum reflection. Our data are in reasonable agreement with recent theoretical calculations.
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.