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Physical review. B, Condensed matter

Reflection of hydrogen atoms from the surface of superfluid helium

Eite Tiesinga, Henk T. C. Stoof, BOUDEWIJN J. VERHAAR

Published May 1, 1990• 3 citations
Publisher

Abstract

We propose a new method for studying the reflection of a hydrogen atom from a superfluid-helium film. Starting from the narrow width of the reflected angular distribution recently found experimentally, we tentatively extrapolate to the extreme limit of low ripplon wave numbers in which the adiabatic or degenerate-internal-states approximation becomes valid. We obtain simple closed expressions for single- and multiple-ripplon processes, which do not require the integration of a Schr\"odinger equation for their evaluation and do not depend on the specific form of the potential.

DOI
10.1103/physrevb.41.8886

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Physical review. B, Condensed matter•Jul 1, 1982•21 citations
We propose a new method for studying the reflection of a hydrogen atom from a superfluid-helium film. Starting from the narrow width of the reflected angular distribution recently found experimentally, we tentatively extrapolate to the extreme limit of low ripplon wave numbers in which the adiabatic or degenerate-internal-states approximation becomes valid. We obtain simple closed expressions for single- and multiple-ripplon processes, which do not require the integration of a Schr"odinger equation for their evaluation and do not depend on the specific form of the potential.
We studied the low-energy limit of atomsurface scattering and the phenomenon of quantum reflection by using hydrogen atoms and the surface of liquid helium. Measuring the specular reflectivity of a liquid-helium-covered hemispheric mirror for a beam of hydrogen atoms we obtained information on elastic and inelastic scattering phenomena. At 100 mK, reflectivities larger than 90% were achieved; this can be used to demonstrate atomic beam focusing. Approximately three-fourths of the atoms escaping from a small orifice in a cell were reflected back into the cell. The dominant inelastic processes at work here are surface absorption and direct inelastic scattering over small angles under excitation of surface ripplons (quantized capillary waves). Helium-covered surfaces maybe useful for atomic-beam manipulation of atomic hydrogen.
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.
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.
Possible acoustic modes in a superfluid 2D gas of hydrogen atoms adsorbed on the surface of liquid helium at T ≲ 0.1 K are considered depending on the oscillation frequency and times of energy and momentum transfers both between 2D subsystems of hydrogen atoms and ripplons and into the bulk liquid or substrate. Analogues of the usual and second sounds are realized in 2D hydrogen at high frequencies. In the case of weak coupling with the bulk liquid and substrate, ripplons provide an addition to the normal hydrogen component, which leads to a change in the speed of the second sound. In the most interesting range of low frequencies, an analogue of the fourth sound is realized, when ripplons and the normal hydrogen component are immobile and only the superfluid hydrogen component moves. In this case, when the rate of heat transfer into the bulk liquid is much lower than the sound frequency, oscillations of the temperature of hydrogen can be observed in phase with density oscillations. Methods for exciting acoustic modes are discussed.