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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Self-collimation in an atomic beam evaporated from a superfluid 4He film

H. H. Hjort, David Olaf Edwards

Published Dec 1, 2000• 1 citation
Publisher

Abstract

Using a scaling Monte Carlo method, we have simulated the scattering in a pulsed atomic beam evaporated from a superfluid 4He film. The simulation assumes that the atoms leaving the surface have the equilibrium Maxwellian distribution at the temperature of the film T. This means that the initial particle flux varies as cos straight theta (Lambert's law). We find that the effect of atomic scattering just above the film is to bias the flux in favor of the forward (small straight theta) direction, in agreement with the experiment of Eckardt et al. The simulation predicts that the deviation from Lambert's law grows rapidly with increasing heat input Q and decreasing pulse length. At the same time, the average kinetic energy per particle in the forward direction is enhanced relative to the global average, 2k(B)T. The distribution with respect to speed is narrower than Maxwellian in the forward direction but broader at large angles. We find that a beam that has passed through a slit is slightly narrower than in a ballistic calculation with no collisions. This effect seems to saturate at values of Q that correspond to 30 or 40 collisions per atom.

DOI
10.1103/physreve.62.8583

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Using a scaling Monte Carlo method, we have simulated the scattering in a pulsed atomic beam evaporated from a superfluid 4He film. The simulation assumes that the atoms leaving the surface have the equilibrium Maxwellian distribution at the temperature of the film T. This means that the initial particle flux varies as cos straight theta (Lambert's law). We find that the effect of atomic scattering just above the film is to bias the flux in favor of the forward (small straight theta) direction, in agreement with the experiment of Eckardt et al. The simulation predicts that the deviation from Lambert's law grows rapidly with increasing heat input Q and decreasing pulse length. At the same time, the average kinetic energy per particle in the forward direction is enhanced relative to the global average, 2k(B)T. The distribution with respect to speed is narrower than Maxwellian in the forward direction but broader at large angles. We find that a beam that has passed through a slit is slightly narrower than in a ballistic calculation with no collisions. This effect seems to saturate at values of Q that correspond to 30 or 40 collisions per atom.
The influence of the collimating conditions of the incident beam on diffraction patterns produced by grazing scattering of fast atoms off crystal surfaces is studied within a semiquantum approach, called the surface initial value representation (SIVR) approximation. In this approach we incorporate a realistic description of the incident particle in terms of the collimating parameters, which determine the surface area that is coherently illuminated. The model is applied to He atoms colliding with a LiF(001) surface after passing through a rectangular aperture. As was experimentally observed [Nucl. Instrum. Methods Phys. Res., Sect. B 350, 99 (2015)], SIVR spectra as a function of the azimuthal angle are very sensitive to the width of the collimating slit. We also found that the length of the collimating aperture affects polar angle distributions, introducing additional interference structures for the longer collimating slits.
Below Tλ = 2.17 K, bulk 4He is a superfluid and has a non-zero Bose-Einstein condensate fraction. This work will focus primarily on how phenomena such as superfluidity, Bose condensation and superfluid vortices are manifested in microscopic, inhomogeneous helium systems. Path Integral Monte Carlo is a powerful method for calculating the equilibrium properties of quantum systems at finite temperature. We have achieved linear scaling of computer time with number of particles through the use of neighbor lists, allowing us to simulate systems of several thousand atoms. We have derived a local superfluid estimator and used it to examine the microscopic superfluid response around a molecule rotating in a helium nanodroplet. We found that the first solvation layer is well-described by a two dimensional superfluid, with thermal excitations occuring at a lower temperature than in bulk helium. The effective moment of inertia of a linear impurity in a helium droplet is calculated, and compared with experimental scattering results. In addition, we calculated the vortex formation energy for both pure droplets and droplets doped with linear impurities, and found that the linear impurities had a negligible impact on the formation energy. A possible spectroscopic signature of vortices in doped helium droplets was suggested. After deriving a local estimator, we calculated the condensate fraction throughout the free helium surface of a semi-infinite slab. These results, along with densitydensity correlation functions, were used to characterize the surface excitations and calculate the extent to which ripplons are present. In addition, the ripplon dispersion relation was calculated using imaginary-time correlation functions, and found to be lll in good agreement with experimental results. Finally, we have calculated the Dey be-Waller factor in solid helium for a range of temperatures and densities, and compared the scaling behavior with the predictions of harmonic theory. The first non-Gaussian contribution to the density distribution was calculated.
Typically one expects that when a heavy particle collides with a surface, the scattered angular distribution will follow classical mechanics. The heavy mass usually assures that the coherence length of the incident particle in the direction of the propagation of the particle (the parallel direction) will be much shorter than the characteristic lattice length of the surface, thus leading to a classical description. Recent work on molecular interferometry has shown that extreme collimation of the beam creates a perpendicular coherence length which is sufficiently long so as to observe interference of very heavy species passing through a grating. Here we show, using quantum mechanical simulations, that the same effect will lead to quantum diffraction of heavy particles colliding with a surface. The effect is robust with respect to the incident energy, the angle of incidence, and the mass of the particle.
Path Integral Monte Carlo was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at T = 0:77 K, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9, before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. A surface dispersion relation was calculated from imaginary-time density-density correlations. Similar calculations of the superfluid density throughout He-4 droplets doped with linear impurities (HCN)(sub n) are presented. After deriving a local estimator for the superfluid density distribution, we find a decreased superfluid response in the first solvation layer. This effective normal fluid exhibits temperature dependence similar to that of a two-dimensional helium system.
Coherence properties of projectiles, found relevant in ion-atom collisions, are investigated by analyzing the influence of the degree of coherence of the atomic beam on interference patterns produced by grazing-incidence fast-atom diffraction (GIFAD or FAD). The transverse coherence length of the projectiles, which depends on the incidence conditions and the collimating setup, determines the overall characteristics of GIFAD distributions. We show that for atoms scattered from a LiF(001) surface after a given collimation, we can modify the interference signatures of the angular spectra by varying the total impact energy, while keeping the normal energy as a constant. Also, the role played by the geometry of the collimating aperture is analyzed, comparing results for square and circular openings. Furthermore, we study the spot-beam effect, which is due to different focus points of the impinging particles. We show that when a region narrower than a single crystallographic channel is coherently illuminated by the atomic beam, the spot-beam contribution strongly affects the visibility of the interference structures, contributing to the gradual quantum-classical transition of the projectile distributions.