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Physical review. B, Condensed matter

Experimental and theoretical study of the radial density distributions of large 3He droplets

Jan Harms, Jan Peter Toennies, M. Barranco, Martí Pi

Published Apr 20, 2001• 42 citations
Publisher

Abstract

The integral cross sections of large ${}^{3}\mathrm{He}$ droplets and the number of atoms in the corresponding droplets $(\overline{N}=2\ifmmode\times\else\texttimes\fi{}{10}^{3}--2\ifmmode\times\else\texttimes\fi{}{10}^{4}\mathrm{atoms})$ have been measured in molecular-beam scattering experiments. The experimental results are in very good agreement with integral cross sections calculated from the radial density distributions predicted from density-functional theory calculations. The experimentally confirmed theoretical 10--90% surface thicknesses vary between 8.0 \AA{} $(\overline{N}{=10}^{3})$ and 7.6 \AA{} $(\overline{N}=4\ifmmode\times\else\texttimes\fi{}{10}^{4})$ and are about 30% larger than calculated for ${}^{4}\mathrm{He}$ droplets of similar sizes.

DOI
10.1103/physrevb.63.184513

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The integral cross sections of large 3He{}^{3}\mathrm{He}3He droplets and the number of atoms in the corresponding droplets (N‾=2\ifmmode×\else\texttimes\fi103−−2\ifmmode×\else\texttimes\fi104atoms)(\overline{N}=2\ifmmode\times\else\texttimes\fi{}{10}^{3}--2\ifmmode\times\else\texttimes\fi{}{10}^{4}\mathrm{atoms})(N=2\ifmmode×\else\texttimes\fi103−−2\ifmmode×\else\texttimes\fi104atoms) have been measured in molecular-beam scattering experiments. The experimental results are in very good agreement with integral cross sections calculated from the radial density distributions predicted from density-functional theory calculations. The experimentally confirmed theoretical 10--90% surface thicknesses vary between 8.0 \AA{} (N‾=103)(\overline{N}{=10}^{3})(N=103) and 7.6 \AA{} (N‾=4\ifmmode×\else\texttimes\fi104)(\overline{N}=4\ifmmode\times\else\texttimes\fi{}{10}^{4})(N=4\ifmmode×\else\texttimes\fi104) and are about 30% larger than calculated for 4He{}^{4}\mathrm{He}4He droplets of similar sizes.
The classical integral cross sections of large superfluid 4HeN{}^{4}{\mathrm{He}}_{N}4HeN​ droplets and the number of atoms in the droplets ${(N=10}^{3}\ensuremath{-}{10}^{4})$ have been measured in molecular beam scattering experiments. These measurements are in good agreement with the cross sections predicted from density functional calculations of the radial density distributions. By using a simple model for the density profile a 10--90 % surface thickness of about 6--8 \AA{} is extracted directly from the data.
Motivated by recent experiments, we study normal-phase rotating 3He droplets within density functional theory in a semi-classical approach. The sequence of rotating droplet shapes as a function of angular momentum is found to agree with that of rotating classical droplets, evolving from axisymmetric oblate to triaxial prolate to two-lobed shapes as the angular momentum of the droplet increases. Our results, which are obtained for droplets of nanoscopic size, are rescaled to the mesoscopic size characterizing ongoing experimental measurements, allowing for a direct comparison of shapes. The stability curve in the angular velocity–angular momentum plane shows small deviations from the classical rotating drop model predictions, whose magnitude increases with angular momentum. We attribute these deviations to effects not included in the simplified classical model description of a rotating fluid held together by surface tension, i.e., to surface diffuseness, curvature, and finite compressibility, and to quantum effects associated with deformation of the 3He Fermi surface. The influence of all these effects is expected to diminish as the droplet size increases, making the classical rotating droplet model a quite accurate representation of 3He rotation.
Helium droplets spanning a wide size range, N(He) = 10(3)-10(10), were formed in a continuous-nozzle beam expansion at different nozzle temperatures and a constant stagnation pressure of 20 bars. The average sizes of the droplets have been obtained by attenuation of the droplet beam through collisions with argon and helium gases at room temperature. The results obtained are in good agreement with previous measurements in the size range N(He) = 10(5)-10(7). Moreover, the measurements give the average sizes in the previously uncharacterized range of very large droplets of 10(7)-10(10) atoms. The droplet sizes and beam flux increase rapidly at nozzle temperatures below 6 K, which is ascribed to the formation of droplets within the nozzle interior. The mass spectra of the droplet beam upon electron impact ionization have also been obtained. The spectra show a large increase in the intensity of the He(4) (+) signal upon increase of the droplet size, an effect which can be used as a secondary size standard in the droplet size range N(He) = 10(4)-10(9) atoms.
The lifetimes of electron bubbles in large size selected HeN−4 droplets have been measured in a molecular beam experiment to lie between 2⋅10−3 and 0.2 s in droplets with sizes between N≈105 and 107 atoms, respectively. The dependence of the lifetimes on the electric fields used to size select the droplets, on the energies of the incident electrons, and on the infrared radiation emitted from the apparatus walls were investigated and taken into account. The experimental lifetimes are many orders of magnitude smaller than predicted by earlier theories but consistent with a recent theory published by the authors in Phys. Rev. Lett. 81, 3892 (1998).
Optical collisions are studied in a crossed beams experiment. Differential cross sections of K-Ar collisions are measured and are used to derive the repulsive parts of the XΣ and BΣ potential curves. The achieved accuracy has not been realized with scattering experiments before. A collision energy resolved analysis of the final state probes the relative population of the fine-structure states K(4p1/2) and K(4p3/2) which depends on details of the outer part of the potentials. Calculations from the determined potentials are in concordance with the experimental results. The relative population of the Na fine-structure states after Na-N2 and Na-O2 collisions is determined similarly. The results for N2 are in very good agreement with the theory. Differential cross sections of Ca-Ar optical collisions are measured for an asymptotically forbidden transition. The spectral dependence of the signal intensity shows a characteristic maximum. The experimental data are in good agreement with ab initio calculations. Wires on a microchip create a magnetic trap that is used to obtain a Rb-87 Bose-Einstein condensate. The roughness of the magnetic potential is characterized by the measured density of a cold atom cloud. The measured roughness is compared to the roughness that is calculated from the geometry of the microwire.
Spin-exchange cross sections between a 3He+{}^{3}{\mathrm{He}}^{+}3He+ ion and a Rb atom were calculated in a 3He+{}^{3}{\mathrm{He}}^{+}3He+ impact-energy range from 0.01 to 10 keV/amu by the semiclassical close-coupling method based on the molecular-orbital expansion. The previous calculation in which only two states of the 3He+{}^{3}{\mathrm{He}}^{+}3He+ (1s2S)+Rb(5s2S)(1s{ }^{2}S)+\mathrm{Rb}(5s{ }^{2}S)(1s2S)+Rb(5s2S) system were taken into account overestimated the experimental result at 6.33 keV/amu by orders of magnitudes, whereas the present calculation, which allowed the target excitation and electron transfer, showed a rough agreement with the experimental result. In view of the application, the spin-exchange cross sections larger than ${10}^{\ensuremath{-}14} {\mathrm{cm}}^{2},$ predicted at 3He+{}^{3}{\mathrm{He}}^{+}3He+ impact energies lower than 0.3 keV/amu will hopefully provide a powerful tool for producing a highly polarized 3He{}^{3}\mathrm{He}3He ion beam.