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Physical Review A

Theoretical and experimental study of He free-jet expansions

L. Pedemonte, G. Bracco, R. Tatarek

Published Apr 1, 1999• 32 citations
Publisher

Abstract

The paper reports on calculations of the flow properties in low-temperature He free-jet expansions by means of the Lennard-Jones potential and the recently appearing He-He van der Waals potential based on perturbation theory. The calculated speed ratios are compared with both the values we measured in the 20--80 K source temperature range and data which were already reported. The comparison points out a better agreement of our experimental results with the speed ratio values obtained by the recent potential whenever the parallel temperature of the beam decreases below ${10}^{\ensuremath{-}2} \mathrm{K}.$ In the same temperature range the light He-cluster size is analyzed.

DOI
10.1103/physreva.59.3084

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The paper reports on calculations of the flow properties in low-temperature He free-jet expansions by means of the Lennard-Jones potential and the recently appearing He-He van der Waals potential based on perturbation theory. The calculated speed ratios are compared with both the values we measured in the 20--80 K source temperature range and data which were already reported. The comparison points out a better agreement of our experimental results with the speed ratio values obtained by the recent potential whenever the parallel temperature of the beam decreases below 10\ensuremath−2K.{10}^{\ensuremath{-}2} \mathrm{K}.10\ensuremath−2K. In the same temperature range the light He-cluster size is analyzed.
The formation of dimers, trimers, and tetramers in a free jet cryogenic expansion of He4 atoms has been studied by diffraction from a nanostructure transmission grating. The final average velocities, speed ratios and ambient temperatures of the expansions for source temperatures of 30, 12, and 6 K and source pressures between 0.1 and 80 bar were determined from time-of-flight measurements of the He atoms. The final mole fractions of the He2, He3, and He4 clusters in the beam were determined from the intensities of the corresponding first-order diffraction peaks for the same range of source conditions. For each source temperature, the final mole fractions of these small clusters first rise, pass through a maximum and then decrease with increasing source pressure. The processes leading to the formation of these clusters are simulated with a kinetic model that allows for density and temperature changes in the expanding beam. The best-fit three-body recombination rate constant for dimer formation increases by over three orders of magnitude as the thermal energy decreases from 1 K to 1 mK, in qualitative agreement with recent theories.
The mathematical term for the mean flow velocity in supersonic beams of ideal gases is extended to include real gas properties. This procedure yields an explicit dependence of the flow velocity on pressure, as observed in recent experiments of free jet expansions. Applied to stagnation conditions slightly above the critical point, the model suggests that seeded high-pressure jet expansions might be suitable for slowing down virtually any molecule with maximum efficiency. Moreover, we discuss the consequence of a pressure-dependent flow velocity v0{v}_{0}v0​ for the speed ratio $S={v}_{0}/\ensuremath{\Delta}{v}_{\ensuremath{\parallel}}$ with respect to collisional cooling and suggest to use the velocity spread $\ensuremath{\Delta}{v}_{\ensuremath{\parallel}}$ as a more nonambiguous measure of translational temperature in high-pressure jet expansions.
A non-adiabatic model is employed to investigate the H-H scattering at low temperatures. Unlike molecular-orbital calculation technique, no separate calculations are required to obtain the potential energies of electrons in the field of hadrons. This model generates the non-adiabatic effective potential automatically. The coefficients of van der Waals and higher-order potentials are estimated in the present model and are found to be in very good agreement with the corresponding standard values. The s -wave singlet and triplet scattering lengths and thermal-average total triplet cross-section at 2 K are reported and compared with the existing theoretical and experimental predictions.
The supersonic free-jet expansion technique has been used in different fields of research in physics, physical chemistry and chemistry to study vibrational and rotational molecular structures in ground and excited electronic energy states as well as in cold chemistry to study chemical reactions in a unique environment. The supersonic beam technique, as a widely used method in laser spectroscopy of molecules, exploits a source of monokinetic, rotationally and vibrationally cold molecules, that are very weakly bound in their ground electronic states (van der Waals molecules). In experiments at Jagiellonian University the supersonic free-jet beam serves as a source of ground-state van der Waals objects in studies of neutral–neutral interactions between group 12 metal (M = Zn, Cd, Hg) and noble gas (NG) atoms. Recently, the method has been applied as a source of entangled 199 Hg atom pairs in order to test Bell's inequality in an experiment at Texas A&M University.
The exact, low-density many-boson expansion for the ground-state energy is rearranged in a quantum-thermodynamic perturbation series. Extrapolation to physical densities is implemented order by order via Pad\'e-type approximants. Several ways of splitting the pair Lennard-Jones (LJ) or Aziz potentials are considered, including the Barker-Henderson (BH) and Weeks-Chandler-Andersen (WCA) schemes familiar from classical fluid studies. Results obtained using the LJ interaction with WCA splitting, when compared with benchmark simulation data, agree excellently in energy and density, but only moderately so in sound velocity. For the Aziz potential, however---perhaps because of a softer core and/or its ability to support a two-particle bound state---, neither potential splitting (BH or WCA) gave results of the LJ quality, but a method intermediate between BH and WCA proves to be superior. Our results are also compared with other recent alternative calculations, both variational and perturbative.