The formation of dimers, trimers, and tetramers in a free jet cryogenic expansion of ~4He atoms has been studied by diffraction from a nanostructure transmission grating. The final average velocities, speed ratios and ambient temperatures of the expanhsions 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 He_2, He_3, and He_4 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 at 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.
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