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The Journal of Chemical Physics

Supersonic Molecular Beams of Alkali Dimers

Robert J. Gordon, Y. T. Lee, Dudley R. Herschbach

Published Mar 15, 1971• 138 citations

Abstract

Intense alkali beams containing up to 30% mole fraction of K2, Rb2, or Cs2 have been generated from a supersonic nozzle expansion, with oven temperatures up to ∼ 900°K (corresponding to alkali vapor pressures up to ∼ 350 torr) and nozzle temperatures ∼ 50–300°K higher. The total beam intensity obtained reached ∼ 5 × 1017 particles sec−1·sr−1. An inhomogeneous deflecting magnet was used to separate the dimer and atom components of the beam, and the variation of dimer concentration with oven pressure and nozzle temperature were studied for a variety of nozzle sizes (throat diameters 0.04–0.15 mm). The velocity distributions of the atom and dimer components were also measured and found to be quite similar; the peaks occur at velocities up to 70% higher than the most probable atom velocity in the oven, and the widths are very narrow, corresponding to random translational temperatures as low as ∼ 30°K, and Mach numbers up to ∼ 15. A simple one-dimensional theory of dimerization which takes into account vibrational relaxation and heat of condensation is found to be consistent with the data. It is shown that the observed velocity distributions and the variation of the dimer yield with pressure and nozzle diameter imply that most of the heat of condensation does not contribute to the beam acceleration but goes into vibrational excitation of the dimer molecules. A nominal value of ∼ 3 × 10−30 cm6 sec−1 at ∼ 600°K is obtained for the recombination rate constant for Cs+Cs+Cs→Cs2+Cs. A reduced variable plot is provided which enables the theory to be applied to nozzle expansions of any substance for which the chemical recombination is governed by three-body collisions.

DOI: 10.1063/1.1675193

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Internal state distribution of alkali dimers in supersonic nozzle beams

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The formation of dimers and trimers in free jet He4 cryogenic expansions

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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.

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Direct images of the virtual source in a supersonic expansion of helium are presented. The images were obtained using a Fresnel zone plate with free-standing zones, 540 microm in diameter and with an outermost zone width of 50 nm. The general method can be extended to other beams, including seeded beams. Measurements were carried out at absolute source pressures ranging from 11 to 171 bar using a 10 microm nozzle with a source temperature of 320 K. The size of the virtual source was found to be strongly dependent on pressure, changing from a diameter of 67+/-6 microm at an absolute nozzle pressure of 11 bar to 180+/-9 microm at 171 bar. The virtual-source brightness displays a maximum at an absolute nozzle pressure of around 30 bar. This phenomenon occurs because of two competing effects: As the pressure increases, the total flux also increases, but at the same time the virtual source broadens. We modeled the expansion process by calculating the velocity distribution with solutions from the Boltzmann equation to estimate the location of the quitting surface where the frequency of interatomic collisions is assumed negligible. Realistic potentials have been used to calculate the cross section for atomic collisions and, for the velocity distribution perpendicular to the center streamline, a proper scaling with distance derived from the continuum expansion model has been introduced. A good agreement between experiments and model has been found and we discuss its approximation limits. For instance, backscattering effects are not included in the calculations and at present we cannot exclude that they also contribute to a broadening of the virtual-source size for the highest pressure regime. The results presented here are important for improving the understanding of the supersonic expansion process. The experimental method might eventually be used as a new way to test molecular and atomic interaction potentials.

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Cold Beam of $^7$Li$^4$He Dimers

Jeremy J. Glick, William Huntington, Daniel J. Heinzen

We demonstrate an approach for producing a high flux beam of $^7$Li$^4$He dimers by performing post-nozzle seeding of a lithium beam into a supersonic helium expansion. The molecular beam has a longitudinal temperature of 13(6) mK and a continuous flux on the order of $10^{11}$ dimers/s. Monte Carlo simulations of molecular formation based on ab-initio quantum scattering calculations are carried out and compared to the experimentally observed molecular flux. Extensions of this work could lead towards a more quantitative understanding of few-body collision processes of alkali and helium atoms.

arXiv:2402.16209•Feb 25, 2024•0 citations

Intense alkali beams containing up to 30% mole fraction of K2, Rb2, or Cs2 have been generated from a supersonic nozzle expansion, with oven temperatures up to ∼ 900°K (corresponding to alkali vapor pressures up to ∼ 350 torr) and nozzle temperatures ∼ 50–300°K higher. The total beam intensity obtained reached ∼ 5 × 1017 particles sec−1·sr−1. An inhomogeneous deflecting magnet was used to separate the dimer and atom components of the beam, and the variation of dimer concentration with oven pressure and nozzle temperature were studied for a variety of nozzle sizes (throat diameters 0.04–0.15 mm). The velocity distributions of the atom and dimer components were also measured and found to be quite similar; the peaks occur at velocities up to 70% higher than the most probable atom velocity in the oven, and the widths are very narrow, corresponding to random translational temperatures as low as ∼ 30°K, and Mach numbers up to ∼ 15. A simple one-dimensional theory of dimerization which takes into account vibrational relaxation and heat of condensation is found to be consistent with the data. It is shown that the observed velocity distributions and the variation of the dimer yield with pressure and nozzle diameter imply that most of the heat of condensation does not contribute to the beam acceleration but goes into vibrational excitation of the dimer molecules. A nominal value of ∼ 3 × 10−30 cm6 sec−1 at ∼ 600°K is obtained for the recombination rate constant for Cs+Cs+Cs→Cs2+Cs. A reduced variable plot is provided which enables the theory to be applied to nozzle expansions of any substance for which the chemical recombination is governed by three-body collisions.

By spectroscopically analyzing the white light and laser-induced fluorescence excited in a nozzle beam of Na2 molecules, we have measured the population distribution of the (v,J) levels of the ground state. The Na2 molecules are produced in nozzle beams with various stagnation pressures (50–240 torr) of alkali metal and with nozzles of different throat diameters (0.12–0.50 mm). We find at a stagnation pressure of 50 torr and a nozzle diameter of 0.5 mm a Boltzmann distribution characterized by a vibrational temperature of 153 ± 5°K and a rotational temperature of 55± 10°K. Beams under different stagnation conditions have essentially the same internal state distribution. Studies of K2 dimers produced in a nozzle beam with various stagnation pressures (20–300 torr) and a 0.25 mm nozzle throat diameter also show cooling in both vibrational and rotational modes. A search is made for atomic fluorescence arising from the photodissociation of dimers in high vibrational levels of the ground state. No evidence is found for the presence of vibrationally-excited dimers in the nozzle beam.

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.

Direct images of the virtual source in a supersonic expansion of helium are presented. The images were obtained using a Fresnel zone plate with free-standing zones, 540 microm in diameter and with an outermost zone width of 50 nm. The general method can be extended to other beams, including seeded beams. Measurements were carried out at absolute source pressures ranging from 11 to 171 bar using a 10 microm nozzle with a source temperature of 320 K. The size of the virtual source was found to be strongly dependent on pressure, changing from a diameter of 67+/-6 microm at an absolute nozzle pressure of 11 bar to 180+/-9 microm at 171 bar. The virtual-source brightness displays a maximum at an absolute nozzle pressure of around 30 bar. This phenomenon occurs because of two competing effects: As the pressure increases, the total flux also increases, but at the same time the virtual source broadens. We modeled the expansion process by calculating the velocity distribution with solutions from the Boltzmann equation to estimate the location of the quitting surface where the frequency of interatomic collisions is assumed negligible. Realistic potentials have been used to calculate the cross section for atomic collisions and, for the velocity distribution perpendicular to the center streamline, a proper scaling with distance derived from the continuum expansion model has been introduced. A good agreement between experiments and model has been found and we discuss its approximation limits. For instance, backscattering effects are not included in the calculations and at present we cannot exclude that they also contribute to a broadening of the virtual-source size for the highest pressure regime. The results presented here are important for improving the understanding of the supersonic expansion process. The experimental method might eventually be used as a new way to test molecular and atomic interaction potentials.

Supersonic molecular beams are used in many applications ranging from spectroscopy and matter wave optics to surface science. The experimental setup typically includes a conically shaped, collimating aperture, the skimmer. It has been reported that microskimmers with diameters below 10 μm produce beams with significantly broader velocity distributions (smaller speed ratios) than larger skimmers. Various explanations for this phenomenon have been proposed, but up till now, only a limited amount of data has been available. Here we present a systematic study of the velocity distribution in microskimmer supersonic expansion helium beams. We compare a 4 μm diameter skimmer with a 390 μm diameter skimmer for room temperature and cooled beams in the pressure range 11-181 bars. Our measurements show that for properly aligned skimmers, the only difference is that the most probable velocity for a given pressure and temperature is slightly lower for a microskimmed beam. We ascribed this to the comparatively narrow and long geometry of the microskimmers which can lead to local pressure variations along the skimmer channel. We compare our measurements to a model for the supersonic expansion and obtain good agreement between the experiments and simulations.

Cold Beam of

^7

Li

^4

He Dimers

We demonstrate an approach for producing a high flux beam of

^7

Li

^4

He dimers by performing post-nozzle seeding of a lithium beam into a supersonic helium expansion. The molecular beam has a longitudinal temperature of 13(6) mK and a continuous flux on the order of

10^{11}

dimers/s. Monte Carlo simulations of molecular formation based on ab-initio quantum scattering calculations are carried out and compared to the experimentally observed molecular flux. Extensions of this work could lead towards a more quantitative understanding of few-body collision processes of alkali and helium atoms.