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The Journal of Chemical Physics

Internal state distribution of alkali dimers in supersonic nozzle beams

M. P. Sinha, A.J. Schultz, Richard N. Zare

Published Jan 15, 1973• 126 citations
Publisher

Abstract

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.

DOI
10.1063/1.1679236

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Review of Scientific Instruments•Aug 1, 2012•12 citations
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.
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.
We have obtained substantial alignment of I2(X 1Σ+g;v″=0;J″=13,15) seeded in supersonic beams of light carrier gases. Laser-induced fluorescence and a variant of the magnetic precession technique were used to measure the ratio n⊥/n∥ of molecules with the rotational angular momentum vector J perpendicular to the beam axis z to those with J parallel (or antiparallel) to z. As the nozzle stagnation pressure P0 is increased, this ratio increases markedly, reaches a maximum, and then decreases steadily. At the maximum, n⊥/n∥=1.6, 1.7, and 2.2, respectively, for He, D2, and H2 as the carrier gases; this occurs at different pressures of the order of 103 Torr for nozzle diameter d=50 μm and temperature T0=315 K and corresponds to nearly the same rotational temperatures of about 6–8 K. We compare the observed dependence of alignment on P0⋅d with a J-dependent model that invokes two mechanisms for alignment, macroscopic gas transport, and anisotropic rotational cooling. The transport processes involve reorientation of J and give rise to alignment with n⊥/n∥>1; this dominates the initial increase with P0⋅d up to the maxima. The anisotropic cooling processes do not in our model involve reorientation of J but are fostered by the anisotropy of the rotational relaxation cross section; the alignment arises from different Boltzmann weights for molecules with J⊥z and J∥z due to their slightly different rotational temperatures (about 5%). At high P0⋅d the net alignment is dominated by the anisotropic cooling term. At the correspondingly low rotational temperatures, this term counteracts the effect of gaseous transport, so the net alignment can reverse. Indeed, at high P0⋅d we do observe n⊥/n∥<1. For a higher rotational state (J″=39,41) we find lower alignment that peaks at a higher rotational temperature (about 27 K), as predicted by the model.
Low energy (thermal) free jet (supersonic) molecular beams are used in a range of applications from surface science and surface deposition to quantum coherence and gas kinetics experiments. A free jet molecular beam is created by a gas expansion from a high pressure reservoir through a small aperture (nozzle). The nozzle typically has a diameter of 2-20 μm. The central part of the beam is selected using a skimmer, typically up to 500 μm in diameter. Recent years have seen the introduction of highly spatially confined beam sources based on micrometer skimmers and micrometer or even sub-micrometer nozzles. Such sources have been applied, for example, in the investigation of superfluidity and in neutral helium microscopy. However, up till now no source design allowing the precise positioning of the micro-skimmer relative to the nozzle has been available. This is an important issue because the relative position of skimmer and nozzle can influence the beam properties considerably. Here we present the design and implementation of a new molecular beam source, which allows an automatized, 50 nm precision positioning of the skimmer relative to the nozzle. The source is liquid nitrogen cooled and the temperature can be controlled between 110 K and 350 K with a temperature fluctuation of less than ±0.1 K over several hours. Beam intensity measurements using a 5 μm nozzle and a skimmer 5 μm in diameter are presented for stagnation pressures po in the range 3-180 bars. A 2D beam profile scan, using a 9.5 μm skimmer and a 5 μm nozzle is presented as a further documentation of the versatility of the new design and as an illustration of the influence of the relative skimmer-nozzle position on the beam properties.
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.
An all-metal pulsed source of van der Waals (vdW) dimers was constructed; it operates at temperatures up to 1000 K and carrier gas stagnation pressures up to 10 bars. Performance of the source was demonstrated in the production and spectroscopy of both CdAr and Cd(2) molecules in a supersonic beam expansion. Simulation of the recorded laser induced fluorescence (LIF) excitation spectra using the B(3)1(5(3)P(1)) ← X(1)0(+)(5(1)S(0)) and b(3)0(u)(+)(5(3)P(1))←X(1)0(g)(+)(5(1)S(0)) transitions in CdAr and Cd(2), respectively, showed that these molecules were produced with a rotational temperature in the range from 3 K to 19 K. The source was incorporated into an experimental set-up dedicated to the realization of Bohm's spin-1/2 particle version of the Einstein-Podolsky-Rosen experiment for ((111)Cd)(2) molecules.