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Physical Review

Velocity Distributions in Potassium and Thallium Atomic Beams

Richard C. Miller, Polykarp Kusch

Published Aug 15, 1955• 98 citations
Publisher

Abstract

A high-resolution, high-intensity, spiral velocity selector has been designed for the study of the velocity distributions of the components of atomic and molecular beams. It has been found possible to design oven slits which closely approximate the ideal aperture of kinetic theory. An analysis has been made of the velocity distributions in beams of potassium and thallium over a range of velocity from 0.3 to 2.5 times the most probable velocity in the oven. The agreement between the observed distribution and that deduced, on the basis of the assumptions that the distribution in the oven is Maxwellian and that the aperture is ideal, is very good.

DOI
10.1103/physrev.99.1314

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Review of Scientific Instruments•Nov 1, 2018•14 citations
A high-resolution, high-intensity, spiral velocity selector has been designed for the study of the velocity distributions of the components of atomic and molecular beams. It has been found possible to design oven slits which closely approximate the ideal aperture of kinetic theory. An analysis has been made of the velocity distributions in beams of potassium and thallium over a range of velocity from 0.3 to 2.5 times the most probable velocity in the oven. The agreement between the observed distribution and that deduced, on the basis of the assumptions that the distribution in the oven is Maxwellian and that the aperture is ideal, is very good.
The free fall of atoms is observed in long molecular beams of potassium and cesium atoms. The measurement of the intensity distribution in a beam deflected by gravity represents the velocity distribution of the beam atoms and permits an accurate determination of this distribution. The results show that the measured values agree in general with those calculated for a modified Maxwellian velocity distribution in the beam. At larger deflections, i.e., for slow atoms, a deficiency of intensity was observed, which increased both with increasing deflection and with increasing pressure in the oven where the beam originates. This deficiency is explained by collisions in the immediate vicinity of the oven slit.
The diffraction of a full thermal neutral atomic potassium beam by a single slit has been observed. Four experimental diffraction patterns of a 23.0(±0.4)μ diffracting slit were obtained with an atomic-beam apparatus which had a 2.5(±1)μ source slit, a 3.0(±0.1)μ detector wire, a source-to-slit distance of 96 cm, a slit-to-detector distance of 100 cm, and an oven temperature of 533° K. The experimental pattern was reproducible and is in good general agreement with the prediction of de Broglie's hypothesis and simple scalar Fresnel diffraction theory. The effect of diffraction is clearly evident; two prominent diffraction fringes are present on the top corners of the beam profiles. The theoretical prediction, calculated with the aid of a computer, included the effects of finite source and detector widths and the Maxwellian speed distribution of the K beam. Additional theoretical calculations showed that no major improvement in the clarity of the diffraction fringes could be obtained by using a velocity-selected beam, a Li7 beam, or a narrower diffracting slit.
Time-of-flight distributions of cesium atoms effusing from the near-ideal orifice of an oven have been measured for Knudsen numbers ranging from 1 to 370. The apparatus consisting of a single-disk chopper and a single-ion counting detector is described. The experimental results are compared with theoretical data computed by using the free-molecule flow model. Experiment and theory are in good agreement. An error analysis is carried out. Deviations from the results of other studies are discussed. The influence of the scattering of cesium atoms by residual gas particles is demonstrated by a distorted distribution curve.
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.
The excitation of a low-energy ground state helium beam to its metastable states by electron impact is analysed. It is shown that the narrowest velocity distribution for the resulting metastable helium beam is obtained by directing the helium and electron beams parallel or antiparallel. A source of metastable helium atoms was constructed according to this analysis which produced a beam of 3*10 14 metastable atoms/s sr with a velocity resolution of 3% FWHM for a room-temperature beam (E=66 meV). A possible source of errors in time-of-flight experiments with metastable atoms is pointed out.
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.