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VELOCITY DEPENDENCE OF THE DIFFERENTIAL CROSS SECTIONS, AND POTENTIAL WELL DEPTHS FROM ATOMIC BEAM SCATTERING MEASUREMENTS: K-Hg AND Cs-Hg SYSTEMS

Fred A. Morse, Richard B. Bernstein

Published Jun 1, 1962• 0 citations
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Abstract

Measurements of the velocity dependence of the angular intensity distribution of potassium and cesium atomic beams scattered by a crossed atomic beam of mercury are presented. The alkali atomic beam was velocity-selected, having a triangular velocity distribution with a halfintensity width of 0.047 of the peak velocity. The alkali velocity could be varied over the range 185 to 1100 m/s. The Hg beam had a thermal velocity distribution. The average speed of the Hg atoms in a typical experiment was 235 m/s (the calculated half-intensity width of the velocity distribution was 190 m/s). A typical angular distribution curve showed the expected very large low angle scattering, but evidenced a region in which the slope changed sharply, often resulting in a bump on the curve. This behavior is indicative of the phenomenon of rainbow scattering. The energy dependence of the rainbow angle was used to evaluate the depth of the interatomic potential wells; values (in ergs x 10/sup 14/) obtained are 7.7/sub 2/ for Cs-Hg and 7.4/sub 6/ for K-Hg. It is difficult to estimate the magnitude of the systematic errors in the absolute differential cross sections. However, reliable values for relative differential cross sections, which are velocity independent, can readilymore » be obtained by the methods described. From the low angle behavior of the differential cross sections, direct experimental evidence for the inverse sixth power dependence of the long-range attractive part of the potential was obtained. (auth)« less

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Velocity Dependence of the Differential Cross Sections for the Scattering of Atomic Beams of K and Cs by Hg

Fred A. Morse, Richard B. Bernstein

Measurements of the velocity dependence of the angular intensity distribution of potassium and cesium beams scattered by a crossed beam of mercury are presented. The alkali beam was velocity selected, with a triangular velocity distribution (half-intensity width 4.7% of peak velocity); the velocity was varied over the range 185–1000 m/sec. The Hg beam had a thermal distribution; the average Hg speed was ∼235 meters per second. The scattering data have been converted to the center-of-mass system. The angular distributions show the expected strong forward scattering and evidence the phenomenon of rainbow scattering. The energy dependence of the rainbow angle is used to evaluate the interatomic potential well depth, interpreted as the dissociation energy De of the 2Σ+ molecular ground state. Values (in erg×1014) thus obtained (±5%) are 7.46 for KHg and 7.72 for CsHg. Absolute values of differential cross sections could not be obtained; only relative cross sections D(θ) are reported. The observed low-angle behavior D(θ) ∝θ- 7/3 serves as direct experimental confirmation of the r—6 dependence of the long-range attractive potential for K–Hg and Cs–Hg systems.

The Journal of Chemical Physics•Nov 1, 1962•90 citations

Observation of Quantum Effects in the Scattering of a Monoenergetic Li Beam by a Crossed Hg Beam

Hans U. Hostettler, Richard B. Bernstein

Data on total and differential cross sections are presented, which are believed to show quantum effects. A velocity-selected beam of lithium, chosen for its small mass and large lambda , was scattered by a crossed beam of mercury at 90 deg incidence. The dependence of the total cross section on the average relative velocity is shown graphically. Owing to the difficulty in determining the number of Hg atoms in the scattering zone, absolute total cross sections, Q, were not calculated. Typical angular distributions for Li scattering, observed in the plane of the crossed beams, are plotted as scattering intensities as a function of laboratory angle in the interior quadrant. It appears that the observed undulations are real interference effects originnating from the wave nature of the interacting beams. (B.O.G.)

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SCATTERING OF A VELOCITY SELECTED POTASSIUM BEAM BY NEON, ARGON, AND XENON GASES AT DIFFERENT TEMPERATURES

Howard Howland Brown, K. Lulla, Benjamin B. Bederson

A thermal K beam was velocity selected, and scattered by Ne, Ar, and Xe gases. The dependence of the total cross section on relative velocity is approximately v/sup -0.4/ for K--Ar and K--Xe, and v/sup 0.8/ for K--Ne. The average relative velocity ranges were 400 to 1430 m/sec for Ne, 480 to 1350 m/sec for Ar, and 380 to 1320 m/sec for Xe. The dependence of the cross section on relative velocity was obtained by removing the cross section from the collision frequency integral. For the v/sup -0.4/ dependences, this gives results correct to 3%. For the v/sup -0.8/ dependences, the error is most likely greater. Three gas temperatures were used: liquid air, room, and 200 deg C. The results for a given gas at different temperatures are consistent with kinetic theory predictions. (auth)

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LOW ENERGY ELECTRON SCATTERING FROM ALKALI METAL VAPORS

A. R. Johnston

Two techniques have been used to study low energy electron scattering processes in the alkali metals. A transmission experiment was used to search for resonance structure in the total scattering cross section of sodium, potassium, rubidium, and cesium. A shape resonance was observed in sodium at 0.08 (+OR-) 0.03 eV. In rubidium, evidence was found for the existence of a shape resonance below 0.05 eV. No shape resonance structure was observed in potassium or cesium for energies above 0.1 eV. For energies near the first excited state to near the lowest ionization potential, a progression of Feshbach resonances was observed in each atom. The graphical analysis technique of Spence was used to group most of these resonances into seven families. An analysis is given of the mechanisms affecting the rejection of scattered electrons in the transmission spectrometer. A quantitative description of two modes of operation of the spectrometer is presented. The second portion of this dissertation concerns the measurement of the near-threshold excitation and ionization cross sections in sodium, potassium, and rubidium. A trapped-electron experiment was used to make a relative measurement of these cross sections. The shapes of the excitation cross sections are, in general, somewhat different from other experimental work but are in good agreement with the close-coupling calculations of Moores and Norcross. The shapes of the ionization cross sections are in reasonable agreement with previous work. The ratio of the excitation cross section at 2.5 eV in sodium, 2.0 eV in potassium, and 1.8 eV in rubidium to the respective ionization cross section at the first peak was measured and found to be 3.9 (+OR-) 13% in Na, 5.8 (+OR-) 10% in K, and 6.4 (+OR-) 13% in Rb. These ratios are generally larger than those derived from independent values of the individual cross sections. An analysis of several systematic effects associated with the measurement of the cross section ratio was made. Results from this analysis were used to correct the measured excitation cross section for effects of the elastically scattered electrons.

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Alkali-Alkali Differential Spin-Exchange Scattering. I

David E. Pritchard, Gary M. Carter, Frank Y. Chu +1 more

We present measurements of differential elastic cross sections for various alkali-alkali pairs, as well as the angular dependence of the probability of electron spin exchange in these collisions. The resolution is sufficient to reveal interference structure in the angular dependence of both quantities. We describe our apparatus, which polarizes one incident beam and analyzes the polarization of the scattered atoms, and discuss the measurement and data-reduction procedures. Results are presented in the range 0.1-0.2 eV for the systems Na-Cs, Na-Rb, Na-K, K-Cs, and K-Rb.

Physical Review A•Nov 1, 1970•25 citations

Low-velocity elastic scattering of Rb-Rb

P. Westphal, S. Koch, A. Horn +2 more

With reference to recent progress in preparing slow and intense Rb beams (rubidium atomic funnel and low-velocity intense source of atoms from a magneto-optical trap) we have calculated total and differential elastic scattering cross sections and scattering lengths for ground-state collisions of ${}^{85}$Rb as well as ${}^{87}$Rb. Our results are based on the state of the art ${X}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potentials. Pronounced resonances in the total scattering cross sections occur for collision velocities below 15 m/s. We propose scattering experiments with slow Rb beams in order to check the currently known singlet and triplet potential-energy curves.

Physical Review A•Oct 1, 1997•4 citations
Measurements of the velocity dependence of the angular intensity distribution of potassium and cesium atomic beams scattered by a crossed atomic beam of mercury are presented. The alkali atomic beam was velocity-selected, having a triangular velocity distribution with a halfintensity width of 0.047 of the peak velocity. The alkali velocity could be varied over the range 185 to 1100 m/s. The Hg beam had a thermal velocity distribution. The average speed of the Hg atoms in a typical experiment was 235 m/s (the calculated half-intensity width of the velocity distribution was 190 m/s). A typical angular distribution curve showed the expected very large low angle scattering, but evidenced a region in which the slope changed sharply, often resulting in a bump on the curve. This behavior is indicative of the phenomenon of rainbow scattering. The energy dependence of the rainbow angle was used to evaluate the depth of the interatomic potential wells; values (in ergs x 10/sup 14/) obtained are 7.7/sub 2/ for Cs-Hg and 7.4/sub 6/ for K-Hg. It is difficult to estimate the magnitude of the systematic errors in the absolute differential cross sections. However, reliable values for relative differential cross sections, which are velocity independent, can readilymore » be obtained by the methods described. From the low angle behavior of the differential cross sections, direct experimental evidence for the inverse sixth power dependence of the long-range attractive part of the potential was obtained. (auth)« less
Measurements of the velocity dependence of the angular intensity distribution of potassium and cesium beams scattered by a crossed beam of mercury are presented. The alkali beam was velocity selected, with a triangular velocity distribution (half-intensity width 4.7% of peak velocity); the velocity was varied over the range 185–1000 m/sec. The Hg beam had a thermal distribution; the average Hg speed was ∼235 meters per second. The scattering data have been converted to the center-of-mass system. The angular distributions show the expected strong forward scattering and evidence the phenomenon of rainbow scattering. The energy dependence of the rainbow angle is used to evaluate the interatomic potential well depth, interpreted as the dissociation energy De of the 2Σ+ molecular ground state. Values (in erg×1014) thus obtained (±5%) are 7.46 for KHg and 7.72 for CsHg. Absolute values of differential cross sections could not be obtained; only relative cross sections D(θ) are reported. The observed low-angle behavior D(θ) ∝θ- 7/3 serves as direct experimental confirmation of the r—6 dependence of the long-range attractive potential for K–Hg and Cs–Hg systems.
Data on total and differential cross sections are presented, which are believed to show quantum effects. A velocity-selected beam of lithium, chosen for its small mass and large lambda , was scattered by a crossed beam of mercury at 90 deg incidence. The dependence of the total cross section on the average relative velocity is shown graphically. Owing to the difficulty in determining the number of Hg atoms in the scattering zone, absolute total cross sections, Q, were not calculated. Typical angular distributions for Li scattering, observed in the plane of the crossed beams, are plotted as scattering intensities as a function of laboratory angle in the interior quadrant. It appears that the observed undulations are real interference effects originnating from the wave nature of the interacting beams. (B.O.G.)
A thermal K beam was velocity selected, and scattered by Ne, Ar, and Xe gases. The dependence of the total cross section on relative velocity is approximately v/sup -0.4/ for K--Ar and K--Xe, and v/sup 0.8/ for K--Ne. The average relative velocity ranges were 400 to 1430 m/sec for Ne, 480 to 1350 m/sec for Ar, and 380 to 1320 m/sec for Xe. The dependence of the cross section on relative velocity was obtained by removing the cross section from the collision frequency integral. For the v/sup -0.4/ dependences, this gives results correct to 3%. For the v/sup -0.8/ dependences, the error is most likely greater. Three gas temperatures were used: liquid air, room, and 200 deg C. The results for a given gas at different temperatures are consistent with kinetic theory predictions. (auth)
Two techniques have been used to study low energy electron scattering processes in the alkali metals. A transmission experiment was used to search for resonance structure in the total scattering cross section of sodium, potassium, rubidium, and cesium. A shape resonance was observed in sodium at 0.08 (+OR-) 0.03 eV. In rubidium, evidence was found for the existence of a shape resonance below 0.05 eV. No shape resonance structure was observed in potassium or cesium for energies above 0.1 eV. For energies near the first excited state to near the lowest ionization potential, a progression of Feshbach resonances was observed in each atom. The graphical analysis technique of Spence was used to group most of these resonances into seven families. An analysis is given of the mechanisms affecting the rejection of scattered electrons in the transmission spectrometer. A quantitative description of two modes of operation of the spectrometer is presented. The second portion of this dissertation concerns the measurement of the near-threshold excitation and ionization cross sections in sodium, potassium, and rubidium. A trapped-electron experiment was used to make a relative measurement of these cross sections. The shapes of the excitation cross sections are, in general, somewhat different from other experimental work but are in good agreement with the close-coupling calculations of Moores and Norcross. The shapes of the ionization cross sections are in reasonable agreement with previous work. The ratio of the excitation cross section at 2.5 eV in sodium, 2.0 eV in potassium, and 1.8 eV in rubidium to the respective ionization cross section at the first peak was measured and found to be 3.9 (+OR-) 13% in Na, 5.8 (+OR-) 10% in K, and 6.4 (+OR-) 13% in Rb. These ratios are generally larger than those derived from independent values of the individual cross sections. An analysis of several systematic effects associated with the measurement of the cross section ratio was made. Results from this analysis were used to correct the measured excitation cross section for effects of the elastically scattered electrons.
We present measurements of differential elastic cross sections for various alkali-alkali pairs, as well as the angular dependence of the probability of electron spin exchange in these collisions. The resolution is sufficient to reveal interference structure in the angular dependence of both quantities. We describe our apparatus, which polarizes one incident beam and analyzes the polarization of the scattered atoms, and discuss the measurement and data-reduction procedures. Results are presented in the range 0.1-0.2 eV for the systems Na-Cs, Na-Rb, Na-K, K-Cs, and K-Rb.
With reference to recent progress in preparing slow and intense Rb beams (rubidium atomic funnel and low-velocity intense source of atoms from a magneto-optical trap) we have calculated total and differential elastic scattering cross sections and scattering lengths for ground-state collisions of 85{}^{85}85Rb as well as 87{}^{87}87Rb. Our results are based on the state of the art ${X}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potentials. Pronounced resonances in the total scattering cross sections occur for collision velocities below 15 m/s. We propose scattering experiments with slow Rb beams in order to check the currently known singlet and triplet potential-energy curves.