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Journal of Physics B Atomic Molecular and Optical Physics

e--Ar scattering length from drift velocities measured in argon-hydrogen mixtures

Zoran Petrović, Thomas F. O'Malley, RW Crompton

Published Aug 14, 1995• 33 citations
Publisher

Abstract

We present experimental data for drift velocities of very low energy electrons in a 5.45% hydrogen-argon mixture and the analysis of these data to determine the e - -Ar scattering length. The addition of a small fraction of hydrogen to argon enables experiments to be made with very low-energy electron swarms without the use of very high gas densities, thus reducing the uncertainty in the e - -Ar cross section derived from the experimental data. A scattering length of -1.459 a 0 is found, lying between the previous swarm determination and that obtained from time-of-flight (TOF) beam measurements. Pressure effects on the transport coefficients measured in earlier experiments are discussed, and evidence presented for a large departure from the Einstein relation at gas densities of 3*10 20 cm -3 .

DOI
10.1088/0953-4075/28/15/020

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We present experimental data for drift velocities of very low energy electrons in a 5.45% hydrogen-argon mixture and the analysis of these data to determine the e - -Ar scattering length. The addition of a small fraction of hydrogen to argon enables experiments to be made with very low-energy electron swarms without the use of very high gas densities, thus reducing the uncertainty in the e - -Ar cross section derived from the experimental data. A scattering length of -1.459 a 0 is found, lying between the previous swarm determination and that obtained from time-of-flight (TOF) beam measurements. Pressure effects on the transport coefficients measured in earlier experiments are discussed, and evidence presented for a large departure from the Einstein relation at gas densities of 3*10 20 cm -3 .
Absolute total cross sections for electron scattering from Ar and Xe at electron energies ranging from 7 meV to 20 eV were obtained with the experimental technique employing the threshold-photoelectron source. The measured total cross sections are in good agreement with those obtained by other groups down to 100 meV, above which several experimental works have been reported. Scattering lengths for electron scattering from Ar, Kr, and Xe were determined from the present total cross sections and our recent results for Kr using the modified effective range theory. The values of the scattering length obtained in the present analysis differ from the values determined from the previous swarm experiments and beam experiments. The resonant structures in the total cross sections due to Feshbach resonances of Ar, Kr, and Xe with an improved energy resolution were also measured. Analyses of the resonant structure were carried out based on the spin-dependent resonant scattering theory in order to determine the values of the natural width of Feshbach resonances of Ar, Kr, and Xe precisely.
A theoretical relation between the electron scattering length and the van der Waals approximation to the equation of state is described. The theory provides a simple calculation for the scattering length of neutral atomic scatterers such as rare gases, using two experimental parameters: the hard-core radius (calculated from the van der Waals equation of state, using critical data) and the atomic polarizability. The results for the calculated electron scattering length agree with measured values derived either from the energy shifts of highly excited molecular Rydberg states, perturbed by He, Ne, Ar, Kr, and Xe, or from swarm electron cross-section data for the same gases.
Elastic cross-sections for electron scattering on neon from 0 energy up to 16 eV are analyzed by an analytical approach to the modified effective range theory (MERT). It is shown that energy and angular variations of elastic differential, integral and momentum transfer cross-sections can be accurately parameterized by six MERT coefficients up to the energy threshold for the first Feshbach resonance. MERT parameters are determined empirically by numerical comparison with large collection of available experimental data of elastic total (integral) cross-sections. The present analysis is validated against numerous electron beams and swarm experiments. The comparison of derived MERT parameters with those found for other noble gases, helium, argon and krypton, is done. The derived scattering length (for the s-partial wave) in neon, 0.227 a 0, agrees well with recent theories; it is small but, differently from Ar and Kr, still positive. Analogue parameters for the p-wave and the d-wave are negative and positive respectively for all the four gases compared.
In this work, we carry out an comprehensive study for the electron scattering with atomic argon in the framework of relativistic box-variational method. The phase shifts first are extracted from relativistic coupled-cluster-theory calculations. Then the properties including total elastic, momentum transfer, viscosity cross sections, and differential cross sections are evaluated and compared with available experimental and theoretical data. The validity and accuracy of present method are verified by the good agreement with experimental values, especially for the differential cross sections at small angle forward and backward scattering where obvious discrepancies exist between experiments and theories. The predicted scattering length of $\ensuremath{-}1.39 {a}_{0}$ for electron-argon system is only 22%2 larger in magnitude than the most recent experimental estimate. In addition, the role of electron correlation effect are also investigated in these properties.
We report accurate measurements of excess electron mobility in high-density Ar gas at a temperature T\ensuremath{\simeq}163 K in the density range (4N70)\ifmmode\times\else\texttimes\fi{}1020{10}^{20}1020 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ as a function of the electric-field strength. The positive-density effect shown by the zero-field density-normalized mobility ${\mathrm{\ensuremath{\mu}}}_{0}$N can be explained within the same theoretical framework recently used for neon gas, where ${\mathrm{\ensuremath{\mu}}}_{0}$N shows a negative-density effect. Thus the analysis of our present measurements indicates that there is no need for two separate theories for both negative- and positive-scattering-length gases.
The collisional angular-momentum mixing of $n=5\ensuremath{-}15$ Na ddd states with the l>2l>2l>2 states of the same nnn has been studied using He, Ne, and Ar as collision partners. At rare-gas pressures of \ensuremath{\sim}1 Torr, the $l\ensuremath{\ge}2$ states are thoroughly mixed and the mixture decays at the average radiative lifetime of all the $l\ensuremath{\ge}2$ states of the same nnn. Using \ensuremath{\sim}1 Torr of neon to collisionally mix the $l\ensuremath{\ge}2$ states, the average lifetime for $l\ensuremath{\ge}2$ was measured for each nnn and compared to the theoretical prediction for hydrogen, with which it is in excellent agreement. The cross section for lll mixing by each of the gases is found to increase sharply from n=5to10n=5 \mathrm{to} 10n=5to10 and decrease above n=10n=10n=10. The magnitudes of the lll-mixing cross sections are found to correlate with the low-energy scattering lengths of the collision partners.