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Brazilian Journal of Physics

Electron Scattering from Neon Via Effective Range Theory

Kamil Fedus

Published Oct 8, 2014• 10 citations
Publisher

Abstract

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.

DOI
10.1007/s13538-014-0265-z

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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.
Absolute total cross sections for electron scattering from He and Ne are obtained in the energy range from 20 eV down to below 10 meV with a very narrow electron energy width of 6--8 meV using the threshold-photoelectron source. Total cross sections obtained in the present study generally agree well with those obtained in the previous experiments for both He and Ne above 100 meV, where several experimental works have been reported. Comparison of the present cross sections with the theoretical cross sections which have been regarded as the ``standard'' cross sections shows very good agreement even at very low energies below 10 meV, which confirms the validity of theoretical cross sections. The scattering lengths for electron scattering from He and Ne are also determined from the present total cross sections using the modified effective range theory. The resonant structures in the total cross sections due to Feshbach resonances of He and Ne are also observed. Analysis of the resonant structure was carried out based on the spin-dependent resonant scattering theory in order to determine the values of natural width of Feshbach resonance of Ne.
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.
In a joint experimental and theoretical effort, we carried out a detailed study of electron scattering from Kr atoms in the energy range of the low-lying Feshbach resonances. Absolute angle-differential cross sections for elastic electron scattering were measured over the energy range 9.3–10.3 eV with an energy width of about 13 meV at scattering angles between 10° and 180°. Using several sets of elastic scattering phase shifts, a detailed analysis of the sharp resonance was carried out, resulting in a resonance width of Γ 3/2 = 3.6(2) meV. By direct comparison with the position of the resonance, the energy for the resonance was determined as E 3/2 = 9.489(3) eV. A Fano-type fit of the higher lying resonance yielded the resonance parameters Γ 1/2 = 33(5) meV and E 1/2 = 10.126(4) eV. In order to obtain additional insights, B -spline R -matrix calculations were performed for both the elastic and the inelastic cross sections above the threshold for excitation. They provide the total and angle-differential cross sections for excitation of long-lived and short-lived levels of the configuration in Kr and branching ratios for the decay of the resonance into the three available exit channels. The results are compared with selected experimental data.
Recent results for positron scattering from noble gases over an energy range from 0.5 to 60eV are presented. Measurements include the grand total ( σ GT ), Ps formation ( σ Ps ) and Grand total – Ps formation ( (σ GT -P s ) cross sections. Some preliminary DCS results will also be presented. Work on a formulation of modified effective range theory (MERT) is being undertaken to determine the value of the scattering length [1] which may be useful for identifying a bound state. Plans for experiments on metal atoms will be outlined.
We analyze negative-ion resonances in elastic and inelastic total scattering cross sections for slow electron collisions with the heavy-alkali-metal atoms Rb, Cs, and Fr. Our calculations are based on the Dirac RRR-matrix method [Thumm and Norcross, Phys. Rev. A 45, 6349 (1992)]. For incident electrons of up to 2.8 eV kinetic energy, we compare a 3Po{}^{3}{P}^{o}3Po shape resonance and 3Pe,{}^{3}{P}^{e},3Pe, 1P1o,{}^{1}{P}_{1}^{o},1P1o​, and 1D2o{}^{1}{D}_{2}^{o}1D2o​ Feshbach resonances, located below the first excitation threshold of the atomic target in the low-lying spectra of the ${\mathrm{Rb}}^{\ensuremath{-}},$ ${\mathrm{Cs}}^{\ensuremath{-}},$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ negative ions, with available experimental data and other calculations. We provide the resonance parameters, partial and converged total elastic and inelastic scattering cross sections, and discuss the relative importance of relativistic effects for the three heavy-alkali-metal targets.
The numerical approach to calculating the SSS-matrix poles associated with virtual states in electron-molecule collisions is proposed within the modified effective-range theory frame. The SSS-matrix continuation into the complex momentum plane is possible thanks to the analytical properties of modified Mathieu functions, that is, the exact solutions of the Schr\"odinger equation with the long-range polarization potential ($\ensuremath{\sim}{r}^{\ensuremath{-}4}$). The short-range electron-molecule interaction is included in the introduced numerical approach by model comparison with experimental integral, differential, and momentum-transfer elastic cross sections. The influence of the polarization potential on the virtual-state pole positions is analyzed for nonpolar targets such as N2,CH4,CO2{\mathrm{N}}_{2}, {\mathrm{CH}}_{4}, {\mathrm{CO}}_{2}N2​,CH4​,CO2​, and SF6{\mathrm{SF}}_{6}SF6​. The relation between the SSS-matrix pole position and the sss-wave scattering length is discussed.