Electron Scattering from Neon Via Effective Range Theory

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 crosssections 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, 0.227a 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.

Markov Chain Monte Carlo Effective Range Analysis of Low-Energy Electron Elastic Scattering from Xenon

“…This article completes our picture of MERT applicability to noble gases [5][6][7]. Figure 6 shows an attempt to correlate the s-wave scattering lengths (A) for all noble gases versus static dipole polarizability (α) as hypothesized by Reisfeld and Asaf [49].…”

“…Figure 6 shows an attempt to correlate the s-wave scattering lengths (A) for all noble gases versus static dipole polarizability (α) as hypothesized by Reisfeld and Asaf [49]. The values of the scattering length, except the present result for Xenon, were determined in our previous MERT studies [5][6][7] using "traditional" fitting techniques. Figure 6 presents also the linear fit to A(α) in order to show a general tendency in the relation between these two quantities.…”

“…Therefore, the most accurate scattering phase-shifts can be derived by fitting MERT to available experimental TCSs. Benefiting from good agreement between experimental TCSs, the scattering phase shifts were first determined by performing simultaneous robust fit of (5) to large collection of TCS data sets (using MATLAB routine for nonlinear leastsquare regression of multiple data sets) similarly as it was done in analogous analysis for neon [6]. For present analysis, only those experimental TCSs were chosen that extend well below the energy corresponding to the R-T minimum: Guskov et al [25], Jost et al [27], Ferch et al [30], Alle et al [31], and Szmytkowski et al [32].…”

“…The advantage of present Markov Chain Monte Carlo effective range analysis is the ability to predict error bars for the theoretical estimates of model parameters when compared to the traditional fitting methods. We plan to apply Bayesian inference for other noble gases: helium, neon, argon, and krypton, in order to estimate the uncertainties of scattering lengths that were determined in our previous "traditional" MERT studies [5][6][7]. We expect that the inclusion of error bars for extrapolated values can explain the small deviations from linear dependency of A(α).…”

“…The effective range approximations are introduced into the analytical solution exclusively for a short-range part of the interaction potential. We showed in a series of papers that such approach allows to extend the applicability of MERT almost to the threshold for the first inelastic process in many simple targets, including He, Ar and H 2 [5], Ne [6], Kr [7], and CH 4 [8].…”