Abstract
We report on an extensive semi-empirical analysis of scattering cross-sections for electron elastic collision with noble gases via the Markov Chain Monte Carlo-Modified Effective Range Theory (MCMC−MERT). In this approach, the contribution of the long-range polarization potential (∼r−4) to the scattering phase shifts is precisely expressed, while the effect of the complex short-range interaction is modeled by simple quadratic expression (the so-called effective range expansion with several adjustable parameters). Additionally, we test a simple potential model of a rigid sphere combined with r−4 interaction. Both models, the MERT and the rigid sphere are based on the analytical properties of Mathieu functions, i.e., the solutions of radial Schrödinger equation with pure polarization potential. However, in contrast to MERT, the rigid sphere model depends entirely upon one adjustable parameter—the radius of a hard-core. The model’s validity is assessed by a comparative study against numerous experimental cross-sections and theoretical phase shifts. We show that this simple approach can successfully describe the electron elastic collisions with helium and neon for energies below 1 eV. The purpose of the present analysis is to give insight into the relations between the parameters of both models (that translate into the cross-sections in the very low energy range) and some “macroscopic” features of atoms such as the polarizability and atomic “radii”.
Highlights
Great attention was devoted to electron collisions with atoms of noble gases over the years [1], scattering in a very low-energy range is still challenging both experimentally and theoretically
In [27], we showed that an even simpler semi-empirical model than Modified Effective Range Theory (MERT) could describe very low-energy positron interaction with noble gases, namely the rigid sphere approach
One can use nonlinear least-square regression procedures to fit MERT to chosen crosssection datasets and determine unknown parameters in the effective range approximation given by Equation (10)
Summary
Great attention was devoted to electron collisions with atoms of noble gases over the years [1], scattering in a very low-energy range is still challenging both experimentally and theoretically. Experiments at very low energies are scarce and burdened with high uncertainties since hard-to-reach energy and angular resolutions are required to carry out trustworthy measurements [2]. A great value in understanding angular and energy variations of low-energy collisions can be brought by semi-empirical models, which give some insight into the relations between cross-sections and some “macroscopic” (i.e., measurable in other phenomena) features of the targets, like their polarizability and/or atomic “radii”. Noble gases are used as additives in swarm experiments, to derive the very-low energy cross sections for molecules with other possible processes, like the vibrational excitations (CH4 , C2 H2 [6,7])
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