Relation between the electron scattering length and the van der Waals approximation to the equation of state

Abstract

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.PACS number(s): 34.80. Bm, 33.20.Ni, 42.25.Ja

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

“…Figure 6 presents also the linear fit to A(α) in order to show a general tendency in the relation between these two quantities. The similar dependency has been already predicted by Reisfeld and Asaf [49] who showed that A(α) can be indeed approximately expressed by the linear relationship if the electron-target interaction potential is approximated by the short-range hard-core repulsive part plus the long-range dipole polarization potential. Our MERT-computed scattering-lengths seem to partially confirm these results though the parametric dependence on the size of the hard core does not seem to be so crucial as it is postulated by the expression derived by Reisfeld and Asaf (see Eq.…”

“…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.…”

“…6 in ref. [49] . In most cases, the scattering lengths for noble gases have been determined by extrapolating experimental or theoretical results using modified effective range theory.…”

Experimental charge density from electron microscopic maps

“…Thus in an EM map at atomic resolution or sub‐Ångstrom resolution, the image of an isolated neutral atom will be a positive peak centered on the position of its nucleus, surrounded by a negative halo. Because the shielding effect afforded by the atom's electrons, the ESP density associated with its peak will fall to zero at a distance from its nucleus that is close to the atom's van der Waals (vdW) radius . However, if the atom is an ion, its ESP will extend indefinitely beyond its vdW radius.…”

“…When EM data are processed using the negative Laplace operation, as advocated below, the images of atoms no longer correspond to their ESP distributions, but rather to their charge density (CD) distributions. Since the CD distributions of atoms are always contained within their vdW envelopes, the images of molecules in maps of this kind resemble sums of images of independent atoms much more closely than the images of molecules in ordinary EM maps. In addition, at high scattering angles, nuclear charges dominate scattering factors, and as a consequence, a CD map will tend to be better resolved than the corresponding EM map.…”