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

Abstract

Modified effective range theory formulated as a Bayesian statistical model through the combination with Markov Chain Monte Carlo integration and fitting techniques is used to check the compatibility of different e − −Xe scattering data such as the total cross-sections, the momentum transfer cross-sections, and the differential cross-sections that were determined experimentally in the region of Ramsauer-Townsend minimum. On the basis of this predictive approach, the most probable value of the scattering length, (−6.51 ± 0.05)a 0 , is proposed. The present analysis suggests that the non-relativistic spinless effective range theory is suitable for the description of angular and energy dependencies of e − −Xe elastic scattering cross-sections below the threshold for first inelastic process.

A rigid sphere approach to positron elastic scattering by noble gases, molecular hydrogen, nitrogen and methane

“…Saying it differently, the shift in the position of infinite barrier gives the same effect as using completly different representations of short-rage part of attractive correlation potential for impact energies at which the longrange polarization interaction (∼r −4 ) is clearly dominant. This observation togehther with succesful applicability of MERT analysis [3,[24][25][26][27][28][29] to the low-energy positron scattering suggests that contribution of short-range correlations become less important with impact energy approaching zero.…”

“…It is more difficult to define equivalent "molecular" radii for H 2 , N 2 and CH 4 due to the lack of typical spherical symetry, though it has been proved [24][25][26][27][28][29] that approximation of spherical dipole polarizability is sufficient to describe low-energy positron (or electron) scattering by these molecules. In Table 1 we give different theoretical estimates of molecular sizes in order to show that values of R 0 used in present model are compatible with a typical molecular length-scale.…”

“…Present model needs only one adjustable parameter -the radius of the rigid sphere, which is found to be compatible with the positions of principal maxima in the radial distribution of outermost atomic orbitals. The requirement for only one adjustable parameter is an advantage when compare to modified effective range theory (MERT) [25][26][27][28][29] where four to six empirical parameters are needed in order to describe variations of elastic scattering cross versus impact energy. In more details, when compared with available experimental and theoretical data for the lightest atom -helium, the model agrees with majority of experiments and theories only at very low impact energies (<1 eV).…”

“…In particular Schrader [23] proposed a simple model with only one adjustable parameter. More recently, in a series of papers [24][25][26][27][28][29] we showed that the low-energy electron and positron scattering by noble gases and simple non-polar molecules (such as H 2 , CH 4 ) can be very well modeled using well-known modified effective range theory (MERT). In MERT the scattering problem is solved analytically considering the target as single object interacting with the incoming projectile through the long-range dipole polarization potential (∼r −4 ).…”

Elastic Scattering of Slow Electrons by Noble Gases—The Effective Range Theory and the Rigid Sphere Model

“…Idziaszek and Karwasz [21] proposed an alternative approach to the MERT series: phase shifts were obtained solving the Schrödinger equation with long-range polarization potential analytically using Mathieu functions, and the effective-range expansion was introduced only for the short-range part of the interaction potential. We showed [22][23][24][25] that such an approach allows expanding MERT applicability to much higher energies, where more accurate data are available. It is true for both positrons and electrons.…”