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Physical Review A

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

G. Reisfeld, Uri Asaf

Published Jan 1, 1994• 13 citations
Publisher

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.

DOI
10.1103/physreva.49.348

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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.
Positronium (Ps) scattering by noble-gas atoms (He, Ne, Ar, Kr, and Xe) is studied in the frozen-target approximation and with inclusion of the van der Waals interaction. Single-particle electron and positron states in the field of the target atom are calculated, with the system enclosed by a hard spherical wall. The two-particle Ps wave function is expanded in these states, and the Hamiltonian matrix is diagonalized, giving the Ps energy levels in the cavity. Scattering phase shifts, scattering lengths, and cross sections are extracted from these energies and compared with existing calculations and experimental data. Analysis of the effect of the van der Waals interaction shows that it cannot explain the recent experimental data of Brawley et al. for Ar and Xe [Phys. Rev. Lett. 115, 223201 (2015)].
A theoretical model for the collision of atoms in high Rydberg states (nl) with neutral atoms or molecules is proposed, based on the assumption that the electron-perturber interaction is of very short range compared with the mean radius of the Rydberg atom. A semiclassical method is used to derive a compact expression for the collision probability. The calculations need total cross sections for the scattering of a free and low-energy electron by the perturber. The model is applied to the calculation of a free and low-energy electron by the perturber. The model is applied to the calculation of cross sections for the quenching of n 2 D or n 2 F Rydberg states of Na and Rb by rare-gas atoms of N 2 . On the whole the calculated cross sections are in reasonable agreement with experimental data for n>10 approximately. The model and the results of the calculations are discussed and compared with other theoretical works.
In a recent paper, Reisfeld and Asaf [Phys. Rev. A 49, 348 (1994)] suggested a simple model explaining an observed correlation between the electron scattering lengths and electric polarizabilities of rare-gas atoms. They proposed an electron-target interaction potential consisting of a short-range hard-core repulsive part plus a long-range dipole polarization potential, and used the Born approximation to evaluate the scattering length. We show that for this model the scattering length may be evaluated analytically and that theoretical predictions based on an exact expression disagree with experimental data.
Neutral atoms interact through a van der Waals potential which asymptotically falls off as ${r}^{\ensuremath{-}6}$. In ultracold gases, this interaction can be described to a good approximation by the atom-atom scattering length. However, corrections arise that depend on the characteristic length of the van der Waals potential. We parametrize these corrections by analyzing the energies of two- and few-atom systems under external harmonic confinement, obtained by numerically and analytically solving the Schr\"odinger equation. We generalize our results to particles interacting through a longer-ranged potential which asymptotically falls off as ${r}^{\ensuremath{-}4}$.