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Physical Review A

Electron-impact detachment of weakly bound negative ions: Threshold and scaling laws

F. Robicheaux

Published Aug 1, 1999• 12 citations
Publisher

Abstract

The details of a recent theoretical formulation of electron-impact detachment of weakly bound negative ions are presented. The formalism is applied at low energies to find the behavior of the cross section near threshold. Also, the applicability of a recently proposed scaling law is discussed. The formulation uses different coordinate systems for the initial and final states. The initial state is a simple product of wave functions of each electron, while the final state is a simple product of wave functions in center-of-mass coordinates.

DOI
10.1103/physreva.60.1206

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The details of a recent theoretical formulation of electron-impact detachment of weakly bound negative ions are presented. The formalism is applied at low energies to find the behavior of the cross section near threshold. Also, the applicability of a recently proposed scaling law is discussed. The formulation uses different coordinate systems for the initial and final states. The initial state is a simple product of wave functions of each electron, while the final state is a simple product of wave functions in center-of-mass coordinates.
The effect of final-state interactions on the photodetachment cross section of negative ions in a magnetic field is discussed. Experiments on the location of the 2P32^{2}P_{\frac{3}{2}}2P23​​ threshold in ${\mathbf{S}}^{\ensuremath{-}}$ as a function of magnetic field show clearly the effect of the zero-point energy of an electron in a magnetic field. The experiments also give a precise value for the electron affinity and provide information about the interaction between the atom and the detached electron.
A very recently method for classical trajectory calculations for three-body collision [J. Pérez-Ríos, S. Ragole, J. Wang and C. H. Greene, J. Chem. Phys. {\bf 140}, 044307 (2014)] has been applied to describe ion-neutral-neutral ternary processes for low energy collisions: 0.1 mK - 10 mK. As a result, a threshold law for the three-body recombination cross section is obtained and corroborated both, experimentally and numerically. The derived threshold law predicts the formation of weakly bound dimers, with binding energies comparable to the collision energy of the collisional partners. In this low energy range, this analysis predicts that molecular ions should dominate over molecular neutrals as the most products formed.
We present a theoretical description of the formation of weakly bound (${E}_{b}\ensuremath{\sim}0.1\text{--}10$ meV) negative ions in collisions of Rydberg atoms with neutral atoms or molecules. Using the adiabatic approximation for the collision, we obtain an analytical expression for the formation cross section. It is shown that the cross section has a sharp peak in its dependence on the principal quantum number of the Rydberg electron. This result is in agreement with the experimental studies. We obtain a simple analytical expression that relates the peak position and the binding energy of the negative ion. This expression generalizes the empirical law previously established by Desfran\ifmmode \mbox{\c{c}}\else \c{c}\fi{}ois [Phys. Rev. A 51, 3667 (1995)]. Comparison of our calculations with the experimental data on dipole-bound anion formation shows that the obtained formula can be used for determination of binding energies of weakly bound negative ions from Rydberg electron transfer reactions with good accuracy.
We study the structure of bound states appearing in systems governed by the Coulomb and short-range interactions. We analyze the binding energies and wave functions of the bound states generated by the Coulomb plus short-range potential. We demonstrate that Coulomb-induced shifts of the binding energy are closely correlated with the spatial distribution of the wave function. Furthermore, we show that the asymptotic behavior of wave functions of weakly bound states is qualitatively altered by Coulomb repulsion, leading to a modification of the near-threshold mass scaling that is otherwise universal for short-range interactions.
Low-energy electron transfer in collisions between a Rydberg atom and a target molecule can result in the formation of negative ions. Depending as to the properties of the target molecule the electron may be bound in a localized molecular orbital (valence-bound) or bound by its dipole potential in a diffuse orbital located at the positive end of the dipole (dipole-bound). Here we examine the properties of valence-bound and dipole-bound negative ions created through electron transfer in collision with Rydberg atoms, in particular, their lifetimes, collisional properties and electric-field-induced detachment characteristics. Intercomparison of the various data also leads to new insights into electron attachment to molecules that can support both valence-bound and dipole-bound negative ion states.
We describe two simple models for the determination of electron binding energies (Eb{\mathit{E}}_{\mathit{b}}Eb​) of several dipole-bound negative ions from field-detachment experiments and charge-transfer formation-rate-constant measurements in collisions between cold neutral molecules and Rydberg atoms. These models are able to correctly reproduce the experimental data, from which we deduce two compatible sets of Eb{\mathit{E}}_{\mathit{b}}Eb​ values. A curve-crossing model for calculating anion formation rate constants allows us to qualitatively understand the sharply peaked shapes of the experimental curves and to derive a simple quantitative law between Eb{\mathit{E}}_{\mathit{b}}Eb​ values and principal Rydberg quantum numbers at which anion formation rate constants are maximum.