Static-exchange Model Research Articles

Positronium - hydrogen atom scattering using the static exchange model

Scattering of positronium atoms by hydrogen atoms has been investigated using the static exchange model and the first Born approximation (FBA) using only the exchange interaction. The FBA elastic total cross section at very low energy is very close to the estimated value of Massey and Mohr in the zero energy limit. We report total elastic, differential and quenching cross sections using the static exchange model for the energy range 0.068 - 100 eV. The present static exchange results are found to differ from the corresponding results of Fraser. The ratio of the quenching to total elastic cross section approaches the value 0.25 with increasing energy as predicted by Massey and Mohr.

Polarization effects in low-energy electron scattering from silane molecules in an exact static-exchange model.

We have investigated the effects of various model polarization potentials in low-energy (below 15 eV) electron-${\mathrm{SiH}}_{4}$ collisions in which electron-exchange correlation is treated exactly via an iterative procedure. Two models of the parameter-free polarization potential are employed; one, the ${\mathit{V}}_{\mathrm{pol}}^{\mathrm{JT}}$ potential, introduced by Jain and Thompson [J. Phys. B 15, L631 (1982)], is based on the polarized-orbital theory; the other, the correlation-polarization potential ${\mathit{V}}_{\mathrm{pol}}^{\mathrm{CP}}$, first proposed by O'Connel and Lane [Phys. Rev. A 27, 1893 (1983)], is given as a density functional. In this low-energy region, the differential as well as integral cross sections are greatly influenced by such short-range-correlation and long-range-polarization interactions. We found that a local parameter-free model to mimic charge-distortion effects is quite successful if it is determined under the polarized-orbital-type approach rather than based on density-functional theory.

Shape resonances in electron–molecule scattering. A proposed model in terms of S matrix poles and associated generalized quantum numbers

AbstractAs an extension of the recent atomic work of Krylstedt et al. [1, 2], we propose the synthesis of the static exchange plus polarization model within the multiple scattering Xα formalism and the exterior complex rotation method for the study of shape resonances occurring in molecular collisional systems. The bound state multiple scattering Xα method is reviewed with special attention to the form of the various wave functions for the different molecular regions. In connection with the inclusion of continuum electron exchange into the scattering model, we analyze a possible solution to the problem of asymptotical behavior caused by the local density‐based free electron gas approximation used in this case. We also propose a method to fix the cutoff parameter, inherent in the polarization potential, for symmetry‐related molecular participants in the scattering process, thereby obtaining a possible predictive power for the one‐parameter scattering model.Titchmarsh–Weyl's theory is used to formally connect the above formulation to scattering theory. The theoretical difficulties in obtaining a unique meromorphic continuation of the S matrix are investigated in connection with the requirements on the actual potential to be exterior dilation analytic. Furthermore, the occurrence of asymptotic quantum numbers is noted and discussed in conjunction with muffin tin‐like approximations and related exterior complex rotated schemes.It is found that the electron exchange part of the nonstatic one‐body potential exhibits a functional form that is not exterior dilation analytic, albeit the general electron and nuclear many‐body problem involving Coulomb forces are dilation analytic. Although the immediate consequences indicate a rotation angle (θ) dependence on the S matrix continuation, a uniquely defined assignment of the cutoff parameter r0 = r0(θ) makes the present nonstatic model “exterior dilation analytic” in the sense that it mimics the dilation analytic structure of the full many‐body problem at the same time obeying “asymptotic” spherical symmetry via the associated constant of evolution. However, in the static exchange approximation the above difficulties are shown to be circumvented via a certain reformulation, leading to a regular analytic asymptotic form for the interaction potential.

A complex rotated approach to resonant electron scattering on atoms in a static exchange plus polarisation formulation

The authors propose the use of the complex coordinate method in conjunction with a local-density, X alpha static exchange plus polarisation model for the analysis of shape resonances in electron-atom scattering with possible extension to electron-molecule collisional processes. The basic model is discussed and the X alpha formalism is briefly reviewed. The authors investigate the inclusion of polarisation and exchange terms for the study of shape resonances in electron-atom scattering. By the use of the exterior complex scaling technique, complex resonance poles of the partial-wave S matrix can be directly evaluated in the positive lower half of the complex energy plane on the second Riemann sheet. The method is illustrated by presenting numerical investigations of the e-Be and e--Mg scattering systems. The behaviour of the partial-wave cross section and its dependence on the corresponding partial-wave S-matrix poles are discussed. Furthermore, the authors examine the appearance of asymmetries in the cross section in the vicinity of the poles.

Elastic scattering of electrons (or positrons) from positronium and the photodetachment of the positronium negative ion

The authors report accurate variational calculations of the 1,3S and 1,3P phaseshifts for the elastic scattering of electrons (or positrons) by positronium up to the n=2 threshold. Higher-order phaseshifts are evaluated both in a static-exchange model and in an adiabatic-exchange model to give the total elastic, momentum transfer, ortho-para conversion and elastic differential cross sections. The positions of the minima in the elastic differential cross section are given for several values of k2. New 3P resonances are reported. The 1P continuum wavefunction is used together with an accurate variational wavefunction for the ground state of Ps- to obtain the photodetachment cross section of Ps-, and both length and velocity results are checked by evaluating the sum rule S-1.

The scattering of low-energy s-wave electrons by positronium

Calculations of the s-wave scattering of electrons by positronium with energy less than 7.35 eV are reported in a simple static exchange model based on the for e--H, the full static exchange model, and an accurate variational model. The pattern of the results is similar to that for scattering by atomic hydrogen. The lowest 1S resonance is seen at Er=4.768 eV with a width of 1.6 meV. The zero-energy limit of the elastic cross section is close to 228 pi a02.

Natural boundary condition methods for low energy electron-helium scattering

The formalism of the natural boundary condition methods has been extended to include exchange effects arising from the Pauli exclusion principle. The methods have been applied to the elastic scattering of low energy (0-10 eV) electrons from helium atoms using both a static-exchange model and a two-channel model which includes a p-wave pseudo-state of the target to describe polarisation effect. The results for the total and momentum transfer cross sections are compared with earlier related calculations and also with experiment.

Cross sections for the elastic scattering of low-energy electrons by molecular fluorine: an approximate theoretical treatment using discrete basis functions

Phaseshifts and total cross sections for the elastic scattering of low-energy (0-13.6 eV) electrons by molecular fluorine are presented. The phaseshifts are obtained by an approximate technique based on the weak asymptotic coupling of orbital angular momenta and are calculated solely from the results of a discrete basis set diagonalization of the molecular Hamiltonian. Correlation and polarization effects are not treated. The elastic cross section is dominated by a Sigma u+ shape resonance at about 2.2 eV in the static-exchange model.

R-matrix theory for electron-molecule collisions using analytic basis set expansions. II. Electron-H2scattering in the static-exchange model

The $R$-matrix formalism developed by the author to treat scattering from nonspherically symmetric potentials is applied to the scattering of electrons from ${\mathrm{H}}_{2}$ in the static exchange approximation. Calculations were performed for ${\ensuremath{\Sigma}}_{g}$, ${\ensuremath{\Sigma}}_{u}$, ${\ensuremath{\Pi}}_{g}$, and ${\ensuremath{\Pi}}_{u}$ symmetries and phase shifts extracted for $s$, $p$, and $d$ partial waves. The inclusion of $p$ orbitals on each center was found to be essential in representing $d$-wave contributions to the phase shift and to have a non-negligible effect on $p$-wave scattering. The results are in good agreement with other calculations based on the static-exchange model using entirely different numerical techniques. We conclude by discussing the outlook for the method and how it may be extended to treat polarization, correlation, and inelastic processes.

Low-energye−-H2elastic cross sections using discrete basis functions

Differential elastic cross sections for the scattering of electrons by hydrogen molecules are calculated for incident momenta \ensuremath{\le}0.7 a.u. Calculations are performed using a Gaussian basis-set expansion technique developed previously by the authors for use with nonspherical potentials. With the static-exchange model, cross sections are computed in the body-fixed frame and then averaged over molecular orientations. Our results agree well with those of previous workers. The method is economical and has wide applicability to the electron-molecule scattering problem.