A Critical Comparison of Electron Scattering Cross Sections measured by Single Collision and Swarm Techniques

Buckman, Stephen; Brunger, M. J.

doi:10.1071/p96077

Cited by 26 publications

(17 citation statements)

References 21 publications

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“…This is within the uncertainty of 0.24% estimated by Nesbet [10]. It is probably not coincidental that the KV elastic cross section is about 1% larger than experiment at k ¼ 0:2a À1 0 [23]. One source of uncertainty with our strategy is the value of the confining potential inner radius, namely, R 0 .…”

Section: H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 50%

“…Another notable calculation was the R-matrix calculation (RM) by O'Malley, Burke, and Berrington [12]. The KV helium elastic cross section of Nesbet is often adopted as the theoretical benchmark cross section [22,23]. There is a 1% scatter among these three calculations with the KV phase shifts being the most negative.…”

Section: H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

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Elastic Scattering Using an Artificial Confining Potential

2008

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The discrete energies of a scattering Hamiltonian calculated under the influence of an artificial confining potential of almost arbitrary functional form can be used to determine its phase shifts. The method exploits the result that two short-range Hamiltonians having the same energy will have the same phase shifts upon removal of the confining potential. An initial verification is performed on a simple model problem. Then the stochastic variational method is used to determine the energies of the confined e À -He 2 S e system and thus determine the low energy phase shifts. The present Letter describes a novel strategy to calculate low energy elastic scattering. An artificial confining potential is added to the scattering Hamiltonian, and the discrete energies of this modified system are determined. We then show that two short-range potentials with the same energies in the confining potential have the same phase shifts when the confining potential is removed. This is similar to the box-variational method [7,9], where the energy inside an infinite-walled box is related to the phase shift. In its simplest form, the box-variational method requires the wave function, and thus the basis functions, to have a zero at the boundary (note that the logarithmic derivative at the boundary can, in principle, be set to any value). The ' ¼ 0 phase shifts for the nth positive energy state with energy E n are then given by the identity. In the present approach, almost any square integrable basis function can be used. Initially, we validate our strategy for scattering with a simple exponential potential. We then determine the low energy phase shifts for e À -He scattering to a higher degree of precision than any previous work [10][11][12] by using an explicitly correlated basis to generate the e À -He energies inside the confining potential.The problem is to solve the Schrödinger equation À r 2 2 þ VðrÞ ÉðrÞ ¼ EÉðrÞfor E > 0. The central potential VðrÞ will be assumed to be zero beyond some finite radius, say, R 0 . Now consider the related equationwhere W CP is a confining potential and E is defined relative to Vðr ! 1Þ. This potential has the property that W CP ! E as r ! 1. We choose W CP $ Oðr n Þ (n > 1) as r ! 1. The potential W CP ðrÞ should have an analytic form which has easy to evaluate matrix elements. Second, W CP ðrÞ should be negligible for r < R 0 . If these conditions are met, then it can be shown that the discrete energies E i of the solution of Eq. (2) can be used to determine the phase shifts of Eq.(1) at those energies. Consider a potential V 0 ðrÞ for which Eq. (2) has an eigenvalue E 0 . When r > R 0 , the solution of Eq. (2) will become an exponentially decreasing solution B 0 ðrÞ when E 0 < V 0 ðrÞ þ W CP ðrÞ. The amplitude B will depend on the specifics of V 0 ðrÞ, but the actual radial dependence of 0 ðrÞ does not depend on the form of V 0 ðrÞ. Now consider the behavior of the wave function for r < R 0 . One simply integrates the Schrödinger equation outward from the origin, and, since W CP ðrÞ is zero her...

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Section: H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 50%

Section: H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Elastic Scattering Using an Artificial Confining Potential

2008

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“…Previous calculations include those using the R-matrix [25], multiconfiguration Hartree-Fock (MCHF) [26] and Kohn-variational approaches [22]. The Kohn variational (KV) calculations of Nesbet have been accepted as giving a benchmark set of theoretical phase shifts that are compatible with experimental data [27,28].…”

Section: Heliummentioning

confidence: 97%

All-order relativistic many-body theory of low-energy electron-atom scattering

et al. 2014

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A generalization of the box-variational method is developed to describe particle scattering with the Dirac equation. The method is applied to extract phase shifts from all-order single + double relativistic many-body perturbation theory calculations of the electron-helium, electron-neon, and electron-krypton systems. Comparisons with experimental elastic and momentum transfer cross sections are made. Agreement at the 1% to 2% level is achieved for helium and neon. The scattering length for krypton is 4% smaller in magnitude than experimental estimates derived from swarm experiments.

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“…They require particle number, momentum, and energy (and higher order) balance relations on the entire ensemble of electrons to be met. While the issue of cross section degeneracy (i.e., different cross section sets capable of reproducing the measured transport coefficients) has limited their use in deriving cross sections, 22,23 swarm experiments do provide a test on the completeness and consistency of any cross section set proposed. 21,22 This paper revisits the issues surrounding computation of electron transport properties in water vapour as a function of E/n 0 in the range 0.01-1200 Td (1 Td = 1 townsend = 10 −21 V m 2 ).…”

Section: Introductionmentioning

confidence: 99%

Transport coefficients and cross sections for electrons in water vapour: Comparison of cross section sets using an improved Boltzmann equation solution

Ness

Robson

Brunger

et al. 2012

The Journal of Chemical Physics

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This paper revisits the issues surrounding computation of electron transport properties in water vapour as a function of E/n0 (the ratio of the applied electric field to the water vapour number density) up to 1200 Td. We solve the Boltzmann equation using an improved version of the code of Ness and Robson [Phys. Rev. A 38, 1446 (1988)], facilitating the calculation of transport coefficients to a considerably higher degree of accuracy. This allows a correspondingly more discriminating test of the various electron–water vapour cross section sets proposed by a number of authors, which has become an important issue as such sets are now being applied to study electron driven processes in atmospheric phenomena [P. Thorn, L. Campbell, and M. Brunger, PMC Physics B 2, 1 (2009)] and in modeling charged particle tracks in matter [A. Munoz, F. Blanco, G. Garcia, P. A. Thorn, M. J. Brunger, J. P. Sullivan, and S. J. Buckman, Int. J. Mass Spectrom. 277, 175 (2008)].

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A Critical Comparison of Electron Scattering Cross Sections measured by Single Collision and Swarm Techniques

Cited by 26 publications

References 21 publications

Elastic Scattering Using an Artificial Confining Potential

Elastic Scattering Using an Artificial Confining Potential

All-order relativistic many-body theory of low-energy electron-atom scattering

Transport coefficients and cross sections for electrons in water vapour: Comparison of cross section sets using an improved Boltzmann equation solution

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