Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

Kilcrease, D. P.; Brookes, S.

doi:10.1016/j.hedp.2013.07.004

Title: Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

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Abstract

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. Additionally, a simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. Furthermore, we also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.

Authors:

Kilcrease, D. P. ^[1]; Brookes, S. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Los Alamos Summer School, NM (United States)

Publication Date:: Mon Aug 19 00:00:00 EDT 2013

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1235662

Report Number(s):: LA-UR-13-25663
Journal ID: ISSN 1574-1818; PII: S157418181300164X; TRN: US1600385

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: High Energy Density Physics

Additional Journal Information:: Journal Volume: 9; Journal Issue: 4; Journal ID: ISSN 1574-1818

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS; plane-wave born approximation; Coulomb wave approximation; electron collisional excitation cross section; NLTE plasma modeling

Citation Formats


                    Kilcrease, D. P., and Brookes, S. Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation.  United States: N. p., 2013. 
Web.  doi:10.1016/j.hedp.2013.07.004.

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                    Kilcrease, D. P., & Brookes, S. Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation.  United States.  https://doi.org/10.1016/j.hedp.2013.07.004

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                    Kilcrease, D. P., and Brookes, S. Mon .  
"Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation".  United States.  https://doi.org/10.1016/j.hedp.2013.07.004.  https://www.osti.gov/servlets/purl/1235662.

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@article{osti_1235662,

  title        = {Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation},

  author       = {Kilcrease, D. P. and Brookes, S.},

  abstractNote = {The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. Additionally, a simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. Furthermore, we also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.},

  doi          = {10.1016/j.hedp.2013.07.004},

  journal      = {High Energy Density Physics},

  number       = 4,

  volume       = 9,

  place        = {United States},

  year         = {Mon Aug 19 00:00:00 EDT 2013},

  month        = {Mon Aug 19 00:00:00 EDT 2013}

}

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