Correction of the near threshold behavior of electron collisional excitation crosssections in the planewave Born approximation
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, deexcitation, ionization and recombination. Additionally, a simple and computational fast way to calculate electron collisional excitation crosssections for ions is by using the planewave Born approximation. This is essentially a highenergy 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 crosssections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a crosssection 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:

^{[1]};
^{[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:
 Report Number(s):
 LAUR1325663
Journal ID: ISSN 15741818; PII: S157418181300164X; TRN: US1600385
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 High Energy Density Physics
 Additional Journal Information:
 Journal Volume: 9; Journal Issue: 4; Journal ID: ISSN 15741818
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; planewave born approximation; Coulomb wave approximation; electron collisional excitation cross section; NLTE plasma modeling
 OSTI Identifier:
 1235662
Kilcrease, D. P., and Brookes, S.. Correction of the near threshold behavior of electron collisional excitation crosssections in the planewave Born approximation. United States: N. p.,
Web. doi:10.1016/j.hedp.2013.07.004.
Kilcrease, D. P., & Brookes, S.. Correction of the near threshold behavior of electron collisional excitation crosssections in the planewave Born approximation. United States. doi:10.1016/j.hedp.2013.07.004.
Kilcrease, D. P., and Brookes, S.. 2013.
"Correction of the near threshold behavior of electron collisional excitation crosssections in the planewave Born approximation". United States.
doi:10.1016/j.hedp.2013.07.004. https://www.osti.gov/servlets/purl/1235662.
@article{osti_1235662,
title = {Correction of the near threshold behavior of electron collisional excitation crosssections in the planewave 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, deexcitation, ionization and recombination. Additionally, a simple and computational fast way to calculate electron collisional excitation crosssections for ions is by using the planewave Born approximation. This is essentially a highenergy 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 crosssections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a crosssection 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 = {2013},
month = {8}
}