Low-Energy Scattering of Electrons by Helium

Burke, P G; Cooper, J.; Ormonde, Stephan

doi:10.1103/physrev.183.245

Cited by 164 publications

(42 citation statements)

References 45 publications

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“…As can be seen in Table 2, all matrix elements, except for I = 0, are greater than -0.25, and consequently, only for l = 0 a complex A appears. This seems to be in accordance with findings in [10], where calculations of the 2S phase shift indicated a narrow resonant (or virtual) state just below the 2*S threshold. However, since the «3 value -0.275 differs very little from the border value -0.25, the present method would not be con venient for determining the position of the resonance, even if a position of a negative ion He~(2S) level, with 2*S parent state, were known (see e.g.…”

Section: Calculations and Resultssupporting

confidence: 92%

“…As seen from Fig. 2, with the exception of the close coupling results [10], there is a general agreement in shape with the other theoretical results and the experimental data. It should be noted that both the distorted-wave results [18] and experimental points are likely to have overestimated actual values, the first in the lower region (neglect of the exchange) and the second in the higher region, where inelastic processes have surely contributed to the values measured [19].…”

Section: I I L Q(2is->2is) Cross Sectionsupporting

confidence: 85%

“…We have adopted the following values for the n = 2 sublevels [10]: e(2*S) = -2.1445 au and £(2X P) = -2.1225 au, with the sublevels separa-tion: J e = 0.022 au. When all channels are open, one has k\2 = qAe, k%2 = &32 = -where q is always taken to be greater than unity.…”

Section: Calculations and Resultsmentioning

confidence: 99%

“…Multipole components of the direct interaction poten tial for e-He are given by (see Burke et al [10]) Vi] = i{ y o ( P r sPTs; r)A {PnhP n.w)…”

Section: The Interaction Potentialmentioning

confidence: 99%

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Low-Energy e-He(2¹L) Scattering Calculations

Koledin

Grujić

1981

Zeitschrift Für Naturforschung A

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Cross sections for e-He(21L) scattering have been calculated in the energy range 1 ^E eV. For I > 0 partial cross sections a simple analytical method, proposed by the authors before, which is essentially an extension of Seaton's exact resonance method, has been applied. In the case 1 = 0, when a complex "angular momentum quantum number" in the rotated space appears, a matching procedure has been adopted, making use of a more realistic model potential.The results for Q(21S-21S), ^(2 1S-21P) and Q(21 P-2*P) cross sections are compared with other theoretical calculations and in the case of the elastic Q(21S-21S) cross section with the available experimental data as well.The applicability of the analytical method used in the electron-atom scattering calculations is discussed, in particular for those processes which play a dominant role in the Stark broaden ing of spectral lines from plasmas. Finally, the relevance of the present method to searching for an eventual resonant (or virtual) state near 2X S threshold has been discussed. I. IntroductionElectron-atom collision processes have been the subject of extensive experimental and theoretical studies, owing to their utmost importance in many physical systems, in particular in not too high tem perature plasmas. However, even in the case of e-H scattering, an exact analytical treatment of the complete collision phenomenon is beyond our pre sent mathematical capabilities, and a number of semianalytical, approximate methods have been de veloped (see e.g. Drukarev [1]). Employing refined numerical procedures, many of these methods are capable to provide accurate cross sections for vari ous processes (see e. g. Burke and Seaton [2]), usually at the expense of a considerable computing time consumed. On the other hand, in some applications scattering matrix elements (or the corresponding cross sections) of moderate accuracy, but in simple analytical form are needed, as is the case with the quantum theory of Stark broadening (Baranger [3]). In particular, in the expression for the halfwidth and shift of an isolated nonhydrogenic line one en counters the quantity I -Si Sr i, where $*(/> are the scattering matrix (diagonal) elements, for the elastic scattering on the initial (final) state of the transition. Since at low impact energies (these are usually met in plasmas where Reprint requests to Dr. P. Grujic, Institute of Physics, P. 0. Box 57, 11001 Belgrade, Yugoslavia. neutral species are still present) coupling with other atomic states are important (see e.g. Barnes and Peach [4]), second and higher order processes, like i -> i, i -> i" -etc., make considerable contributions to S^f) [5].One of the most powerful low-energy approxima tions for treating electron-atom (ion) scattering is the close coupling equations method. Within this approximation, the only analytically completely tractable case, to our knowledge, has been the dipole exact resonance model, due to Seaton [5], which applies to the hydrogen (degenerate) target. The principal shortcoming of the original Seaton t...

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Section: Calculations and Resultssupporting

confidence: 92%

Section: I I L Q(2is->2is) Cross Sectionsupporting

confidence: 85%

Section: Calculations and Resultsmentioning

confidence: 99%

“…Multipole components of the direct interaction poten tial for e-He are given by (see Burke et al [10]) Vi] = i{ y o ( P r sPTs; r)A {PnhP n.w)…”

Section: The Interaction Potentialmentioning

confidence: 99%

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Low-Energy e-He(2¹L) Scattering Calculations

Koledin

Grujić

1981

Zeitschrift Für Naturforschung A

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“…For an indirectly related situation involving He', see Drake et al (1969), Burke et al (1969), Griem (1969), and Drake (1971). Krolik and McKee (1978) have discussed various radiative processes involving the low-energy {infrared, millimeter-wave) continuum a, nd its effects on some transitions.…”

Section: B Quasars As Observed Opticallymentioning

confidence: 99%

The emission lines of quasars and similar objects

1979

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Much of our information about quasars is derived from their emission-line spectra. The analysis of such spectra has become an intricate subject which differs considerably from traditional, low-density nebular astrophysics. This review is intended to explain our present understanding of the situation, including some aspects of galactic nuclei whose luminosities are more modest than quasars. Quasars line-emitting regions are probably photoionized (even if supplementary heating processes also occur). So fax, models have been constructed which include ionization and thermal equilibria, the transfer of resonance-line and related photons, and the likely effects of absorption and scattering by dust grains. From comparisons between emission-line intensities produced in these models and observed quasars spectra, it appears that certain densities and pressures and size scales occur in or around quasars. The relative abundances of elements are not very far from solar values, although it is suspected that heavy elements -carbon, nitrogen, and oxygen in particular -are moderately "overabundant" in quasars. The emission-line intensities also provide indirect information about quasars ultraviolet and soft-x-ray continua; there are hints that photons with energies between 20 and 300 eV -which are not directly observable -may even represent the peak of the luminous output of a typical quasar. Finally, some gas-dynamical questions, while extremely important, are very difficult to answer, because of a lack of observables. CONTENTS 715

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