Non-coherent scattering in subordinate lines

III. Generalized redistribution functions

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27 Citations (Scopus)

Abstract

The concept of the redistribution function, which was originally introduced in order to describe a correlation between frequencies and directions of the absorbed and emitted photon in resonance scattering, has been extended to other resonance two-photon processes including resonance Raman scattering, resonance two-photon absorption and emission, and inverse Raman scattering. We have derived, within the frame of the impact approximation, the appropriate form of the generalized redistribution function. Using a suitable formalism, the generalized redistribution function takes the same form for all types of two-photon processes and contains all the redistribution functions, considered previously, as various limiting cases. In analogy to Hummer's original scheme of redistribution functions, we have derived a similar set of generalized redistribution functions, denoted as pi(i = I, II, III, IV, V), and we have shown that the most general case is described by a linear combination of pIII and pV, analogously to the previous results. Explicit formulae for the velocity-averaged (laboratory-frame) generalized redistribution functions pi(i = I, II, III, IV, V) are given and possible numerical methods for their evaluation are briefly indicated.

Original languageEnglish (US)
Pages (from-to)593-609
Number of pages17
JournalJournal of Quantitative Spectroscopy and Radiative Transfer
Volume27
Issue number6
DOIs
StatePublished - 1982
Externally publishedYes

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Scattering
scattering
Two photon processes
resonance scattering
photons
Raman scattering
Photons
Raman spectra
inverse scattering
Numerical methods
formalism
evaluation
approximation

ASJC Scopus subject areas

  • Spectroscopy
  • Atomic and Molecular Physics, and Optics

Cite this

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title = "Non-coherent scattering in subordinate lines: III. Generalized redistribution functions",
abstract = "The concept of the redistribution function, which was originally introduced in order to describe a correlation between frequencies and directions of the absorbed and emitted photon in resonance scattering, has been extended to other resonance two-photon processes including resonance Raman scattering, resonance two-photon absorption and emission, and inverse Raman scattering. We have derived, within the frame of the impact approximation, the appropriate form of the generalized redistribution function. Using a suitable formalism, the generalized redistribution function takes the same form for all types of two-photon processes and contains all the redistribution functions, considered previously, as various limiting cases. In analogy to Hummer's original scheme of redistribution functions, we have derived a similar set of generalized redistribution functions, denoted as pi(i = I, II, III, IV, V), and we have shown that the most general case is described by a linear combination of pIII and pV, analogously to the previous results. Explicit formulae for the velocity-averaged (laboratory-frame) generalized redistribution functions pi(i = I, II, III, IV, V) are given and possible numerical methods for their evaluation are briefly indicated.",
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TY - JOUR

T1 - Non-coherent scattering in subordinate lines

T2 - III. Generalized redistribution functions

AU - Hubeny, Ivan -

PY - 1982

Y1 - 1982

N2 - The concept of the redistribution function, which was originally introduced in order to describe a correlation between frequencies and directions of the absorbed and emitted photon in resonance scattering, has been extended to other resonance two-photon processes including resonance Raman scattering, resonance two-photon absorption and emission, and inverse Raman scattering. We have derived, within the frame of the impact approximation, the appropriate form of the generalized redistribution function. Using a suitable formalism, the generalized redistribution function takes the same form for all types of two-photon processes and contains all the redistribution functions, considered previously, as various limiting cases. In analogy to Hummer's original scheme of redistribution functions, we have derived a similar set of generalized redistribution functions, denoted as pi(i = I, II, III, IV, V), and we have shown that the most general case is described by a linear combination of pIII and pV, analogously to the previous results. Explicit formulae for the velocity-averaged (laboratory-frame) generalized redistribution functions pi(i = I, II, III, IV, V) are given and possible numerical methods for their evaluation are briefly indicated.

AB - The concept of the redistribution function, which was originally introduced in order to describe a correlation between frequencies and directions of the absorbed and emitted photon in resonance scattering, has been extended to other resonance two-photon processes including resonance Raman scattering, resonance two-photon absorption and emission, and inverse Raman scattering. We have derived, within the frame of the impact approximation, the appropriate form of the generalized redistribution function. Using a suitable formalism, the generalized redistribution function takes the same form for all types of two-photon processes and contains all the redistribution functions, considered previously, as various limiting cases. In analogy to Hummer's original scheme of redistribution functions, we have derived a similar set of generalized redistribution functions, denoted as pi(i = I, II, III, IV, V), and we have shown that the most general case is described by a linear combination of pIII and pV, analogously to the previous results. Explicit formulae for the velocity-averaged (laboratory-frame) generalized redistribution functions pi(i = I, II, III, IV, V) are given and possible numerical methods for their evaluation are briefly indicated.

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