Accurate Gaunt factors for non-relativistic quadrupole bremsstrahlung

Abstract

The exact result for non-relativistic quadrupole bremsstrahlung in a Coulomb field was established only recently in Pradler & Semmelrock (2020). It requires the evaluation and integration of hypergeometric functions across a wide range of parameters and arguments, which, in practice, is unfeasible. Here we provide a highly accurate tabulation of the Gaunt factor for quadrupole radiation, its thermal average in a Maxwellian plasma, and the associated cooling function over the entire kinematically relevant range. In addition, we provide a simple approximate formula for the emission cross section which works to within a few percent accuracy for all practical purposes. The results can be applied to the scattering of electrons with themselves, for which quadrupole radiation is the dominant process.

14 pages, 5 figures, 6 tables + 10 ancillary files with machine readable versions of the tables; minor typos corrected; journal version

References in corpus (4)

• Accurate determination of the free-free Gaunt factor; I - non-relativistic Gaunt factors
• Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Poschl-Teller-Ginocchio potential wave functions
• Improved calculations of electron-ion Bremsstrahlung Gaunt factors for astrophysical applications
• Soft Bremsstrahlung

Cited by in corpus (4)

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• Non-relativistic electron-ion bremsstrahlung: an approximate formula for all parameters