J/MNRAS/441/2855 Bound-bound Gaunt factor values (Morabito+, 2014)
Exact bound-bound Gaunt factor for quantum levels up to n=2000.
Morabito L.K., van Harten G., Salgado F., Oonk J.B.R., Rottgering H.J.A.,
Tielens A.G.G.M.
<Mon. Not. R. Astron. Soc. 441, 2855 (2014)>
=2014MNRAS.441.2855M 2014MNRAS.441.2855M
ADC_Keywords: Atomic physics
Keywords: atomic data - ISM: genera
Abstract:
Comparison of observations of radio recombination lines in the
interstellar medium with theoretical models can be used to constrain
electron temperature and density of the gas. An important component of
the models is spontaneous transition rates between bound levels.
Calculating these rates relies on accurate bound-bound oscillator
strengths, which can be cast in terms of the Gaunt factor. The Gaunt
factor contains terminating hypergeometric functions that cannot be
calculated with sufficient accuracy for high quantum levels (n≳50) by
standard machine-precision methods. Methods to overcome the accuracy
problem have been developed, which include asymptotic expansions and
recursion relations. These methods, used in astrophysical models to
calculate oscillator strengths, can introduce errors, sometimes up to
as much as ∼8 per cent. Detections of radio recombination lines with
the new Low Frequency Array have prompted an examination of
theoretical models of the interstellar medium. We revisit the
calculation of the Gaunt factor, employing modern arbitrary-precision
computational methods to tabulate the Gaunt factor for transitions up
to quantum level n=2000, sufficient to model low-frequency carbon
radio recombination lines. The calculations provide a relative error
of ∼3x10-4 when compared to more detailed calculations including
relativistic corrections. Our values for the Gaunt factor are provided
for download in a tabular format to be used for a wide range of
applications.
Description:
Tabulation of the Gaunt factor values for quantum levels up to n=2000.
These were calculated using arbitrary precision with the hypergeometric
function in MATHEMATICA.
The fits file is a 2000x2000 square matrix, where every element
corresponds to the Gaunt factor for that transition. For example,
element [3,2] contains the Gaunt factor value for the transition from
the n=3 to n=2 quantum level. The only elements that do not have a
value are the n=n elements. The Gaunt factor is a dimensionless
quantity.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
bbgaunt.fit 2880 5557 Bound-Bound Gaunt Factor Values
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Acknowledgements:
Leah Morabito, morabito(at)strw.leidenuniv.nl
(End) Leah Morabito [Leiden Observatory], Patricia Vannier [CDS] 19-Dec-2013