Exact Bound-Bound Gaunt Factor Values for Quantum Levels up to n=2000


Comparison of observations of radio recombination lines in the interstellar medium with the-oretical 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 func-tions 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 meth-ods, used in astrophysical models to calculate oscillator strengths, can introduce errors, some-times up to as much as ∼ 8 per cent. Detections of radio recombination lines with the new Low Frequency Array (LOFAR) has prompted an examination of theoretical models of the in-terstellar 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 cal-culations provide a relative error of ∼ 3 × 10−4 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. Key words: atomic data – ISM: general

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