A program to compute exact hydrogenic radial integrals and Einstein coefficients Original Research Article

An exact expression for the dipole radial integral of hydrogen has been given by Gordon [Ann. Phys. 2 (1929) 1031]. It contains two hypergeometric functions image, which are difficult to calculate directly, when the (negative) integers a, b are large, as in the case of high Rydberg states of hydrogenic ions. We have derived a simple method [D. Hoang-Binh, Astron. Astrophys. 238 (1990) 449], using a recurrence relation to calculate exactly F, starting from two initial values, which are very easy to compute. We present here a numerical code using this method. The code computes exact hydrogenic radial integrals, oscillator strengths, Einstein coefficients, and lifetimes, for principal quantum numbers up to 1000.