Analytic formulae of bound-free Gaunt factor under the hydrogenic Coulomb field

In this paper, analytic formulae of the bound-free (photoelectric) Gaunt factor for nl from 6s to 10l are given. The formulae are obtained by using hydrogen-like Coulomb wave functions. Analytic results are presented and agree very well with those of numerical method. The formulae are useful to calculate conveniently the bound-free cross-sections and absorption coefficients in plasma simulations.