Natural widths and blackbody radiation induced shift and broadening of Rydberg levels in magnesium ions

Theoretical analysis is presented of the natural lifetimes and blackbody-radiation (BBR)-induced shifts and widths of Rydberg states with small and large angular momenta l. Asymptotic presentations in elementary functions are derived for matrix elements of bound-bound, bound-free and threshold radiative transitions from hydrogenic-type states with large angular momenta, applicable to both hydrogen-like and many-electron atoms and ions. For states with small angular momenta two numerical methods based on the quantum defects were used and corresponding data are compared with one another and with the most reliable data of the literature. Asymptotic approximations are derived for natural lifetimes, thermal shifts and broadening of Rydberg states of small and high l and principal quantum numbers n >> 1.