Relativistic screened hydrogenic radial integrals

The computation of dipole matrix elements plays an important role in the study of absorption or emission of radiation by atoms in several fields such as astrophysics or inertial confinement fusion. In this work we obtain closed formulas for the dipole matrix elements of multielectron ions suitable for using in the framework of a Relativistic Screened Hydrogenic Model.

► Analytical expressions for semi-relativistic and fully-relativistic matrix elements for ions are presented. ► The expression is derived in the screened hydrogenic model framework. ► The final formula is expressed in terms of a sole Gauss hypergeometric function. ► The proposed formula gives exact values when comparing numerical integration. ► Oscillator strengths for Li-like ions have been computed to test the formula.