On forms of the Coulomb approximation as a useful source of atomic data for the spectroscopy of astrophysical and fusion plasmas

The Coulomb approximation (CA) has long been regarded as a useful tool for rapid estimates of line strengths, absorption oscillator strengths, and spontaneous transition probabilities of the lighter multi-electron atoms and ions, in situations where large quantities of atomic data are required for the analysis of spectroscopic measurements from a variety of plasma sources, in particular interesting stellar objects (e.g. white dwarf stars) and magnetically confined fusion plasmas. This applies especially in cases where the plasma is spatially inhomogeneous, and produces several ionisation stages of the same impurity element, emitting copious radiation in bound-bound transitions from cascade processes following charge-exchange recombination. While more advanced theoretical methods are routinely used by the specialist, the CA provides a very convenient method of checking atomic data chosen by the experimentalist from extensive compilations through the internet, or by the use of machine codes provided by others. The origins, advantages and shortcomings of the method are described and discussed, as well as convenient modifications thereof, which may readily be implemented for these purposes. Particular attention is paid to the choice of electron coupling of states in which the optical electron has a large orbital angular momentum ( ≥ 3 ) . The text is illustrated by numerous examples of application to spectra of practical interest from astrophysical and laboratory plasmas.