Coulomb Methods in Atomic Transition Probability Calculations

The simplest possible picture of a complex atom or atomic ion undergoing a transition is of a single active electron undergoing a transition in the field due to a fixed core consisting of the nucleus and the remaining electrons. At large distances from the nucleus this field will be Coulombic; hence any method for calculating atomic transition probabilities which has this basic model is called a Coulomb method. It is at once clear that Coulomb methods are particularly appropriate to the alkalis and their isoelectronic sequences, and also to transitions between excited states of more complex atoms when the active electron can be considered outside the core. Part of the purpose of this paper is to explore to what extent Coulomb methods can be developed to provide useful results in more general situations. In addition, and by way of example, we discuss transition probabilities in the trivalent atoms Aluminium, Gallium, Indium and Thallium, which have been the subject of much discussion in recent years, in particular at the last two Beam-Foil conferences.