Line strengths, A-factors and absorption cross-sections for fine structure lines in multiplets and hyperfine structure components in lines in atomic spectrometry—a userʹs guide

This work summarizes and elucidates a number of fundamental concepts in atomic spectrometry regarding the ‘strengths’ of transitions between various energy levels and states in atoms. Although several of the expressions and rules for line strengths of transitions reported here can be found, in one way or another, in various books dealing with atomic structure, atomic spectrometry or quantum mechanics, the treatment in such books can be variously complex and difficult to follow for a non-experienced reader. In addition, detailed information about transition-specific ‘strengths’ of transitions used to be restricted to line strengths, whereas most experiments rather need transition-specific A-factors or transition-specific absorption cross-sections. This work therefore aims at pointing out the most important aspects of the concept of ‘strengths’ of transitions between various energy levels and states in atoms by presenting explicit expressions for not only relative and absolute line strengths but also oscillator strengths (f-values), A-factors and absorption cross-sections, for transitions between fine structure levels within a multiplet as well as for hyperfine structure components within a line (i.e. between hyperfine structure levels), including their mutual relations, in a consistent and user-friendly manner. The work also recapitulates the most important summation rules for line strengths, oscillator strengths (f-values), A-factors and absorption cross-sections for lines within multiplets and hyperfine structure components within lines. Many of the expressions are illustrated with clear and intelligible examples. For the sake of clarity and completeness, the work also comprises a short review of the nomenclature for atomic structure and transitions.