The calculation of the absolute strengths of spectral lines

TLDR

The elementary form of the method is limited for complex systems with unclosed shells due to difficulties in identifying certain energy parameters. The study tested self‑consistent field wave functions (including exchange) by evaluating line strengths using both dipole moment and dipole velocity formulas. The authors derived a general analytical expression for transition integrals by neglecting deviations from the asymptotic Coulomb potential, compiled tables of absolute spectral line strengths for s‑p, p‑d, and d‑f transitions, and showed that the method yields accurate results for simple systems—often outperforming traditional wave‑function calculations—and remains useful for complex systems, though some wave‑function inaccuracies were identified.

Abstract

It is shown that in calculating transition integrals it is permissible to neglect the departure of the potential of an atom or ion from its asymptotic Coulomb form. This enables a general analytical expression for the transition integral to be derived. Tables are compiled from which the absolute strengths of large numbers of spectral lines can at once be obtained if the term values of the upper and lower levels are known. s-p , p-d and d-f transitions are all treated. Comparison with experimental data shows that for the simpler systems (i. e. systems with a single electron outside closed shells) the method gives remarkably accurate results; indeed, it appears superior to the normal rather laborious procedure involving the computation of the necessary wave functions, in each individual case, by solution of the appropriate Hartree or Fock differential equation. The method (in its most elementary form) may not be so satisfactory for complex systems (i. e. systems with unclosed shells) owing to difficulties associated with the identification of certain energy parameters. However, the rather scanty comparison data available suggest that even for such systems it yields useful (and in some cases precise) information on the line strengths. Incidentally, in the course of the work the accuracy of a few wave functions based on the self consistent field approximation (including exchange) was tested by using them to evaluate line strengths from both the dipole moment and the dipole velocity formulae. Appreciable defects were revealed.