An alternative method for determination of oscillator strengths: The example of Sc II

•The method of simultaneous determination of all the attributes of atomic structure.•The semi-empirical method of parameterization of oscillator strengths.•Illustration of the method application for the example of Sc II data.

We describe our method for determining oscillator strengths and hyperfine structure splittings that is an alternative to the commonly used, purely theoretical calculations, or to the semi-empirical approach combined with theoretically calculated transition integrals.We have developed our own computer programs that allow us to determine all attributes of the structure of complex atoms starting from the measured frequencies emitted by the atoms. As an example, we present the results of the calculation of the structure, electric dipole transitions, and hyperfine splittings of Sc II. The angular coefficients of the transition matrix in pure SL coupling were found from straightforward Racah algebra. The transition matrix was transformed into the actual intermediate coupling by the fine structure eigenvectors obtained from the semi-empirical approach. The transition integrals were treated as free parameters in the least squares fit to experimental gf values. For most transitions, the experimental and the calculated gf-values are consistent with the accuracy claimed in the NIST compilation.