Determination of the energy splitting between [formula omitted][formula omitted] and [formula omitted] states in phosphorus-like ions

The spectroscopic investigations on 3p32D5/2−2D3/2 transitions of phosphorus-like Ge17+, As18+, Se19+, Br20+, and Kr21+ ions at an electron beam ion trap were presented. The direct wavelength measurements were reported for the first time for Ge17+−Br20+ ions. All the measurements reached precision levels of a few ppm. The theoretical calculations were carried out using multi-configuration Dirac–Hartree–Fock and relativistic configuration interaction methods including a large set of configuration state functions, in which the Breit interaction and QED effects were taken into account. The present results showed a good agreement between the theory and the experiment, and the divisions were less than 0.6%. Especially for the Kr21+ ions, meticulous scrutiny of line strengths with charge state distributions and continuity of results with isoelectronic sequence were performed to identify the measured spectral line as 3p32D5/2−2D3/2 transition. The present work resolved the long-standing confusion of the Kr21+ spectral line. Our accurate experimental results could be reference data for further calculations.