Determination of the energy splitting between 3p3 2D5/2 and 2D3/2 states in phosphorus-like ions

The spectroscopic investigations on $3p^3$ ${}^2{D}_{5/2}$ $-$ ${}^2{D}_{3/2}$ transitions of phosphorus-like Ge${}^{17+}$, As${}^{18+}$, Se${}^{19+}$, Br${}^{20+}$, and Kr${}^{21+}$ ions at an electron beam ion trap were presented. The direct wavelength measurements were reported for the first time for Ge${}^{17+}$ $-$Br${}^{20+}$ 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 Kr${}^{21+}$ 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 $3p^3$ ${}^2{D}_{5/2}$ $-$ ${}^2{D}_{3/2}$ transition. The present work resolved the long-standing confusion of the Kr${}^{21+}$ spectral line. Our accurate experimental results could be reference data for further calculations.