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Energy levels, wavelengths, magnetic-dipole and electric-quadrupoletransition rates between the low-lying states are evaluated for W$^{51+}$ toW$^{54+}$ ions with $3d^n$ (n = 2 to 5) electronic configurations using anapproach combining configuration interaction with linearized coupled-clustersingle-double method. The QED corrections are directly incorporated into thecalculations and their effect is studied in detail. Uncertainties of thecalculations are discussed. This first study of such highly charged ions withthe present method opens the way for future applications allowing an accurateprediction of properties for a very wide range of highly charged ions aimed atproviding precision benchmarks for various applications.

physical review. a/physical review, a

Relativistic all-order many-body calculation of energies, wavelengths,  and $M1$ and $E2$ transition rates for the $3d^n$ configurations in tungsten  ions