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

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