  We investigate the influence of spin-orbit coupling $\lambda$ in
strongly-correlated multiorbital systems that we describe by a three-orbital
Hubbard-Kanamori model on a Bethe lattice. We solve the problem at all integer
fillings $N$ with the dynamical mean-field theory using the continuous-time
hybridization expansion Monte Carlo solver. We investigate how the
quasiparticle renormalization $Z$ varies with the strength of spin-orbit
coupling. The behavior can be understood for all fillings except $N=2$ in terms
of the atomic Hamiltonian (the atomic charge gap) and the polarization in the
$j$-basis due to spin-orbit induced changes of orbital degeneracies and the
associated kinetic energy. At $N=2$, $\lambda$ increases $Z$ at small $U$ but
suppresses it at large $U$, thus eliminating the characteristic Hund's metal
tail in $Z(U)$. We also compare the effects of the spin-orbit coupling to the
effects of a tetragonal crystal field. Although this crystal field also lifts
the orbital degeneracy, its effects are different, which can be understood in
terms of the different form of the interaction Hamiltonian expressed in the
respective diagonal single-particle basis.
