Strong relativistic effect on (quasi)resonance electron-capture processes in non-symmetrical heavy ion-atom collisions

(Quasi)resonance electron-capture processes in non-symmetrical $(Z_{\rm P} \simeq 2Z_{\rm T})$ heavy ion-atom collisions are studied employing a semiclassical atomic Dirac-Fock-Sturm orbital coupled-channel approach within an independent-particle model. %A special attention has been paid to study a role of the relativistic effects. Systematic calculations of the electron-capture cross sections of the target $K$-shell electrons to the $L$ subshells of the projectile have been carried out for the collisions of bare thorium $(Z_{\rm P}=90)$ and zinc $(Z_{\rm P}=30)$ nuclei with hydrogenlike ions $(Z_{\rm T}=36$-$47)$ and $(Z_{\rm T}=12$-$15)$, correspondingly. Strong relativistic effects, crucial for the case of Th$^{90+}$-Ru$^{43+}(1s)$ collisions in the low-energy regime, are found. Various one- and two-electron capture processes occurring in course of the collisions of the two-electron system Th$^{90+}$-Ru$^{42+}(1s^2)$ have been investigated in details in the wide range of collision energies $0.5$-$50$~MeV/u. The impact parameter dependencies of the double electron-capture processes are also presented. Our study demonstrates a very significant role of the relativistic effects for the processes, which becomes crucial in the low-energy regime.