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We consider the electron-positron pair production in relativistic heavy ioncollisions, in which the produced electron is captured by one of the nucleiresulting, thus, in the formation of a hydrogen--like ion. These ions emergefrom the collision point and hit the vacuum chamber wall inside superconductingmagnets. Therefore, this process may be important for the problems of beam lifetime and for the quenching the irradiated magnet. A theoretical investigationfor such a bound-free pair production (BFPP) at the colliders from NICA to HELHC is presented. We obtain an approximate universal formula for the totalcross section of the process. We compare it with the results of availablenumerical calculations and estimate that an accuracy of our calculations isbetter than $30$ % at the energies of the NICA collider and becomes of theorder of a few percent for the RHIC and HE LHC colliders. Based on the obtainedresults, the detailed calculations are performed for future experiments at theNICA collider. We find that the expected BFPP cross sections for theAu$^{79+}$-Au$^{79+}$ and Bi$^{83+}$-Bi$^{83+}$ collisions are in the rangefrom $10$ to $70$ barn, while for the p-Au$^{79+}$ and p-Bi$^{83+}$ collisionsthey are in the range of a few mbarn.

Bound-free pair production in relativistic nuclear collisions from the NICA to the HE LHC colliders