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Aims. We carry out the self-consistent dynamic evolution of the orbitalstructure of Milky Way globular clusters. This allows us to estimate possibleand probable close passages and even collisions of the clusters with eachother. Methods. We reproduced the orbits of 147 globular clusters in 10 Gyrlookback time using our own high-order N-body parallel dynamic phi-GPU code.The initial conditions (three coordinates and three velocities for the presenttime) were derived from the Gaia DR3 catalogue. The galaxy is represented byfive external potentials from the IllustrisTNG-100, whose masses and sizes ofthe disk and halo components are similar to the physical values of the MilkyWay at present. Results. We present a statistical analysis of the cumulativeclose passages rate: About ten close passages with relative distances shorterthan 50 pc for every billion years for each of the five external potentials. Wepresent the 22 most reliable collision pairs with a good probability. As anexample: Terzan 4 versus Terzan 2 (49%), Terzan 4 versus NGC 6624 (44%), Terzan4 versus Terzan 5 (40%), Terzan 4 versus NGC 6440 (40%), and Terzan 4 versusLiller 1 (42%). The most active globular cluster in the collision sense isTerzan 4, which has 5.65 collision events on average (averaged over allindividual 1000 initial condition realisations). Most collisions are locatedinside the Galactic disk and form two ring-like structures. The first ring-likestructure has the highest collision number density at 1 kpc, and the secondsturcture has a maximum at 2 kpc. Conclusions. Based on our numericalsimulations, we can conclude that the few dozen Milky Way globular clustersprobably undergo some close encounters and even possible collisions duringtheir lifetimes, which can significantly affect their individual dynamicalevolution and possibly even their stellar content.

Milky Way globular clusters on cosmological timescales. III. Interaction rates