A variety of phenomena, which reveal itself in distant collisions of ultrarelativistic nuclei is discussed. One or both nuclei may be disintegrated in a single collision event by the long-range electromagnetic forces due to the impact of the Lorentz-boosted Coulomb fields of collision partners.The process is considered in the framework of the Weizs{a}cker-Williams method and simulated by the RELDIS code, which takes into account all possible channels of nuclear disintegration, including multiple neutron and proton emission and meson production. Mutual electromagnetic dissociation of nuclei in peripheral collisions can best be studied at RHIC and LHC. The contributions of next-to-leading-order processes with multiple photon absorption of equivalent photons by collision partners are considered in detail. As demonstrated, the rates of the correlated forward-backward 2n and 3n emission are very sensitive to the presence of double and triple excitations of Giant Resonances in colliding nuclei. A practical application consists in the possibility of beam luminosity monitoring in colliders via the registration of the correlated 1n and 2n emission in mutual electromagnetic dissociation.
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