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Collective bremsstrahlung of vector meson fields in relativistic nuclear collisions is studied within the time-dependent Walecka model. Mutual deceleration of the colliding nuclei is described by introducing the effective stopping time and average rapidity loss of baryons. It is shown that electromagnetic decays of virtual omega-mesons produced by bremsstrahlung mechanism can provide a substantial contribution to the soft dilepton yield at the SPS bombarding energies. In particular, it may be responsible for the dilepton enhancement observed in 160 AGev central Pb+Au collisions. Suggestions for future experiments to estimate the relative contribution of the collective mechanism are given.

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