We develop a theory of spin relaxation in Zeeman-splitted superconductingfilms at low temperatures. A new mechanism of spin relaxation, specific onlyfor Zeeman-splitted superconductors is proposed. It can explain the extremelyhigh spin relaxation lengths, experimentally observed in Zeeman-splittedsuperconductors, and their strong growth with the magnetic field. In theframework of this mechanism the observed spin signal is formed by thespin-independent nonequilibrium quasiparticle distribution weighted by thespin-split DOS. We demonstrate that the relaxation length of such a spin signalis determined by the energy relaxation length at energies of the order of thesuperconducting gap.
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