The theory of controlling and changing the spontaneous nuclear gamma-decay is discussed. The phenomenon of nuclear decay controlling is a result of the interaction of radioactive nuclei with zero-energy electromagnetic modes, which in turn interact with distant controlling and controlled screen. It was shown that the decay parameters greatly depend on the sign and magnitude of the radiation shift (radiation correction) of the resonance level position. In the experiment we have discovered the change (increase) of radiative life-time of excited nucleus Co⁵⁷ (Fe⁵⁷*) (in relation to resonant Mossbauer gamma-channel of decay) by 10-40% and total life-time (including non-controlled non-Mossbauer radiation and non-controlled electron conversion channel of nucleus decay) by 1%.