  The physical principles that determine the effect of the electron shell of an
atom on the alpha decay rate of the nucleus are presented. The effect is shown
to be negative. Numerical calculations of the effect in helium-like ions are
performed. It accounts for more than 80% of the effect in neutral atoms. The
prospects for experimental detection of the effect in the storage rings of the
GSI Darmstadt, ISF Lanzhou are discussed.
