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Parity and time invariance violating (${\cal P},{\cal T}$-odd) nuclear forces produce ${\cal P},{\cal T}$-odd nuclear moments, for example, the nuclear Schiff moment. In turn, this moment can induce electric dipole moments (EDMs) in atoms. We estimate the contribution to the Schiff moment from the soft collective octupole vibrations existing in many heavy nuclei. Two possible mechanisms are considered, mixing of the ground state of an odd-$A$ nucleus with the octupole phonon state, and ${\cal P},{\cal T}$-odd admixture to the single-particle wave function of the valence nucleon. We found practically the same contribution to the Schiff moment as that of the static octupole deformation calculated earlier. This confirms a suggestion that the soft octupole vibrations can replace the (controversial) static octupoles in development of the collective Schiff moments. The values of atomic EDM predicted for $^{223,225}$Ra and $^{223}$Rn are enhanced by factors up to $10^{3}$ compared to experimentally studied spherical nuclei $^{199}$Hg and $^{129}$Xe.

Enhancement of nuclear Schiff moments and time-reversal violation in atoms due to soft nuclear octupole vibrations