  The reduced magnetic dipole and electric quadrupole transition probabilities
for the radiative decay of the $^{229}$Th 7.8 eV isomer to the ground state are
predicted within a detailed nuclear-structure model approach. We show that the
presence and decay of this isomer can only be accounted for by the Coriolis
mixing emerging from a remarkably fine interplay between the coherent
quadrupole-octupole motion of the nuclear core and the single-nucleon motion
within a reflection-asymmetric deformed potential. We find that the magnetic
dipole transition probability which determines the radiative lifetime of the
isomer is considerably smaller than presently estimated. The so-far disregarded
electric quadrupole component may have non-negligible contributions to the
internal conversion channel. These findings support new directions in the
experimental search of the $^{229}$Th transition frequency for the development
of a future nuclear frequency standard.
