  The hyperfine splitting of the ground and low-energy $3/2^+(7.8 \pm 0.5$ eV)
levels in the $^{229}$Th nucleus in muonic atom
($\mu^-_{1S_{1/2}}{}^{229}$Th$)^*$ has been calculated considering the
distribution of the nuclear magnetization in the framework of collective
nuclear model with the wave functions of the Nilsson model for the unpaired
neutron. It is shown that (a) the hyperfine splitting of the $3/2^+$ isomeric
state is anomalously weak, and the reduction of hyperfine structure in
comparison with the model of a point nuclear magnetic dipole is close to 100\%,
(b) partial inversion of levels of the $^{229}$Th ground-state doublet and
spontaneous decay of the ground state with excitation of the isomeric state
take place, (c) the energy of the isomeric transition lies in the range of
120--140 eV, which makes possible the direct observation of the transition,
registration of conversion electrons and measurement of the nuclear matrix
element.
