  [Background] Predictions of spectroscopic properties of low-lying states are
critical for nuclear structure studies. Theoretical methods can be particularly
involved for odd-mass nuclei because of the interplay between the unpaired
nucleon and collective degrees of freedom. Only a few models have been
developed for systems in which octupole collective degrees of freedom play a
role. [Purpose] We aim to predict spectroscopic properties of odd-mass nuclei
characterized by octupole shape deformation, employing a model that describes
single-particle and collective degrees of freedom within the same microscopic
framework. [Method] A microscopic core-quasiparticle coupling (CQC) model based
on the covariant density functional theory is developed, which includes
collective excitations of even-mass core nuclei and single-particle states of
the odd nucleon, calculated using a quadrupole-octupole collective Hamiltonian
combined with a constrained reflection-asymmetric relativistic
Hartree-Bogoliubov model. [Results] Model predictions for low-energy excitation
spectra and transition rates of odd-mass radium isotopes $^{223, 225, 227}$Ra
are shown to be in good agreement with available data. [Conclusions] A
microscopic CQC model based on covariant density functional theory has been
developed for odd-mass nuclei characterized by both quadrupole and octupole
shape deformations. Theoretical results reproduce data in odd-mass Ra isotopes
and provide useful predictions for future studies of octupole correlations in
nuclei and related phenomena.
