  Octupole deformation and the relevant spectroscopic properties of
neutron-rich odd-mass barium isotopes are investigated in a theoretical
framework based on nuclear density functional theory and the particle-core
coupling scheme. The interacting-boson Hamiltonian that describes the
octupole-deformed even-even core nucleus, as well as the single-particle
energies and occupation probabilities of an unpaired nucleon, are completely
determined by microscopic axially-symmetric $(\beta_{2},\beta_{3})$-deformation
constrained self-consistent mean-field calculations for a specific choice of
the energy density functional and pairing interaction. A boson-fermion
interaction that involves both quadrupole and octupole degrees of freedom is
introduced, and their strength parameters are determined to reproduce selected
spectroscopic data for the odd-mass nuclei. The model reproduces recent
experimental results both for the even-even and odd-mass Ba isotopes. In
particular, for $^{145,147}$Ba our results indicate, in agreement with recent
data, that octupole deformation does not determine the structure of the lowest
states in the vicinity of the ground state, and only becomes relevant at higher
excitation energies.
