On vibrational states in deformed odd-A nuclei

The equations for the description of vibrational states in deformed odd-A nuclei are obtained within the quasiparticle-phonon nuclear model. In these equations the Pauli principle is taken into account in the quasiparticle plus phonon components of the wave functions. It is shown that if in these components the Pauli principle is not violated or is slightly violated, the corresponding vibrational states may exist in deformed odd-A nuclei. If the Pauli principle is strongly violated in the quasiparticle plus phonon state, is centroid energy is shifted towards higher energies, and it can be fragmented over several levels. The analysis of the available experimental data on the low-lying vibrational states in deformed odd-A nuclei has shown that the experimental data do not contradict the results of these calculations. (orig.)