  Beyond mean-field methods are very successful tools for the description of
large-amplitude collective motion for even-even atomic nuclei. The
state-of-the-art framework of these methods consists in a Generator Coordinate
Method based on angular-momentum and particle-number projected triaxially
deformed Hatree-Fock-Bogoliubov (HFB) states. The extension of this scheme to
odd-mass nuclei is a long-standing challenge. We present for the first time
such an extension, where the Generator Coordinate space is built from
self-consistently blocked one-quasiparticle HFB states. One of the key points
for this success is that the same Skyrme interaction is used for the mean-field
and the pairing channels, thus avoiding problems related to the violation of
the Pauli principle. An application to 25Mg illustrates the power of our
method, as agreement with experiment is obtained for the spectrum,
electromagnetic moments, and transition strengths, for both positive and
negative parity states and without the necessity for effective charges or
effective moments. Although the effective interaction still requires
improvement, our study opens the way to systematically describe odd-A nuclei
throughout the nuclear chart.
