There are two fundamental kinds of excitation modes in the atomic nucleus: collective and single-particle
excitations. So far, most of the theoretical effort has focused on the study of the former and the latter has
been mostly treated by using the quasiparticle spectrum of neighboring nuclei  or the equal-filling
approximation . However, these approaches explicitly neglect time-odd fields that can modify in a
substantial way the properties of excited states. In order to take them into account, the Hartree- Fock-
Bogoliubov (HFB) method with full blocking has to be introduced. The implementation has to be flexible
enough as to allow for one-quasiparticle excitations (odd and odd-odd nuclei), two quasiparticle
excitations (built on top of both even and odd systems), four quasiparticle excitations (as to study high K
isomers), etc. Also, a careful handling of the orthogonality of the different states has to be made in order to
obtain an excitation spectrum containing more than one state per quantum number.
In order to study those multiquasiparticle excitations a computer code has been developed to solve in an
efficient way the HFB equation with full blocking in the case of the Gogny force . It preserves axial
symmetry so that K is a good quantum number. Parity is allowed to break but it turns out that most of the
solutions only have a slight breaking of reflection symmetry and therefore the parity quantum number can
also be used to characterize the states. The code includes the possibility to impose orthogonality
constraints to previously computed states. The results obtained show differences with respect to simpler
calculations [1,2] that can amount to a few hundred keV in excitation energy, showing the importance of
the time-odd fields and the self-consistency of the HFB+Blocking method. The quenching of pairing
correlations is also very strong in the HFB+Blocking method.
Using the HFB+Blocking method along with the finite range, density dependent Gogny force, we have
carried out calculations of high-K two and four- quasiparticle isomeric states in even-even and odd-A
nuclei. The quite good agreement with experimental data for excitation energies shows the suitability and
predictive power of the Gogny force in this kind of physics.
One of the most important consequences of blocking is the severe quenching of pairing correlations. This
effect points to an increasing relevance of dynamics pairing in those affected excitations. To gain some
understanding on this effect, we have analyzed the sensitivity of the results to the amount of pairing
correlations by using larger pairing strengths. The results will also be discussed.
 T. Duguet, P. Bonche, P.-H. Heenen, and J. Meyer, Phys. Rev. C 65, 014310 (2001)
 S. Perez-Martin and L. M. Robledo, Phys. Rev. C 78, 014304 (2008)
 L. M. Robledo, R. Bernard, and G. F. Bertsch, Phys. Rev. C 86, 064313 (2012)