High-$K$ isomers in a self-consistent mean-field approach with the Gogny force

High-$K$ isomeric states in even-even and odd-mass nuclei are described within a mean-field framework with full blocking and using the finite range Gogny force. Theoretical calculations of low energy spectra of several nuclei across the nuclear chart are compared with equal filling approximation results and experimental data. Despite the global character of the employed interactions, a good agreement between the different many-body methods and experimental data is found.