Least action description of spontaneous fission in fermium and nobelium nuclei based on the Gogny energy density functional

The systematic of the spontaneous fission half-lives for the nuclei $^{242-262}$Fm and $^{250-260}$No is analyzed, within a least action scheme, with the parametrization D1M of the Gogny energy density functional. The properties of the dynamic (least action) fission paths are analyzed and compared to those of the static (minimal energy) ones. The constrained Hartree-Fock-Bogoliubov approximation is used to compute deformed mean-field configurations, zero-point quantum corrections and collective inertias. It is shown that a cumbersome full variational search of the least action fission path, within the space of HFB states, might not be required if the relevant degrees of freedom are taken into account in the minimization of the Wentzel-Kramers-Brillouin action. The action is minimized in terms of pairing fluctuations that explore the pairing content of the HFB states along the fission paths of the considered nuclei. It is found that, for a given shape, the minimum of the action in fermium and nobelium nuclei corresponds to a value of the pairing fluctuations larger than the one associated with the minimal energy solution for the same shape. The reduction of the action, via larger pairing correlations, has a significant impact on the predicted spontaneous fission half-lives improving their comparison with the experiment by several orders of magnitude.