Least action description of dynamic pairing correlations in the fission of Curium and Californium isotopes based on the Gogny energy density functional

The impact of dynamic pairing correlations and their interplay with Coulomb antipairing effects on the systematic of the spontaneous fission half-lives for the nuclei $^{240-250}$Cm and $^{240-250}$Cf is analyzed, using a hierarchy of approximations based on the parametrization D1M of the Gogny energy density functional (EDF). First, the constrained Hartree-Fock-Bogoliubov (HFB) approximation is used to compute deformed mean-field configurations, zero-point quantum corrections and collective inertias either by using the Slater approximation to Coulomb exchange and neglecting Coulomb antipairing or by fully considering the exchange and pairing channels of the Coulomb interaction. Next, the properties of the {\it{least action}} and {\it{least energy}} fission paths are compared. In the {\it{least action}} case, pairing is identified as the relevant degree of freedom in order to minimize the action entering the Wentzel-Kramers-Brillouin (WKB) approximation to the tunneling probability through the fission barrier. Irrespective of the treatment of Coulomb exchange and antipairing, it is shown that the {\it{least action}} path obtained taking into account the pairing degree of freedom leads to stronger pairing correlations that significantly reduce the spontaneous fission half-lives $t_{SF}$ improving thereby the comparison with the experiment by several orders of magnitude. It is also shown that the Coulomb antipairing effect is, to a large extent, washed out by the {\it{least action}} procedure and therefore the $t_{SF}$ values obtained by the two different treatments of the Coulomb exchange and pairing are of similar quality.