  Studies of fission dynamics, based on nuclear energy density functionals,
have shown that the coupling between shape and pairing degrees of freedom has a
pronounced effect on the nonperturbative collective inertia and, therefore, on
dynamic (least-action) spontaneous fission paths and half-lives.
  Collective potentials and nonperturbative cranking collective inertia tensors
are calculated using the multidimensionally-constrained relativistic mean-field
(MDC-RMF) model. Pairing correlations are treated in the BCS approximation
using a separable pairing force of finite range. Pairing fluctuations are
included as a collective variable using a constraint on particle-number
dispersion. Fission paths are determined with the dynamic programming method by
minimizing the action in multidimensional collective spaces.
  The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm are
explored. Fission paths, action integrals and corresponding half-lives computed
in the three-dimensional collective space of shape and pairing coordinates,
using the relativistic functional DD-PC1 and a separable pairing force of
finite range, are compared with results obtained without pairing fluctuations.
Results for $^{264}$Fm are also discussed in relation with those recently
obtained using the HFB model.
  The inclusion of pairing correlations in the space of collective coordinates
favors axially symmetric shapes along the dynamic path of the fissioning
system, amplifies pairing as the path traverses the fission barriers,
significantly reduces the action integral and shortens the corresponding SF
half-life.
