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By breaking both the axial and the spatial reflection symmetries, we developmultidimensionally constrained relativistic mean field (MDC-RMF) models. Thenuclear shape is assumed to be invariant under the reversion of $x$ and $y$axes, i.e., the intrinsic symmetry group is $V_{4}$ and all shape degrees offreedom $\beta_{\lambda\mu}$ with even $\mu$, such as $\beta_{20}$,$\beta_{22}$, $\beta_{30}$, $\beta_{32}$, $\beta_{40}$, $\dots$, are includedself-consistently. The Dirac wave functions are expanded in an axially deformedharmonic oscillator basis. The RMF functional can be one of the following fourforms: the meson exchange or point-coupling nucleon interactions combined withthe nonlinear or density-dependent couplings. The pairing effects are takeninto account with the BCS approach. The 1-, 2-, and 3-D potential energysurfaces (PES's) of $^{240}$Pu are illustrated for numerical checks and for thestudy of the effect of the triaxiality on the fission barriers. Potentialenergy curves of even-even actinide nuclei around the first and second fissionbarriers are studied systematically. Besides the first ones, the second fissionbarriers in these nuclei are also lowered considerably by the triaxialdeformation. This lowering effect is independent of the effective interactionsused in the RMF functionals. Further discussions are made about differentpredictions on the effect of the triaxiality between themacroscopic-microscopic and MDC-RMF models, possible discontinuities on PES'sfrom self-consistent approaches, and the restoration of broken symmetries.MDC-RMF models give reasonably good description of fission barriers ofeven-even actinide nuclei. It is important to include both the nonaxial and thereflection asymmetric shapes simultaneously for the study of PES's and fissionbarriers of actinide nuclei and of those in unknown mass regions such as, e.g.,superheavy nuclei.

Multidimensionally-constrained relativistic mean field models and potential energy surfaces of actinide nuclei