Abstract
Microscopic studies of nuclear fission require the evaluation of the potential-energy surface as a function of the collective coordinates. A reasonable choice of constraints on multipole moments should be made to describe the topography of the surface completely within a reasonable amount of computing time. We present a detailed analysis of fission barriers in the self-consistent Hartree-Fock-Bogoliubov approach with the D1S parametrization of the Gogny nucleon-nucleon interaction. Two heavy isotopes representing different spontaneous fission modes, $^{252}\mathrm{Cf}$ (asymmetric) and $^{258}\mathrm{No}$ (bimodal), have been chosen for the analysis. We have shown the existence of complicated structures on the energy surface that cannot be fully described in two-dimensional calculations. We analyze apparent problems that can be encountered in this type of calculations: multiple solutions for given constraints and transitions between various overlapping potential-energy surfaces. These issues may be partially solved by the analysis of the potential-energy surface spanned by triple constraints, but even in this case one may find multiple solutions and surface discontinuities. Analysis of the potential-energy surface in two dimensions is often very successful but it must be carried out with special attention to possible discontinuities.
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