Description of the multidimensional potential-energy surface in fission of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Cf</mml:mi><mml:mprescripts/><mml:none/><mml:mn>252</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>No</mml:mi><mml:mprescripts/><mml:none/><mml:mn>258</mml:mn></mml:mmultiscripts></mml:math>
A. Zdeb, M. Warda, L. M. Robledo
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.