Numerical search of discontinuities in self-consistent potential energy surfaces

Abstract

Potential energy surfaces calculated with self-consistent mean-field methods are a very powerful tool, since their solutions are, in theory, global minima of the non-constrained subspace. However, this minimization leads to an incertitude concerning the saddle points, that can sometimes be no more saddle points in bigger constrained subspaces (fake saddle points), or can be missing on a trajectory (it missing saddle points). These phenomena are the consequences of discontinuities of the self-consistent potential energy surfaces (SPES). These discontinuities may have important consequences, since they can for example hide the real height of an energy barrier, and avoid any use of a SPES for further dynamical calculations, barrier penetrability estimations, or trajectory predictions. Discontinuities are not related to the quality of the production of a SPES, since even a perfectly converged SPES with an ideally fine mesh can be discontinuous. In this paper we explain what are the discontinuities, their consequences, and their origins. We then propose a numerical method to detect and identify discontinuities on a given SPES, and finally we discuss what are the best ways to transform a discontinuous SPES into a continuous one.

14 pages, 9 figures

References in corpus (6)

• Potential Energy Surfaces of Actinide Nuclei from a Multi-dimensional Constraint Covariant Density Functional Theory: Barrier Heights and Saddle Point Shapes
• Fission barriers in actinides in covariant density functional theory: the role of triaxiality
• Structure properties of ${}^{226}$Th and ${}^{256,258,260}$Fm fission fragments: mean field analysis with the Gogny force
• Augmented Lagrangian Method for Constrained Nuclear Density Functional Theory
• Microscopic description of oblate-prolate shape mixing in proton-rich Se isotopes
• Fission modes of 256Fm and 258Fm in a microscopic approach

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