Numerical accuracy of mean-field calculations in coordinate space

W. Ryssens, P.-H. Heenen, and M. Bender
Phys. Rev. C 92, 064318 – Published 23 December 2015

Abstract

Background: Mean-field methods based on an energy density functional (EDF) are powerful tools used to describe many properties of nuclei in the entirety of the nuclear chart. The accuracy required of energies for nuclear physics and astrophysics applications is of the order of 500 keV and much effort is undertaken to build EDFs that meet this requirement.

Purpose: Mean-field calculations have to be accurate enough to preserve the accuracy of the EDF. We study this numerical accuracy in detail for a specific numerical choice of representation for mean-field equations that can accommodate any kind of symmetry breaking.

Method: The method that we use is a particular implementation of three-dimensional mesh calculations. Its numerical accuracy is governed by three main factors: the size of the box in which the nucleus is confined, the way numerical derivatives are calculated, and the distance between the points on the mesh.

Results: We examine the dependence of the results on these three factors for spherical doubly magic nuclei, neutron-rich 34Ne, the fission barrier of 240Pu, and isotopic chains around Z=50.

Conclusions: Mesh calculations offer the user extensive control over the numerical accuracy of the solution scheme. When appropriate choices for the numerical scheme are made the achievable accuracy is well below the model uncertainties of mean-field methods.

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  • Received 2 September 2015

DOI:https://doi.org/10.1103/PhysRevC.92.064318

©2015 American Physical Society

Authors & Affiliations

W. Ryssens* and P.-H. Heenen

  • PNTPM, CP229, Université Libre de Bruxelles, B-1050 Bruxelles, Belgium

M. Bender

  • Université de Bordeaux, Centre d'Etudes Nucléaires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan, France and CNRS/IN2P3, Centre d'Etudes Nucléaires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan, France

  • *wryssens@ulb.ac.be
  • phheenen@ulb.ac.be

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Vol. 92, Iss. 6 — December 2015

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