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The Nuclear Energy Density Functional Formalism

  • T. DuguetEmail author
Part of the Lecture Notes in Physics book series (LNP, volume 879)

Abstract

The present document focuses on the theoretical foundations of the nuclear energy density functional (EDF) method. As such, it does not aim at reviewing the status of the field, at covering all possible ramifications of the approach or at presenting recent achievements and applications. The objective is to provide a modern account of the nuclear EDF formalism that is at variance with traditional presentations that rely, at one point or another, on a Hamiltonian-based picture. The latter is not general enough to encompass what the nuclear EDF method represents as of today. Specifically, the traditional Hamiltonian-based picture does not allow one to grasp the difficulties associated with the fact that currently available parametrizations of the energy kernel E[g′,g] at play in the method do not derive from a genuine Hamilton operator, would the latter be effective. The method is formulated from the outset through the most general multi-reference, i.e. beyond mean-field, implementation such that the single-reference, i.e. “mean-field”, derives as a particular case. As such, a key point of the presentation provided here is to demonstrate that the multi-reference EDF method can indeed be formulated in a mathematically meaningful fashion even if E[g′,g] does not derive from a genuine Hamilton operator. In particular, the restoration of symmetries can be entirely formulated without making any reference to a projected state, i.e. within a genuine EDF framework. However, and as is illustrated in the present document, a mathematically meaningful formulation does not guarantee that the formalism is sound from a physical standpoint. The price at which the latter can be enforced as well in the future is eventually alluded to.

Keywords

Symmetric Nuclear Matter Energy Density Functional Generator Coordinate Method Pseudo Potential Skyrme Parametrization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

It is a great pleasure to thank deeply all those I have had the chance to collaborate with on topics related to the matter of the present lecture notes, i.e. B. Avez, M. Bender, K. Bennaceur, P. Bonche, B. A. Brown, P.-H. Heenen, D. Lacroix, T. Lesinski, J. Meyer, V. Rotival, J. Sadoudi, N. Schunck and C. Simenel. I also wish to thank M. Bender for providing me with several of the figures that are used in the present lecture notes.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.CEA-Saclay DSM/Irfu/SPhNGif sur Yvette CedexFrance
  2. 2.NSCL and Department of Physics and AstronomyMichigan State UniversityEast LansingUSA

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