Improved density matrix expansion for spin-unsaturated nuclei

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PHYSREVC.82.014305· OSTI ID:21389177

Gebremariam, B; Bogner, S K ^[1]; Duguet, T ^[1]

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1. National Superconducting Cyclotron Laboratory, 1 Cyclotron Laboratory, East Lansing, Michigan 48824 (United States)

A current objective of low-energy nuclear theory is to build nonempirical nuclear energy density functionals (EDFs) from underlying internucleon interactions and many-body perturbation theory (MBPT). The density matrix expansion (DME) of Negele and Vautherin is a convenient method to map highly nonlocal Hartree-Fock expressions into the form of a quasi-local Skyrme functional with density-dependent couplings. In this work, we assess the accuracy of the DME at reproducing the nonlocal exchange (Fock) contribution to the energy. In contrast to the scalar part of the density matrix for which the original formulation of Negele and Vautherin is reasonably accurate, we demonstrate the necessity to reformulate the DME for the vector part of the density matrix, which is needed for an accurate description of spin-unsaturated nuclei. Phase-space-averaging techniques are shown to yield a significant improvement for the vector part of the density matrix compared to the original formulation of Negele and Vautherin. The key to the improved accuracy is to take into account the anisotropy that characterizes the local momentum distribution in the surface region of finite Fermi systems. Optimizing separately the DME for the central, tensor, and spin-orbit contributions to the Fock energy, one reaches a few-percent accuracy over a representative set of semi-magic nuclei. With such an accuracy at hand, one can envision using the corresponding Skyrme-like energy functional as a microscopically constrained starting point around which future phenomenological parametrizations can be built and refined.

• OSTI ID: 21389177
• Journal Information: Physical Review. C, Nuclear Physics, Vol. 82, Issue 1; Other Information: DOI: 10.1103/PhysRevC.82.014305; (c) 2010 The American Physical Society; ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANISOTROPY
COUPLING
DENSITY
DENSITY MATRIX
DISTRIBUTION
EXPANSION
HARTREE-FOCK METHOD
INTERACTIONS
MAGIC NUCLEI
MANY-BODY PROBLEM
NUCLEAR ENERGY
NUCLEAR THEORY
ORBITS
PERTURBATION THEORY
PHASE SPACE
SKYRME POTENTIAL
SPIN
SURFACES
ANGULAR MOMENTUM
APPROXIMATIONS
CALCULATION METHODS
ENERGY
MATHEMATICAL SPACE
MATRICES
NUCLEI
NUCLEON-NUCLEON POTENTIAL
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
POTENTIALS
SPACE