Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at NLO
arXiv:0912.3086 · doi:10.1016/j.cpc.2010.02.020
Abstract
We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at NLO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the nonlocal HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions.
26 pages and a set of Mathematica notebooks and Python script
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Cited by in corpus (5)
- Properties of the nuclear medium
- Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
- Applying the Density Matrix Expansion with Coordinate-Space Chiral Interactions
- Optimized nuclear energy density functionals including long-range pion contributions
- Symbolic integration of a product of two spherical bessel functions with an additional exponential and polynomial factor