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Symbolic computation of the Hartree–Fock energy from a chiral EFT three-nucleon interaction at N2LO

B. Gebremarian
S.K. Bogner
T. Duguet
Journal / Anthology

Computer Physics Communications
Year: 2010
Volume: 181
Issue: 6
Page range: 1167-1177

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 N2LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the non-local 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.