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

## Description

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 N^2 LO. 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 simplific... Title of program: SymbHFNNN Catalogue Id: AEGC_v1_0 Nature of problem The calculation of the HF energy from the chiral EFT three-nucleon interaction at N 2 LO involves tremendous spin-isospin algebra. The problem is compounded by the need to eventually obtain a quasi-local approximation to the HF energy, which requires the HF energy to be expressed in terms of scalar/vector-isoscalar/isovector parts of the one-body density matrix. The Mathematica notebooks discussed in this paper solve the latter issue. Versions of this program held in the CPC repository in Mendeley Data AEGC_v1_0; SymbHFNNN; 10.1016/j.cpc.2010.02.020 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)