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Manuscript Title: Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N2LO
Authors: B. Gebremariam, S. K. Bogner, T. Duguet
Program title: SymbHFNNN
Catalogue identifier: AEGC_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 181(2010)1167
Programming language: Mathematica 7.1.
Computer: Any computer running Mathematica 6.0 and later versions.
Operating system: Windows Xp, Linux/Unix.
RAM: 256 Mb
Keywords: three-nucleon interaction, Symbolic Hartree-Fock, Symbolic Density matrix expansion.
PACS: 02.30.GP, 02.60.Jh.
Classification: 5, 17.16, 17.22.

Nature of problem:
The calculation of the HF energy from the chiral EFT three-nucleon interaction at N2LO 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.

Solution method:
The HF energy from the chiral EFT three-nucleon interaction at N2LO is cast into a form suitable for an automatic simplication of the spin-isospin traces. Several Mathematica functions and symbolic manipulation techniques are used to obtain the result in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix.

Running time:
Several hours