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

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)摘要 本文介绍了两部分Mathematica笔记本集合的第一部分，该集合实现了一种符号化方法，用于将密度矩阵展开（density matrix expansion, DME）应用于手征有效场论（chiral effective field theory, EFT）下N^2 LO阶三核子相互作用的哈特里-福克（Hartree-Fock, HF）能量。该笔记本的最终输出为类Skyrme能量密度泛函，可对非局域HF能量进行准局域近似。本文将讨论HF能量的推导及其简化…… 程序名称：SymbHFNNN 目录编号：AEGC_v1_0 问题本质 从N^2 LO阶手征EFT三核子相互作用计算HF能量涉及极为复杂的自旋-同位旋代数运算。此外，最终还需获得HF能量的准局域近似，这要求将HF能量表示为单体密度矩阵的标量/矢量-同标量/同矢量分量形式，进一步加剧了问题复杂度。本文所述的Mathematica笔记本可解决上述后者问题。 曼德利数据集（Mendeley Data）中的CPC程序库内的该程序版本：AEGC_v1_0; SymbHFNNN; 10.1016/j.cpc.2010.02.020 本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2018）