能量密度泛函形式中的粒子数恢复：依赖于密度矩阵非整数幂的项的非生存性
Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
摘要：
我们讨论了起源的病理行为，最近已确定在核能密度功能框架内进行的粒子数恢复计算。在[D]中提出了一种正则化方法，该方法从多参考能量密度泛函中去除有问题的项，并且适用于（i）任何基于对称性恢复和/或生成坐标方法的构型混合计算和（ii）仅取决于密度矩阵的整数幂的能量密度泛函。Lacroix，T. Duguet，M. Bender，arXiv：0809.2041]，并在[M.本德，T. Duguet，D. Lacroix，arXiv：0809.2045].本文讨论了核能密度泛函中密度矩阵的非整数幂的生存性。我们的讨论建立在已经在[J. Dubaczewski \emph{et al.}，Phys. Rev. \textbf{76}，054315（2007）]中进行的分析的基础上。首先，我们建议减少依赖于密度矩阵的非整数幂的项的病态性质，通过使用[D. Lacroix，T. Duguet，M. Bender，arXiv：0809.2041]。然后，我们讨论了由剩余分数幂带来的虚假特征。最后，我们得出结论，非整数幂的密度矩阵是不可行的，应该避免在第一位时，构建核能密度泛函，最终用于多参考计算。
英文摘要：
We discuss the origin of pathological behaviors that have been recently identified in particle-number-restoration calculations performed within the nuclear energy density functional framework. A regularization method that removes the problematic terms from the multi-reference energy density functional and which applies (i) to any symmetry restoration- and/or generator-coordinate-method-based configuration mixing calculation and (ii) to energy density functionals depending only on integer powers of the density matrices, was proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] and implemented for particle-number restoration calculations in [M. Bender, T. Duguet, D. Lacroix, arXiv:0809.2045]. In the present paper, we address the viability of non-integer powers of the density matrices in the nuclear energy density functional. Our discussion builds upon the analysis already carried out in [J. Dobaczewski \emph{et al.}, Phys. Rev. C \textbf{76}, 054315 (2007)]. First, we propose to reduce the pathological nature of terms depending on a non-integer power of the density matrices by regularizing the fraction that relates to the integer part of the exponent using the method proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041]. Then, we discuss the spurious features brought about by the remaining fractional power. Finally, we conclude that non-integer powers of the density matrices are not viable and should be avoided in the first place when constructing nuclear energy density functionals that are eventually meant to be used in multi-reference calculations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
