能量密度泛函形式中的组态混合：从非对角能核中去除寄生贡献
Configuration Mixing within the Energy Density Functional Formalism: Removing Spurious Contributions from Non-Diagonal Energy Kernels
摘要：
在核能密度泛函（EDF）框架内，沿着生成坐标方法的多参考计算或对称性破坏的恢复正成为原子核结构物理中的标准工具。这些计算依赖于Gogny或Skyrme类型的单参考能量泛函到非对角能量核的扩展。到目前为止，这一延长还没有严格的建设性框架。普遍接受的方式进行正式的类比时，得到的表达式应用广义威克定理的非对角矩阵元素之间的两个产品状态的汉密尔顿算子。有人指出，这一过程是不好的定义时，扩展到EDF计算的广义威克定理是其适用范围之外。特别是，这样的程序是负责的外观虚假的分歧和步骤，在多参考EDF能量，最近观察到的计算恢复粒子数或角动量。在本工作中，我们给出了一个正式的分析，这个问题的起源计算和没有配对，即构造密度矩阵从斯莱特行列式或准粒子真空。我们提出了一个修正的能量内核，删除的分歧和步骤，这是适用于计算的基础上，任何对称性恢复或发电机坐标。该方法是正式说明粒子数恢复和指定的配置混合计算的基础上斯莱特行列式。
英文摘要：
Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics. These calculations rely on the extension of a single-reference energy functional, of the Gogny or the Skyrme types, to non-diagonal energy kernels. There is no rigorous constructive framework for this extension so far. The commonly accepted way proceeds by formal analogy with the expressions obtained when applying the generalized Wick theorem to the non-diagonal matrix element of a Hamilton operator between two product states. It is pointed out that this procedure is ill-defined when extended to EDF calculations as the generalized Wick theorem is taken outside of its range of applicability. In particular, such a procedure is responsible for the appearance of spurious divergences and steps in multi-reference EDF energies, as was recently observed in calculations restoring particle number or angular momentum. In the present work, we give a formal analysis of the origin of this problem for calculations with and without pairing, i.e. constructing the density matrices from either Slater determinants or quasi-particle vacua. We propose a correction to energy kernels that removes the divergences and steps, and which is applicable to calculations based on any symmetry restoration or generator coordinate. The method is formally illustrated for particle number restoration and is specified to configuration mixing calculations based on Slater determinants.
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