AI 中文总结
本研究基于Mookerjee增广空间方法，提出无序体系X射线吸收谱的全多重散射理论，可处理两类无序，适用于XANES区域，解决了路径展开法的局限并修正了回访格点路径的二阶项。
AI 中文摘要
我们基于Mookerjee的增广空间方法，提出了针对无序体系的X射线吸收谱（XAS）全多重散射理论公式。该方法将置换型（化学）无序与热型（振动）无序置于同等地位，转化为作用于增广希尔伯特空间上非随机算符的精确矩阵元。由此，通过对非随机久期矩阵求逆，可得到构型平均的散射路径算符，无需进行散射路径展开、无需采用单-site近似，也无需对无序分布的形状做任何假设。这正是近边区域定量分析的要求：X射线吸收近边结构（XANES）位于多重散射级数不收敛的区域，因此与路径展开相关的无序处理在此处不可用。该逆运算通过连分数（Lanczos）递推实现，无需构建完整的构型基或对角化增广算符即可获取所需矩阵元。作为高斯特例，可恢复谐理论的算符德拜-沃勒因子，且无需额外机制即可通过非高斯位移分布的矩纳入非谐无序。在级数收敛的区域，该构造还解决了一个原则性问题：对于统计独立的格点变量，将每个t矩阵替换为其构型平均仅对每个格点仅出现一次的散射路径是精确的，而对于回访某一格点的路径，我们得到了精确的二阶修正。
英文摘要
We present a formulation of the full multiple-scattering theory of X-ray absorption spectroscopy (XAS) for disordered systems based on the augmented-space method of Mookerjee. Both substitutional (chemical) and thermal (vibrational) disorder are cast, on the same footing, as exact matrix elements of a non-random operator acting on an enlarged Hilbert space. The configuration-averaged scattering-path operator is thereby obtained by inverting a non-random secular matrix, with no expansion in scattering paths, without recourse to the single-site approximation and without any assumption on the shape of the disorder distribution. This is what the quantitative analysis of the near-edge region requires: XANES lies where the multiple-scattering series does not converge, so that a treatment of disorder tied to a path expansion is unavailable there. The inversion is carried out by a continued-fraction (Lanczos) recursion, which accesses the required matrix element without constructing the full configuration basis or diagonalising the augmented operator. The operator Debye-Waller factor of the harmonic theory is recovered as the Gaussian special case, and anharmonic disorder is included with no additional machinery, through the moments of a non-Gaussian displacement distribution. Where the series does converge, the construction also settles a question of principle: for statistically independent site variables, replacing each t-matrix by its configuration average is exact only for scattering paths in which every site occurs once, and for paths that revisit a site we obtain the exact second-order correction.
Comments35 pages; 1 figure
