原子形状因子的分析计算：应用于瑞利散射
Analytical evaluation of atomic form factors: application to Rayleigh scattering
摘要：
原子形状因子广泛用于从晶体学到生物学的目标和样品的表征。利用最近的数学结果，在这里，我们推导出一个解析表达式的原子形状因子内的独立粒子模型构造的非相对论屏蔽类氢波函数。通过将解析得到的形状因子与Hartee-Fock方法得到的形状因子进行比较，检查了该解析表达式的有效性范围。作为一个例子，我们应用我们的原子形状因子的解析表达式来计算中性原子的瑞利散射的微分截面。
英文摘要：
Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wavefunctions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.
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