X-ray scattering by many-particle systems
X-ray scattering by many-particle systems
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DOI：
10.1088/1367-2630/15/1/015014
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发表时间：
2013-01-22
影响因子：
3.3
通讯作者：
Gregori, G.
中科院分区：
文献类型：
--
作者：
Crowley, B. J. B.;Gregori, G.
本文回顾了非相对论和近相对论区域中高频汤姆逊散射的处理，主要目的是了解微分截面频率重分布校正的本质。该校正通常由涉及辐射的散射频率（α）与主频率（β）的欧米伽（α）/欧米伽（β）之比的因子来表示。在文献中给出的一些公式中，该比率显示为平方，而在其他公式中则不是。在康普顿散射中，频率变化通常被理解为由于光子-电子系统中能量和动量守恒而导致粒子的反冲。在这种情况下，Klein-Nishina 公式给出的重新分配因子为 (omega(alpha)/omega(beta))(2)。然而，在多粒子系统散射的情况下，频率和动量变化不再直接相互依赖，而是还取决于介质的属性，这些属性被编码在动态结构因子中。我们证明，量子横截面（光子看到的）中显式的重新分布因子是 omega(alpha)/omega(beta)，它不是平方的。文献中给出的多体横截面公式（其中因子为平方）通常可以归因于横截面的不同（经典）定义，尽管并非所有作者都明确他们使用的是哪个定义。事实证明，结构因子只是给出了多电子与单电子微分截面的比率，正如有时所假设的那样，这一点并不正确。在描述 X 射线散射时，混合横截面定义可能会导致错误。我们通过推导经典和量子散射测量的能量积分角分布（具有一阶相对论校正）以及汤姆逊散射介质中光子扩散的辐射不透明度（通常被认为受量子过程控制）来说明差异的本质。
This paper reviews the treatment of high-frequency Thomson scattering in the non-relativistic and near-relativistic regimes with the primary purpose of understanding the nature of the frequency redistribution correction to the differential cross-section. This correction is generally represented by a factor involving the ratio omega(alpha)/omega(beta) of the scattered (alpha) to primary (beta) frequencies of the radiation. In some formulae given in the literature, the ratio appears squared, in others it does not. In Compton scattering, the frequency change is generally understood to be due to the recoil of the particle as a result of energy and momentum conservation in the photon-electron system. In this case, the Klein-Nishina formula gives the redistribution factor as (omega(alpha)/omega(beta))(2). In the case of scattering by a many-particle system, however, the frequency and momentum changes are no longer directly interdependent but depend also upon the properties of the medium, which are encoded in the dynamic structure factor. We show that the redistribution factor explicit in the quantum cross-section (that seen by a photon) is omega(alpha)/omega(beta), which is not squared. Formulae for the many-body cross-section given in the literature, in which the factor is squared, can often be attributed to a different (classical) definition of the cross-section, though not all authors are explicit about which definition they are using. What is shown not to be true is that the structure factor simply gives the ratio of the many-electron to one-electron differential cross-sections, as is sometimes supposed. Mixing up the cross-section definitions can lead to errors when describing x-ray scattering. We illustrate the nature of the discrepancy by deriving the energy-integrated angular distributions, with first-order relativistic corrections, for classical and quantum scattering measurements, as well as the radiative opacity for photon diffusion in a Thomson-scattering medium, which is generally considered to be governed by quantum processes.