An introduction to the theory of nuclear neutron scattering in condensed matter
An introduction to the theory of nuclear neutron scattering in condensed matter
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凝聚态核中子散射理论简介
DOI：
10.3233/jnr-140016
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发表时间：
2014
影响因子：
1.1
通讯作者：
H. Schober
中科院分区：
文献类型：
--
作者：
H. Schober
我们给出了一个介绍凝聚态物质中子散射的理论，重点是非弹性散射。磁散射和极化将被排除在讨论之外。势场中非相对论粒子的散射引出了散射振幅、分波、散射长度和玻恩级数的概念。为了用简单的例子来说明形式主义，我们允许自己绕一小段路到衍射。玻恩近似，然后扩大到包括非弹性散射的化合物与内部自由度。这导致了中子散射的主方程，建立了实验截面和量子力学跃迁振幅之间的联系。主方程重新制定的相干和非相干散射函数，这反过来又表示在密度相关函数。抽象的形式主义说明了明确计算的横截面为一些简单的模型系统。相当多的注意力被给予涉及谐波系统中的振动的散射。导出耦合非弹性散射截面的声子态密度和色散关系的显式表达式。我们将通过讨论多声子的影响来完成非弹性部分，并以一些关于非谐效应识别的评论作为结论。最后一节致力于把散射理论的形式主义的粒子束的统计描述的上下文中。
We give an introduction into the theory of neutron scattering in condensed matter with a strong focus on inelastic scattering. Magnetic scattering and polarisation will be excluded from the discussion. The scattering of non-relativistic particles in a potential leads to the concepts of scattering amplitude, partial waves, scattering length, and the Born series. In order to illustrate the formalism with simple examples we allow ourselves a short detour to diffraction. The Born approximation is then augmented to include inelastic scattering from compounds with internal degrees of freedom. This leads to the master equation of neutron scattering that establishes a link between the experimental cross sections and quantum mechanical transition amplitudes. The master equation is reformulated in terms of coherent and incoherent scattering functions, which in turn are expressed in terms of density correlation functions. The abstract formalism is illustrated by explicitly calculating the cross sections for some simple model systems. Considerable attention is given to the scattering involving vibrations in harmonic systems. Explicit expressions are derived that couple inelastic scattering cross sections to the phonon density of states and dispersion relations. We will finish the inelastic part by discussing the effect of multi-phonons and conclude with some remarks concerning the identification of anharmonic effects. The last section is devoted to putting the formalism of scattering theory into the context of a statistical description of the particle beam.