X射线弹性散射与非弹性散射和相干散射与非相干散射之间有什么区别？

先来看看这四个散射的定义

弹性散射的定义：弹性散射是散射过程中粒子的动能不发生改变，只改变方向的散射。(Goldstein, Classical Mechanics, 1950)

维基百科原文：Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified (by interaction with other particles and/or potentials) meaning the two particles in the collision do not lose energy. (https://en.wikipedia.org/wiki/Elastic_scattering)

非弹性散射定义：非弹性散射是指在散射过程中粒子的动能发生改变的散射。

维基百科原文：In chemistry, nuclear physics, and particle physics, inelastic scattering is a process in which the kinetic energy of a particle or a system of particles changes after a collision. Formally, the kinetic energy of the incident particle is not conserved (in contrast to elastic scattering). (https://en.wikipedia.org/wiki/Inelastic_scattering)

相干散射定义：散射波与入射波具有相同的振动方向、相同的振动频率以及恒定的相位差，即散射波与入射波满足光的干涉条件。(https://blog.sciencenet.cn/blog-3447891-1250526.html)

非相干散射定义：由于散布于空间各个方向的量子散射波与入射波波长不同，位相也不存在确定的关系，因此不能产生干涉效应，因此这种散射被称为非相干散射。(https://blog.sciencenet.cn/blog-3447891-1250526.html)

维基百科原文：Incoherent scattering is a type of scattering phenomenon in physics. The term is most commonly used when referring to the scattering of an electromagnetic wave (usually light or radio frequency) by random fluctuations in a gas of particles (most often electrons). (https://en.wikipedia.org/wiki/Incoherent_scatter)

接下来，对于以上四个概念之间的关系，目前有以下三种解释：

1、部分教材、论文以及百科词条将弹性散射和相干散射概念混用，认为两者意思一致。

E.g.

百度百科原文：相干散射是指入射线光子与原子内受核束缚较紧的电子(如内层电子)发生弹性碰撞作用，仅其运动方向改变而没有能量改变的散射，相干散射又称为弹性散射.

Maged Marghany, in Nonlinear Ocean Dynamics, 2021一书在介绍相干散射时，认为相干散射、瑞利散射、经典散射和弹性散射为同一概念。

2、相干散射和非相干散射、弹性散射和非弹性散射是两组部分重叠的概念，因此，从定义出发我们可以得到，存在非相干弹性散射和相干非弹性散射。（个人认为比较有说服力的一种解释）

E.g.

来自https://physics.stackexchange.com/questions/297574/difference-between-coherent-scattering-and-elastic-scattering的Wolpertinger的解答，说明了弹性散射和非弹性散射关注的是入射粒子的动能是否改变，而相干散射和非相干散射关注的是入射波和散射波之间的相位关系，两组概念之间部分重叠，所以四种组合的散射均存在。

 原文：

In the literature, the two terms are often mixed up and used differently. In my answer, I will use the most distinct and most common interpretation of the two.

In simple terms, elastic scattering is about energy. Specifically, "the kinetic energy of the scattering particle is conserved in the center-of-mass frame" (see wikipedia). Inelastic scattering is then a process where the scattering particle loses energy (see wikipedia).

Coherent vs. incoherent scattering is not about energy, it is about the phase or fluctuations of a the wave or scattering particle. There does not seem to be a wikipedia article on coherent scattering, but there is one for incoherent scattering. Coherent scattering is then the case where the scattered particle or wave has a fixed phase relation relative to the initial wave, such that you can observe interference between the two. This coherence can be destroyed by fluctutations of the scattering medium or by quantum effects such as inversion of level systems.

Importantly, all combinations of the two categories are allowed. That is coherent elastic scattering, incoherent elastic scattering, coherent inelastic scattering and incoherent inelastic scattering are all different physical processes.

In mathematical terms, the processes can be categorized by properties of the difference between the initial and final state of the scattering particle in the scattering process ψ_i→ψ_f. For elastic scattering, ψ_i and ψ_f have the same energy, for inelastic scattering they do not. To investigate incoherent scattering, one usually leaves the framework of wavefunctions and introduces density matrices or statistical ensembles. A common example of coherent and incoherent scattering is the famous Mollow triplet in resonance fluorescence, where both processes occur simultaneously.

来自https://www.researchgate.net/post/What-is-the-difference-between-coherent-incoherent-elastic-and-inelastic-neutron-scattering-diffuse-scattering的Gail N. Iles的四种散射概念举例

Elastic coherent - collective atomic positions - e.g. lattice structure

Elastic incoherent - relative atomic positions - e.g. amorphous / liquid samples

Inelastic coherent - correlated motions - e.g. phonons, magnons

Inelastic incoherent - single atom motion - e.g. diffusion, vibrational density of states

3、相干散射和非相干散射是指入射光源的相干性，弹性散射和非弹性散射是指散射过程的能量变化，两组概念相互独立。

E.g.

关于相干背散射的词条中，相干概念指的是激光束的相干性

维基百科原文：In physics, coherent backscattering is observed when coherent radiation (such as a laser beam) propagates through a medium which has a large number of scattering centers (such as milk or a thick cloud) of size comparable to the wavelength of the radiation. (https://en.wikipedia.org/wiki/Coherent_backscattering)