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Scattering is phenomenon of deviation from its trajectory due to non-uniformities in medium through which it is passing. Eg. When a ball is deviated by tennis bat due to its motion. Flourescnce is consuming the photon, and emitting back lower energy photon.


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By definition, Thomson scattering is the elastic scattering of light by a free charged particle. Atoms cannot be described as such, but the electrons in an atom may approximate to free electrons if their binding energy is much lower than the photon energy. This might be true for X-ray wavelengths, although if the photon energy gets too high then elastic ...


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You may visualize atom as nucleus surrounded by an electron cloud. Now imagine the incident plane wave is scattered by two parts of the electron cloud (front and back). If rays are going in forward direction (near 0 angle, low momentum transfer vector) then the path difference between two beams is less and you will have good constructive interference i.e. ...


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I consider the scattering process $A+B \to 1 + 2$. The differential cross-section is always given by \begin{equation} \begin{split}\label{eq1} d\sigma &= \frac{1}{(2E_A)(2E_B)|v_A - v_B|} \frac{d^3p_1}{(2\pi)^3} \frac{1}{2E_1} \frac{d^3p_2}{(2\pi)^3} \frac{1}{2E_2} \left| {\cal M} \right|^2(2\pi)^4 \delta^4( p_A + p_B - p_1 - p_2) \end{split} ...


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Crossing symmetry tells you that you should not only exchange $$p_2\leftrightarrow -p_4$$ in the amputated matrix elements, but also replace the wavefunction polarizations $$ u^{\pm}(p_2)\rightarrow v^{\mp}(p_4) $$ (where the spin polarizations have been reversed), and finally multiply the amplitude for a factor $-1$ (Since you are crossing a fermionic ...


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I think this is an interesting question. Unfortunately, many hasty sketches of the history of physics, as they are taught, tend to draw somewhat biased conclusions for the sole purpose of avoiding delving into these types of questions (some people consider it to be a waste of time apparently). As far as I can tell, the classical scattering theory at the ...


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Yes, the Probability current is defined as $$J(x,t)=\frac{i\hbar}{2m}\bigg(\Psi\frac{\partial \Psi^*}{\partial x}-\frac{\partial \Psi}{\partial x}\Psi^*\bigg)$$ If the scattering matrix is defined as $$ \begin{bmatrix} S_{11}&S_{12}\\ S_{21}&S_{22}\\ \end{bmatrix} $$ The transmission coefficient $T$ is given by $(S_{21})^2$, this is only true in ...


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The rule of thumb is to note that $$M(k_1,k_2)=-M(k_2,k_1)$$ so that $M(k,k)=0$, i.e., you just need the Pauli Exclusion principle! The requirement of antisymmetry fixes the relative sign, so that's all you need here. Equivalently, there is a rule that the sign of a certain diagram is $(-1)^n$ where $n$ is the number of crossing fermion lines. This fixes, ...


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I figured it out. The problem was that I was simply adding the two phase shifts, ignoring the periodicity in the tangent and arctangent functions. In order to get the proper result/plot, one can resort to the addition formula for tangents $$\delta=\delta_1+\delta_2=\arctan ...


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Any finite object illuminated by an infinite planar wave scatters a part of its energy. The ratio of the overall scattered energy to the power density of the incoming wave has the dimensions of meter squared, and thus is described as scattering cross-section. A large mirror has scattering cross-section A similar to its geometrical dimensions. However, in ...


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Transmission probability is independent of energy if the density of states of the scattering region is approximately constant near the Fermi energy, ie. if it is metallic. The transmission probabilities in the formula given in your posting actually correspond to the energy dependent transmission function taken at the Fermi energy $T_n=T_n(E_f)$. Also note ...


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The approximation you are referring to is the scattering length. Neutron scattering lengths are tabulated in a few places, such as at NIST; more elaborate cross-section data is tabulated at the National Nuclear Data Center. Note that the cross section depends on the neutron energy. Most tabulated cross sections are for "thermal" neutrons with kinetic ...


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If you find my above answer a little bit confusing I will simplify it: At the fundamental level, it's about what light is and how it reacts with matter. We know that light is just electromagnetic waves - just like water or sound (which is air waves!), except instead of water or air transporting the waves, it's the electromagnetic field; you can try to ...


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See, a good reflector of light is a very good conductor of electricity as light is an electromagnetic wave. That's one essential criterion for light reflection. Reflection of light (and other forms of electromagnetic radiation) occurs when the waves encounter a surface or other boundary that does not absorb the energy of the radiation and bounces the waves ...


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A clean metallic surface appears shiny because it is reflecting light. The interaction is due to the conductivity of the surface of the metal. When surface conditions change, the reflectivity is reduced. For example, a clean aluminum surface is very reflective, and aluminum coatings are used on the back side of mirrors; the glass protects the clean aluminum ...


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Refraction occurs when a large number of dipoles scatter coherently. Each individual dipole scatters light in response to the incident radiation in (almost) all directions, but when you have a large collection of scatterers, each one scattering in many directions, you have to sum the contributions of each one in order to arrive at the total field. Each ...


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Generally speaking, the first and main difference is that refraction happen upon transmission of the light, while scattering happen upon reflection of the light (namely, diffusive reflection, where the angle of reflection does not equal to the angle of incident).


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I've been collecting wave theory explanations of QM phenomena for years. The photo-electric effect is the easiest one. The much-talked about frequency dependence is an obvious consequence of the Schroedinger equation. The Compton effect is different: here, the coupling between the e-m field and the electron states is not controlled by the shared frequency of ...



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