Questions tagged [scattering]

Scattering is a general term for several physical processes in which radiation of some sort changes direction due to an interaction with a particle. Scattering can be classified by the type of radiation (ie, electromagnetic, x-ray, neutron), or by the relative sizes of the wave and the particle (ie, Rayleigh, Mie, geometric).

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52 views

Difference, in terms of completeness, between the Dirac well and barrier

I was in my undergraduate QM lecture and we just finished with the Dirac barrier. My question is as follows: We know that the Dirac well’s complete set of solutions requires one bound state and an ...
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114 views

Angle between velocities: Elastic collision question in 3D

I have been given a scenario of a proton (particle 1) travelling with u1 = 3î+ 4j–6k and a Helium-3 nucleus (particle 2) travelling with u2= 3î+ 4j–2k. The two particles collide and the proton (...
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79 views

How is red colour from from rainbow hotter than blue (W. Hershel) if it has lower frequency than the latter?

We know that blue light has a smaller wavelength and higher frequency than red light, which is a consequence of higher energy in the former, then how is it true that, when scattering light from the ...
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83 views

How does the reflection coefficient change with scattering and absorption?

My professor of Biomedical Optics course asked us to think upon the evolution of the reflection coefficient with the absorption coefficient $\mu_a$, the reduced scattering coefficient $\mu_s'$ and the ...
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81 views

Why don't images bend when looking through window glass like they do when looking through water?

From this section on wikipedia, the phenomenon of an image appearing warped or slightly displaced when looking through water is due to its index of refraction (1.33) deviating from that of air (~1). ...
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Vertex with spinorial structure and scattering amplitude

Consider the Lagrangian $$\mathcal{L}=\bar\psi_1\left(i\partial\!\!\!/-m_1\right)\psi_1 + \bar\psi_2\left(i\partial\!\!\!/-m_2\right)\psi_2 - g\bar\psi_1\gamma_\mu\psi_1\bar\psi_2\gamma^\mu\psi_2.$$ ...
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How can I calculate scattering cross section of Yukawa potential classically?

https://en.wikipedia.org/wiki/Yukawa_interaction#Classical_potential Here is classical form of Yukawa potential. I want to calculate classical scattering cross section of this potential ...
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100 views

Why are distant mountains grey?

I have read this question: Where in the atmosphere is the blue light scattered? where John Rennie says: For the same reason, distant mountains keep their color. Also, the distant mountains don't ...
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183 views

Why is the laboratory frame energy always greater than the center of mass frame energy for collisions? [duplicate]

I looked through lots of sources to answer the question, 'Why is lab frame energy (total energy) always greater than the center of mass frame energy?' Many of them provided lots of mathematical ...
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Why is the laboratory frame energy always greater than the center of mass frame energy?

I have been looking for an answer to 'Why is the laboratory frame energy always greater than the center of mass frame energy during collisions?'. A lot of resources provided mathematical explanations....
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112 views

Derivation of quantum scattering of 1D square well

The above is the question. In my book, I'm given this formula for calculating the transmission probability (when E>V_nought): Here, k1 = sqrt(2m(E-V_0))/h_bar However, the problem is that this ...
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71 views

Probability Flux reduced to imaginary part?

I'm looking at Sakurai, page 400. The probabilityflux (j) can be reduced to the imaginary part of the first part of j. Can somebody explain this? j(x,t) $=-\frac{i\hbar}{2m}[\psi^*\nabla\psi-(\nabla\...
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Scattering amplitude ($s$-, $t$-, $u$-channels)

Given the Lagrangian $$\mathscr{L}=\bar{\psi}\left(i\partial\!\!\!/-m\right)\psi+\frac{1}{2}\left(\partial\phi\right)^2-\frac{1}{2}M^2\phi^2-g\bar\psi\psi\phi^2-g'\bar\psi\gamma_\mu\psi\partial^\mu\...
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Which structure function is G(x)?

I found a question about structure functions where they ask what is the $F_2(x)$, $xF_3(x)$ and $G(x)$ shape as a function of $x$ (for a given $q^2=10$ GeV$^2$) and also as a function of $x$. I found ...
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How to interpret and calculate scattering in a dark-field microscopy?

Dark-field microscopy setup from wikipedia, which says the images in dark-field microscopy are scattering lights from the sample. My questions: When the sample is illuminated, is it correct to ...
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Are the diagonal entries of the S-matrix in 1D equal?

Looking at the S-matrix of some potential barrier in one dimension one can show that is has the form $$ S = \begin{bmatrix} u & v \\ v & w\end{bmatrix} $$ with $u, v, w \in \mathbb{C}$ ...
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Probability that a photon has suffered its last scattering

An important consideration in the post-recombination epoch is the issue of the optical depth $\tau$ of the Universe due to Compton scattering. This is a dimensionless quantity such that $exp(−\tau)$ ...
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Clarifications on the assumptions made for QFT interactions

I am reading about scattering and S-matrix in the context of quantum field theory and although I understand the math and the physical interpretation of the final results, I am confused about some ...
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317 views

Is diffuse reflection same as Rayleigh scattering?

Is there a fundamental difference in their definitions?
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115 views

Is photon's direction entangled?

Consider a free electron, with photon, that runs to electron under some angle(as everybody says). Compton scattering is happening, and electron instantly reemits photon in different angle. First, ...
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Why isn't Rayleigh scattering a concern in analog communication?

The Rayleigh scattering effect applies to 'light' signals, and the scattering of a signal when passing through a material medium, the amount of light scattered is proportional to 1/$\lambda^4$. I am ...
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168 views

The model of photon scattering, is actually about a complete absorbtion?

I was wondering about the things like Compton scattering. As I understand, it is an inelastic scattering of photon on free electron. Inelastic means, that photon changes it's angle and frequency. As ...
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Can light cool down materials?

I was studying Raman scattering and I computed the probability of anti-Stokes scattering (with density of states n, at the numerator) over Stokes (n+1 at denominator). The densities are based on the ...
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Deep inelastic scattering

Quarks can not observed directly in isolation so that they only can exist in the form of colorless hadron. So we may suggest some questions like "Is quark actually exist?", "Is it just mathematical ...
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Literature on Reflection/Refraction of Waves

I completed the first year of my bachelor in Physics and astronomy in July. One of the courses was 'Waves and Optics' which we used the second half of Alonso & Finn's 'Fields and Waves' for. I ...
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What is the Relative Radiation Absorbtion per unit Mass of the various states of matter?

I am trying to find information on the relative merits of using a gas, liquid, solid or even a plasma as a radiation shield. Examples Ice, water and water vapour. Iron, molten Iron, Iron ...
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What is the procedure to get the scattering cross-section expression?

In Peskin and Schroeder's book (P&S), on the botton of page 106, the authors say that the total cross section transforms as its only non-invariant factor, namely: $$ {1 \over E_{A} E_{B} |v_A - ...
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What's the “effective potential” for photons in $X$-ray diffraction?

The slickest way to introduce $X$-ray diffraction is to invoke scattering theory in quantum mechanics. One treats the incoming photon as just another particle in a scattering problem; by Fermi's ...
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How are Maxwell equations satisfied when inelastic scattering occurs?

Consider two media, A and B (example air/dieletric). One finds conditions that the $\vec E$ and $\vec B$ fields must satisfy at the interface, namely $\hat n_\text{A-B}\times(\vec E_A-\vec E_B) = \vec ...
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Rigorous-ish mathematical meaning of having two total differentials in the denominator

When I'm doing, say, $\pi^0 \rightarrow \gamma \gamma$ decay, and I want to find the angular distribution for the number of photons with energy $E$, $N(E, \Omega)$. To get the probability I then need ...
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93 views

Orthogonality of Scattering states

The scattering states solution ($E>V_0$) to the time independent Schrodinger equation for a finite square barrier ($V_0$ ) in an otherwise free region has the form: $$\psi(x)=\begin{cases}e^{i k x}...
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How do I include scattering in the Optical Transfer Matrix Method?

I am using the Transfer Matrix Method (TMM) to model a system I have. Due to the size of my system effects such as Mie and Rayleigh scattering should be important. How do I include Mie and Rayleigh ...
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Significance of Compton scattering being second order?

In the Compton scattering equation for changes in wavelength, for small angles the equation is second order in the angle. Is there any significance to this? To me it seems to say that,if a photon ...
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Explicitly verifying a scattering theory identity

I have recently studied scattering theory on a formal level and I think I understand the subject quite well by now. However what I often struggle with is to translate the abstract identities into ...
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Only sea water appears blue in color, why this is not happening in river water?

Is the salt in the water the reason for scattering sunlight into blue?
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Delta function from poles of Green's function

In quantum mechanical scattering theory, we often use Green's functions which contain poles. For example, in Schroedinger quantum mechanics the free Green's function is given by $$ G_0(\vec{p}) = \...
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Some Rayleigh Scattering questions

Last week I've heard about Rayleigh scattering for the first time, when the classic 'why is the sky blue?' question has crossed my mind and I must admit that it is fascinating! However, I do have a ...
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Fourier transform involving Bessel functions

I need help finding the Fourier transform of the function $$ \rho(\vec{r}) = \alpha \delta_{\vec{r},0} \left(\lambda\lambda' J_1 (\beta |\vec{r}|)Y_1(\beta |\vec{r}|) - \pi^2 J_0 (\beta |\vec{r}|)Y_0(...
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290 views

Optical theorem applied to forward scattering of a single particle

I'm slightly confused. Write the S-matrix as $$ S = 1 + i T $$ Unitarity implies $$ T - T^\dagger = i T^\dagger T $$ In scattering from $|i\rangle$ to $|f\rangle$, $$ T_{f,i} - T^\dagger_{f,i} = i \...
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If you knew the full interacting 2-point correlation function, do you know everything?

I'll specify to the case of a real scalar field to be concrete. If you have some interacting theory with Lagrangian $$ \mathscr{L}[\phi] = -\tfrac{1}{2} (\partial_{\mu} \phi)(\partial^{\mu} \phi) - \...
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Dyson Equation and scattering amplitude

For scattering theory in quantum mechanics, one can use the Dyson Equation which states that the Green's function which is a solution to the equation $$ (E - H_0 - V)G = 1$$ is given by $$ G = ...
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Notation: Dividing by a partial differential

Setup Hi, I am working on a DIS scattering problem in the Light Cone Gauge, and this has me needing to calculate the currents. In doing this, I have come across the following equation $$ t^a \...
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What are the types of infrared scattering?

There are various types of scattering of electromagnetic wave. what type of scattering involves infrared electromagnetic wave?
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Optical scattering Vs size of wavelength

I am having trouble understanding the my slide was given in my lectures in intro to optics. The reason when why I am having trouble is because when I went to research more about each scattering, I ...
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Bragg scattering off an array of wiggly lines

I'm currently working through some problems in Chaiken and Lubensky and I found that my understanding of scattering theory is weaker than I thought. So I could use a sanity check on this problem ...
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312 views

Fermion-Fermion scattering in Yukawa theory

The interaction term in the Lagrangian for Yukawa theory is given by $$ \mathcal{L}_\text{int} = -g\phi\bar{\Psi}\Psi, $$ where $g$ is the coupling constant, $\phi$ some scalar field and $\Psi$ a ...
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Is the converse of Weinberg's statement on the cluster decomposition principle true?

In Weinberg's "The Quantum Theory of Fields, Vol. 1", Section 4.4, page 182, the author says: We now ask, what sort of Hamiltonian will yield an $S$-matrix that satisfies the cluster decomposition ...
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Relativistic scattering off Dirac delta potential

Consider the case of a relativistic electron on a graphene lattice described by the Hamiltonian $$ \mathcal{H} = v\begin{pmatrix} 0 & p_x+ip_y \\ p_x-ip_y & 0 \end{pmatrix}, $$ where $v$ is ...
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Can Rayleigh scattering explain the orange color of the Titan sky?

It is my understanding that Rayleigh scattering depends on both the length of the particle as well as the wavelength. Due to the similar lengths of molecular nitrogen and oxygen it is blue light that ...
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Lorentz invariant interaction: why restrict attention to interactions built by integrating a Hamiltonian density?

In Weinberg's QFT book, Chapter 3, he shows that if the interaction term $V(t)$ is of the form $$V(t)=\int \mathcal{H}(t,\mathbf{x}) \ {\rm d^3}\mathbf{x},$$ where the operators $\mathcal{H}(x)$ are ...