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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Why do we analyse the step potential problem in quantum mechanics with non-normalizable solutions?

While reading Griffiths Introduction to Quantum mechanics and using MIT 8.04 QP-1 lectures by Adam Allans as a supplementary source to understand the topic of scattering of particles for step ...
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Photon-phonon scattering problem

I have to calculate the following: a) The speed of the acoustic phonons b) Which phonons(frequency and wavevector) can be observed for scattering angles between 0° and 180° and how much of the ...
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Fermi’s golden rule integral over energy states, time constraints

In perturbation theory, we can, to first-order, arrive at an expression for transition rates that looks like $$ \Gamma = \frac{2}{\hbar} |M_{if}|^2 \frac{\sin{\frac{E_f-E_i}{\hbar} t}}{E_f-E_i}. $$ ...
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Scattering from a delta function [closed]

Show that for a potential of type 𝑉 (𝑟⃗) = 𝑔𝛿 (𝑟⃗), where 𝑔 is a constant and 𝛿 (𝑟⃗) is the delta function of Dirac in 3D. Using the Born approximation, determine the scattering amplitude and ...
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Electron tunneling: transmission>1? [duplicate]

Assume a simple electron tunneling scheme from medium 1 into medium 2. By applying the boundary conditions (continuity of the wave function and its derivative at the interface), it is straightforward ...
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Møller scattering amplitute computation

I'm trying to compute the squared matrix element of these 2 diagrams in the high energy limit(ignoring the masses). Now I know that $|\mathcal{M}|^2=|\mathcal{M}_1-\mathcal{M}_2|^2$ since the 2 ...
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Quantum mechanics: bounded states and scattering states

So in quantum physics, we can solve solutions of the schroedinger equation and have that the eigenvalues are either positive or negative, which means it is either a scattering state or a bound state. ...
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Is there energy losses due to Screening /Shielding Effect?

Elastic scattering can be modeled by Mott cross-sections which include the screening factor. We assume there is not energy losses in elastic scattering events. I imagine that the free electron ...
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Scattering cross section from sum of delta functions in 3D

we had the following question in our exam: I know basic scattering concepts like partial waves, born approximation etc. and the solution of common potentials like coulomb or hard spheres but have ...
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Why is the probability density oscillating in region $x<0$ before the potential barrier?

My understanding was that the standing wave solution is that of a free particle in the region before it enters the classically forbidden region. Does multiplying the wave function by its complex ...
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How is a horizontal sunset possible? [closed]

Source: @PHSXES/Reddit Normally, sunset moves vertically, from up to down in the sky. But in this photo, it appears to be moving horizontally, from left to right. It might be an instant of a ...
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How can the sky be blue and transparent at the same time, from below and above?

The sky is blue, when looking from below. That's based on scattering, no problem with that: Why is the sky blue? But it is also colorless transparent from above. No problem with that either, we look ...
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Why is elastic scattering of photons (largely) non-isotropic, but inelastic scattering is isotropic?

I'm working on an experiment regarding Raman spectroscopy, and i'd like to fully understand the reasoning behind this fact. I assume it is related to the photons momentum. My apparatus has a '...
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Is my way for calculation of intermediate scattering function right?

I have a C++ code for below formula: $$F_{\text{s}} (\mathbf{k},t) = \frac{1}{N} \langle \sum_{j=1}^{N} exp\left( i \mathbf{k} \cdot \left[ \mathbf{r}_j (t) - \mathbf{r}_j (0) \right] \right) \...
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Reference request: Scattering from action

Consider a separable solution to a Hamilton-Jacobi equation of an $n$-dimensional autonomous system of the form $$W(\alpha_1,...,\alpha_n,x^1,...,x^n) = \sum_j \int_0^{x^j} w^j(\alpha_1,...,\alpha_n,x'...
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Probability current for a one dimensional step potential for a reflected wave [closed]

I've been following the step potential problem from my textbook and I've got the set of equations right which are: $$\psi_1 = A_1\left(e^{ik_{1}x} + \frac{k_{1} - k_{2}}{k_{1} + k_{2}}e^{-ik_{1}x}\...
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Explicit form of S-matrix on the line

Consider the Hamiltonian $H$ on functions on the line with \begin{eqnarray} H=H_0+V,\\ H_0=-\frac{1}{2m}\frac{d^2}{dx^2} \end{eqnarray} where $V$ is a potential vanishing outside of a bounded interval....
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Effect of layout on text visibility [closed]

My college recently switched to whiteboards. Though writing on a whiteboard with a black ink sounds similar to the conventional way of writing with white chalk on a blackboard, it feels very different....
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When does transmittion coefficient be able to calculate directly from the probability amplitude?

It's been so long so I could not recall just in a second. Let the usual setting $Ae^{ikx}+Be^{-ikx}$ for incident and reflected beam and $Ce^{ikx}$ for transmitted beam. The probability of ...
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Quantum scattering from delta potential Barrier and well

Scattering from delta potential potential at $x=0$ it is observed that for $E>0$ both for potential well and barrier the reflection and transmission coefficient becomes same.As, in both the context ...
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WKB for $E > V(x)$

When we use the WKB method, at least when I learned it, all of our examples had $V(x) > E$ at some point, allowing for turning points. Say we have some $V(x) < E$ for all $x$. How would we ...
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bombarding Electrons into the nucleus!

Recently, in a workshop on Electron microscopy, our professor asked us a question over the backscattering of electron. his question goes like this "Why doesn't this electron falls straight into the ...
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“In” and “Out” states in the Heisenberg picture

When studying scattering in quantum mechanics, we define the "in" and "out" states as states that are eigenfunctions of the free Hamiltonian at ${t \rightarrow \mp\infty}$. This makes sense to me ...
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$\alpha$-particles scattering at Al foil

I am currently reading myself into the topic of scattering experiments and (differential cross sections) and stumbled across the following problem which I really dont know how to solve (this is $\...
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The use of the Hartree-Fock Hamiltonian in the Moller operators

Consider the scattering of a particle with momentum $p$ and mass $m$ by any target. If $|\Psi \rangle$ is the scattering state, we can write it as $|\Psi \rangle = \Omega_{\pm} | \psi \rangle$, where ...
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Where can I learn about the reflection/refraction of sound waves and acoustic impedance in a way similar to quantum tunnelling?

I have learnt about the reflection and transmission of a particle at a potential barrier in quantum mechanics. I vaguely remember there is something similar in acoustics - things such as acoustic ...
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Derivation of unitarity condition for partial wave amplitudes

In Gribov's lectures "The Theory of Complex Angular Momentum," he states that the condition of unitary of the scattering matrix $$2 \text{ Im} A = A A^\dagger$$ can be restated, upon expanding out $...
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Factorisation of tree level amplitudes from unitarity

Is there a simple argument to explain why tree level amplitudes must factorize on their pole into products of lower point tree level amplitudes, not by ispection of Feynman diagrams but as a ...
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A relation for the state of a scatteing process

I am studying the article "A Formal Optical Model", of Bell and Squires (the article is here https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.3.96) where they proof that the self-energy of ...
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Why does the scattering cross section equal to the sum over all differential cross section; including the incident angle?

According to Beer Lambert's law, the intensity of light passing through a homogeneous medium diminishes at a rate proportional to the incident intensity; i.e. $$ \frac{dI(s)}{ds} = -I(s)\sigma\, , $$ ...
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Explanation of why poles in the S-matrix corresponding to particle production/bound states?

I've frequently heard the statement that the only singularities of the S-matrix in QFT correspond to things like the existence of bound states and the possibility of multi-particle production. I'm ...
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Is there a noun for a material that absorbs, scatters and luminesces?

I know Luminophore is used for molecules or nanocrystals which absorbs and emit light, and Scatterer is used for materials which scatter light (elastically or inelastically). I suppose it would be ...
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Is pair production a type of elastic scattering?

Pair production is the creation of a subatomic particle and its antiparticle from a boson. Pair production often refers specifically to a photon creating an electron–positron pair near a ...
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Intensity increase in Monte Carlo radiative transfer simulations (in case of Rayleigh scattering)?

I came across something weird (at least for me) while looking at the Müller matrix for Rayleigh-scattering. If I see it correctly, for some scattering angles, it can actually increase the intensity up ...
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What is the difference between scattering and absorption/emission?

As far as I know, scattering occurs when light excites the atoms or molecules to their higher energy state(virtual state for scattering) followed by emitting photons corresponding to energy ...
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Do loop-level three-point scattering amplitudes have branch cuts?

I know that higher point scattering amplitudes at a sufficiently high loop level have branch cuts and discontinuities. I wonder whether the number of scattering particles plays a role in this? Is ...
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Ray Tracing in Concentric Spheres

Consider the following model: a) Assume a spherical earth. b) Assume that the ionosphere is a spherical mirror that is concentric with the center of the earth. For the purpose of this question, we ...
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Surface States and Fermi Level

In work Gelmont, B. L., Shur, M., & Stroscio, M. (1995). Polar optical-phonon scattering in three- and two-dimensional electron gases. Journal of Applied Physics, 77(2), 657–660 when author moving ...
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Are there scattering targets other than nuclei, protons or electrons in experimental particle physics?

I am not too familiar with particle physics, so maybe I missed something. Typical scattering targets seem to be nuclei, protons, electrons, i.e. stable targets, which of course makes some sense. Have ...
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How is a T-violation inherited in a QFT?

CP violation In quantum field theory (QFT), ${\rm CP}$ symmetry or ${\rm CP}$ violation is a property of the Lagrangian. For a ${\rm CP}$ violating QFT, in general, the absolute square of the Feynman ...
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Dynamic Light Scattering based o Rayleigh or Mie theory?

I know the difference between Rayleigh and Mie scattering theory, but I am confused regarding: Dynamic Light Scattering theory. Is this last one constructed using Rayleigh theory or Mie theory? ...
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A relation for a scattering state using second quantization

Consider the scattering of a particle with momentum $\textbf{k}$ and energy $\varepsilon$ by any target. I saw in an article that, if $\Psi_{\textbf{k}}^{(+)}$ is the scattering state with outgoing ...
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Asymptotic quantization and scattering theory

There is one idea presented on some papers by Ashtekar called "asymptotic quantization". This is reviewed in the case of gravity on this paper. Moreover, this seems to be the basis of the recent work ...
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Expansion of a transition amplitude

Consider that $|\Psi \rangle$ is a scattering state and we have the matrix element $\langle \Psi | \hat{V} | \Psi \rangle$, where $\hat{V}$ is a perturbation. Is t possible expand it using the $S$-...
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$S$-matrix and in and out states

So, I have a short one. When observing scattering, we say that the amplitude for transition from one interacting state to some other interacting state same as this amplitude for free hamiltonian ...
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Why x-ray diffraction occur only in forward direction?

When x-ray falls on an atom,the atom scatters it in all 4pi solid angles. In case of a crystal also the atoms sitting in different planes scatter light in all 4pi direction. But when it comes to Bragg ...
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Relation of specific angular momentum $h$ with velocity and impact parameter for massive particle?

I am computing the path of an incoming massive (!!) particle with speed $v$ far from the black hole in the schwarzchild metric. To determine its path, i need to input the specific angular momentum ...
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City songbirds sing in higher pitch?

In this What I've Learnt Youtube video How Did Language Begin starting at the marked point, the author claims that the songbird in the city uses higher pitch to reduce echo bouncing. He later also ...
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Transformation to get rid of distribution multiplets

Are there any well-known distribution transformations that account for doublets, triplets, higher multiplets due to time series independent peaks occasionally being too close to resolve? I feel like ...
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Off-shell angular momentum conservation

In QFT, when the scattering process occur, the mass does not conserved in off-shell. What I'm curious about is whether the angular momentum is conserved or not in off-shell. Thank you for answering ...