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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What is the relationship between Mie scattering amplitudes, incident intensity and outgoing intensity?

Wikipedia's Mie scattering Mathematics discusses the scattering amplitudes $S_1(\theta), \ S_2(\theta)$ for each outgoing polarization of an incident EM plane wave on a uniform sphere. It defines the ...
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Why does the red light from Sun bend towards the moon during the total lunar eclipse?

During the total lunar eclipse the earth, moon and the sun are in perfect alignment so that the moon is within the umbral shadow of the earth. However, instead of turning invisible the moon actually ...
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Light in atmosphere versus space

The atmosphere appears bright because of scattering of light whereas space appears dark due no atmosphere to aid scattering. Is it possible to demonstrate it with such darkness in a huge vaccum ...
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Fourier transform of a scatering potential

The Fermi golden rules states $$ \Gamma(\vec{k},\vec{k}') = \frac{2\pi}{\hbar} \left| \left \langle \vec{k}|V|\vec{k}' \right \rangle \right|^2 \delta(E(\vec{k})-E(\vec{k}')) \, .$$ Many places (for ...
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Doppler shift in Acousto-Optic modulators

The interaction between a beam of light and an acoustic wave is commonly modelized as a photon-phonon scattering phenomenon. Applying the conservation of energy we have that $$ \hbar\nu_1=\hbar\nu_0\...
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Centre of mass collision

A proton with momentum 3 GeV in LAB frame of reference is difussed elastically by a stationary proton. The angle of diffusion of one of the protons, in the CM system is 10º, corresponding to a moment ...
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Rate of reaction of collision in relation to the geometric cross-section

I am reading "Particles and nuclei : an introduction to the physical concepts / Bogdan Povh" and on page 44 of the book there is a section about the geometric cross section in a idealised scattering ...
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Why are there no radiative corrections to the electron charge for (an on-shell interaction)?

My question stems from the preliminary discussion of the electron vertex function found in section 6.2 of Peskin and Schroeder's Introduction to Quantum Field Theory. Specifically, they calculate the ...
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Adding helicities

The background: I am looking at Compton scattering in its most general form with $p+\gamma^*\rightarrow p'+\gamma'^*$ in the Breit-frame (which implies that in my case $\vec{p} = -\vec{p}'$). The ...
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Momentum of projectile in the centre of mass frame in a two body system

The COM frame is defined as the coordinate system in which the centre of mass of the system is at rest. In the case of a 2-body system the center of mass coordinate is: $$\vec{R_{CM}} = \frac{M_A \...
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Potential from scattering matrix [duplicate]

Given a scattering matrix, is there a procedure to find the potential from the scattering matrix? I think there should be a way as the scattering matrix holds the information of the boundary ...
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What are soft theorems in context of scalr fields

What are soft theorems ? I tried reading Weinberg’s paper but couldn’t understand it, are there any resources on this ? I am very interested in the case of scalars.
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Electrodynamics of inhomogeneous media

I'm interested in electromagnetic scattering and for that purpose I would like to write out Maxwell's equations for space-dependent permittivity (and permeability). Actually I only need them for ...
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$\psi\psi \longrightarrow \psi\psi$ scattering in Scalar Yukawa model

In David Tong's lecture notes, Equation 3.48 In line 2, how is $|0\rangle \langle 0|$ introduced between $\psi^{\dagger}(x_1)\psi^{\dagger}(x_2)\psi(x_1)\psi(x_2)?$ Why is $\langle p_2',p_1'|\psi^{\...
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Average differential cross section of neutron scattering on diatomic molecules

I am using Born Approximation to calculate this problem and I've already got the solutions to both of the problems. What confused me is the definition of the unpolarized differential cross section: $$\...
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Scattering of light in Quantum Vacuum

The quantum mechanical vacuum (i.e. the vacuum of a typical QFT) viewed as the zero-point state of the system has an energy (of course, here enters the Vacuum Catastrophe and all the mess that follows)...
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Why is intensity decreasing for higher orders of Bragg (x-ray)diffraction?

Bragg diffraction for x-rays by a crystal structure is governed by $$ n\lambda=2dsin\theta ,$$ where $n$ is an integer and the diffraction order, $\lambda$ is the x-ray wavelength, $d$ the lattice ...
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How does scattering of light happen in atmosphere?

I know that the scattering of light decreases as inversely proportional to the 4th power of wavelength. But what happens at the atomic level? Does the photon get absorbed and re-emitted? Does the ...
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Difference between Scattering and Reflection

I am confused: What exactly is the difference between optical scattering and optical reflection? To me, both terms are distinguished by where we place the observation plane. Reflection: Observation ...
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Second Order Correction to the Perturbative Approximation of the Transition Amplitudes in RQM

I am studying Relativistic Quantum Mechanics from my professor's notes. When calculating the second order perturbative correction to the transition coefficient $T_{fi}$* in a scattering process by a ...
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QFT Why do in and out states have a non-trivial overlap?

Im trying to follow chapter 4 about interacting fields in Peskin and Schröder. They define the S matrix by $_{out}<p_1 p_2 | k_a k_b>_{in} = <p_1 p_2 | S | k_a k_b>$, where $S = \lim_{T\...
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Universal curve of inelastic mean free path - why large at low energy?

I have seen the "universal" curve of inelastic mean free path (MFP) of electrons in many places (both experimental data, and just sketches of the curve) e.g. https://en.wikipedia.org/wiki/...
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Laser guns and scattering

I recently read an article that explained how the US Navy would like to use laser guns in the infrared region, with a high power - 500,000 W I guess. However, because of Rayleigh scattering that ...
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Radiative Transfer Equation: What's “multiple scattering”?

In the presence of multiple scattering, the radiative transfer equation cannot be solved analytically. But what's multiple scattering? Particularly if the RTE has the scatter coefficient, say, $\...
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Completeness of an electron-electron-scattering in the Feynman diagram

During an electron-electron-scattering in any case the electrons change their directions and by this undergo accelerations. Shouldn’t the electrons emit photons in this time, loosing a part of its ...
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Inelastic scattering and Mie theory

In most contexts in which I've come across Mie theory so far, authors do not even mention inelastic scattering but just seem to imply that all scattering is elastic. The only exception I've found is ...
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QFT cross section: missing information?

So I'm having a hard time understanding how the (QM) cross section fits into the general picture, of e.g. collider experiments. So we can calculate cross sections (for one reaction) exactly in QFT ...
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Rayleigh Scattering, Atmosphere-Dependant

I've come across the Wikipedia article on Rayleigh Scattering and it quotes that In detail, the intensity $I$ of light scattered by any one of the small spheres of diameter $d$ and refractive ...
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Basics of Compton scatter interactions? Forces behind it?

What is the force that governs compton scattering interaction? Also how is it that we are able to approximate that compton scattering probability is proportional to the mass density of the target ...
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Time-dependent Quantum step potential: Short-time tunneling possible?

Consider the Schrödinger equation $i \partial_t \psi(x,t) = -\frac{\hbar^2}{2m} \Delta \psi(x,t) + V(x) \psi(x,t) + W(t) \psi(x,t)$ where $\psi(x,t)$ is the wave function, $m$ the particle mass and $...
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What is the model for wave reflection?

in this animation from the Fresnel equation wiki we can see a wave bouncing back in the "negative" compared to the "positive" incoming wave. What physics model govern such behavior in transverse waves?...
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Analytical Solution: EM Scattering from Hemispherical Indentation in Plane

I have a problem of trying to calculate the losses that occur when a beam of light reflects from the surface of a partially transparent medium that has an open cavity. The circumference of the cavity ...
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Equivalence between $t$ and $u$ channels

Reading about QFT diagrams, I've seen examples like Bhabha scattering where the channel $u$ wasn't necessary due to the final states are distinguisable for being made of the different particles and ...
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Time-reversal invariance and resonances

I'm having problems understanding the relevance of time-reversal symmetry for scattering amplitudes when we have resonant states. Although my question is essentially conceptual, it was raised by an ...
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How does one prove the channel independent inequality satisfied by the product of the three Mandelstam variables?

How does one prove the following equation (67.5) from the BLP Quantum Electrodynamics book? The q's are the 4 momenta, and h is the sum of all four masses. Two q's written after one another in the ...
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Can we see stars in day time by making use of a blue notch-filter?

Given on a clear sunny day, the only light that is blocking the star light is the scattered blue light of atmosphere. If we make use of a notch filter, which blocks only the blue light, can we get ...
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Rayleigh Scattering and Red Giants

Rayleigh scattering is responsible for the color of the sky. Consider a planet with an atmospheric composition similar to Earth's but orbiting a red giant. Suppose further that the planet is in the ...
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Electron travelling through a step potential from $V_0$ to 0

Most of the time you discuss the step potential case when $E>V_0$, you consider an electron (or a beam of electrons) travelling from a region of space $x<0$ in which $V=0$, to a region $x>0$ ...
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Feshbach resonance and the Gross-Pitaevskii equation

I have a question about Feshbach resonance and the (generalized) Gross-Pitaevskii equation. If we consider a BEC at a finite temperature $T_{BEC}$ and a static mean-field thermal cloud at temperature $...
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Scattering by a Delta Function Well in 1D [closed]

Let us consider a scattering process by a delta function well in 1D: $$ V(x) = -\alpha \, \delta(x), \quad \alpha > 0. $$ I solve the Schrödinger equation for the scattering states and get the ...
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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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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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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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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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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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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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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....