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 are Raman lidars and Rayleigh-Mie lidars operated at those specific wavelengths for aerosol study?

A study of several Atmospheric lidar stations around India shows that in order to study properties of aerosols, all Rayliegh-Mie lidars are operated at 532 nm, and Raman lidars are operated at 355, ...
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Feynman diagrams for gravity

Feynman rules is the basic tool to compute amplitudes in perturbation theory for a QFT. Here, I am trying to understand perturbation theory in GR around the flat space metric, in terms of Feynman ...
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Diagonal T matrix elements in Multi-scattering theory: Green's Function Approach

In Phys. Rev. B 41,1990 pp. 8139, Rehr and Albers utilize a separable Green's function to arrive at a simple expression for energy-dependent scattering amplitudes. I am not very knowledgeable in the ...
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Optical theorem for low energy soft sphere scattering

Problem 10.15 in the third edition of Griffith's Quantum Mechanics textbook asks to compute the scattering amplitude $f(\theta)$ for the low-energy scattering off the soft-sphere potential $V(\vec r) ...
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(Coleman's lecture note) scattering in QFT

I am currently reading Coleman's lecture note on QFT.(https://arxiv.org/abs/1110.5013) I have several questions regarding the scattering theory. Let $\phi$ be a real scalar field, and consider the ...
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Off-shell vs half off-shell vs fully off-shell $T$-matrix

I know what are on-shell particles, but I want to know what are off-shell, and half off-shell, and fully off-shell states? and how we decide to consider one of these states in evaluating $T$-Matrix?
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Polarization by scattering - Gas dependence

It is known that the sunlight that traverses the atmosphere is scattered. The scattered light is polarized, particularly if we look perpendicularly to the light's direction. All the explanations I ...
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Is resonance an energy eigenstate?

In the particle physics book of Martin & Shaw, they used QM to derive the decay distribution, namely, breit wigner formula. What confused me was that, here they assumed the resonance state $\psi_0 ...
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Why sky is blue? [closed]

The major factor of different scattering is the ratio of wavelength to the size of particles which are working as microscopic scattering mirrors. In a sparse particle medium like air, the longer the ...
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Mott Scattering

I had this old homework that I never completely understood. A scatterng experiment is performed with electrons ($E_0=450$MeV) colliding at an atomic nucleus.Following form factor is measured $\left |F(...
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Rutherford Backscattering spectrometry [duplicate]

I recently read about Rutherford Backscattering spectrometry and stumbled upon following equation $$\frac{d\sigma}{d\Omega}=\left(\frac{Z_1Z_2e^2}{8\pi\epsilon_0mv_0^2}\right)^2\csc^4(\frac{\Theta}{2})...
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Particle deflection in a magnetic dipole field

Consider a small magnetic dipole of magnetic moment $\vec{\boldsymbol{\mu}} = (\mu_x, \; \mu_y, \; \mu_z)$ sitting at the origin. The magnetic field all around is \begin{equation}\tag{1} \mathbf{B} = ...
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How to write down the collision integral for any interaction in the Boltzmann equation?

I'm studying the Boltzmann equation \begin{equation} \Big[\frac{\partial}{\partial t}+\vec{v}\cdot\nabla_{r}+\frac{1}{m}\vec{f}\cdot\nabla_{v}\Big]f(v,r,t)=\frac{df}{dt}\Bigg|_{coll} \end{equation} ...
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Tadpole diagrams in 1-loop massive scalar amplitudes?

Consider a massive scalar diagram such as or The loop momentum enters and exits the tadpole vertex, so that in the first diagram the momentum in the propagator connecting the two vertices is zero ...
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EM-wave interaction with particles

I'm interested in EM waves acting on particles, but have a poor understanding since I haven't yet read a proper EM book and currently am doing more mathematical stuff. I've looked through a couple of ...
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Necessary and suficient conditions for Scattering to be Elastic

Pretty straightforward: what basic assumptions must we make in constructing a Scattering Theory, in Quantum Mechanics, in order for it to conserve energy of the incident particle (i.e. to be elastic)? ...
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Contour for integration in 1D scattering problem

A plane wave scattered by a 1D potential can be described by, $$\psi(x) = \begin{cases} e^{ikx} + R e^{-ikx}, & x<0\\ T e^{ikx}, & x>0 \end{cases}$$ where $R$ is the reflection ...
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Direction of neutron scattering

When neutrons interact with matter scattering, what direction to they scatter? Is it random, or some probability distribution of directions? I'm trying to understand why neutron reflectors reflect ...
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How can light travelling forward send an electron forward?

Light travels along the x-axis and strikes a stationary free electron. Its E field oscillates along the y-axis. The electron moves off at an angle with respect to the x-axis less than 90 degrees. ...
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Eigenstates of the scattering matrix?

Consider a single-particle non-relativistic problem. Consider a 3D spherically symmetric potential. What are the eigenstates of the $S$-matrix? Are they spherically symmetric? And what are the ...
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Scattering amplitudes vs correlators

What are the practical differences between correlators and scattering amplitudes in quantum field theory? On a very practical level: scattering amplitudes describe the evolution of an IN state into ...
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Is the phase shift defined mod $\pi$ in scattering theory?

I've recently starting studying scattering theory (combination of QM by Shankar and Molecular Collision Theory by Child) and this doesn't seem to be stated anywhere but it seems like a reasonable ...
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Rayleigh scattering at magic angle

It is known that the intensity of the scattered light is proportional to $\frac{3}{4}(1+(\cos(\theta))^2 )$ in the case of unpolarized light and that the $s$ component is proportional to $1$ while the ...
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What is the order of the number of significantly scattered particles in Møller scattering?

in an electron-electron collision with a low speed and in the nonrelativistic case, approximately what fraction of electrons get significantly deflected (say more than 10 degrees)? Generally, with ...
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Matrix representation in angular momentum basis

I'm trying to find a way to verify that the following expansion is valid for any potential, including noncentral ones, $$ \langle \textbf{k}' |V|\textbf{k}\rangle = \frac2\pi\sum_{lm} V_l (k', k) Y_{...
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How is the probability density for the deflection angle calculated from the differential cross-section?

In a scattering process, the probability density for the deflection angle of the incident particle is proportional to the differential cross-section of that scattering process. Given the differential ...
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Why does a prism refract light into a rainbow? [duplicate]

Why does a prism refract light such that the different frequencies of light “spread out”? The same goes for rainbows, why do the raindrops “spread out” the different frequencies of light?
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(What causes) the *other* Compton edge?

The question If one exposes a scintillator to a gamma source, one will observe two features for each characteristic energy in the source: a photopeak, due to complete absorption of photons, and a ...
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What happens to the scattering cross section of two fermions with different spins at low temperature?

The scattering cross section for two identical fermions at low temperature is given by: $\sim 8\pi a_1^2(ka_1)^4$. I was wondering what happens if the two fermions have different spins - does it ...
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A question on 't Hooft's paper “Computation of the quantum effects due to a four-dimensional pseudo-particle”

In the avove paper 't Hooft considers the following (rotation invarinat) operators on the Euclidean space $\mathbb{R}^4$: \begin{eqnarray} \mathcal{M}_0=-\left(\frac{\partial}{\partial r}\right)^2-\...
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Spinless $e^{-}\gamma\rightarrow e^{-}$ Cross section

I was trying to figure out the cross section $\frac{d\sigma}{d\Omega}$ for spinless $e^{-}\gamma\rightarrow e^{-}$ scattering. First I wrote the terms associated with each component. Vertex: $$ie(...
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Could ultrasound pings and triangulation really help de-scatter diffuse red light for imaging?

Does the science explanation in the latest OpenWater TED talk make sense in principle? The claim involves taking advantage of the doppler effect. Could someone give a more detailed explanation as to ...
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Can Compton scattering increase a photon's energy?

I've read (in Hagai Netzer's book The Physics and Evolution of Active Galactic Nuclei) that "Comptonization in the [black hole's accretion] disk atmosphere can increase the energy of some photons..." [...
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Brillouin scattering in multimode fibers

Fiber ring resonators made up of single mode fibers often incorporate an optical isolator to suppress the build-up of Brillouin scattering. However, ring resonators made of multimode fibers generally ...
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1D string reflection and transmission phase

Ok, I must be missing something very obvious here. After applying the boundary conditions, we can write: $$ A_R e^{i \delta_R} = (\frac{v_2 - v_1}{v_1 + v_2}) A_I e^{i \delta_I} $$ and $$ A_T e^{...
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Does the electron act as point charge in scattering theory?

We know that an electron behaves like a point charge, and the probability density of its position is given by the Born rule. Now suppose that we shoot an electron toward an atom, so the electron gets ...
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Necessity to consider the square of Four Momentum

Why do we often need to consider the square of four momentum transfer $Q$ in scattering experiment or particle physics/cosmology instead of just the $Q$ itself?
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How to write the Rutherford differential cross section in terms of the momentum transfer?

The Rutherford differential cross section is: $$\frac{d\sigma}{d\Omega} = \frac{Z^2 \alpha^2}{4E^2 \sin^4 (\theta/2)}.$$ I need to write this in terms of the momentum transfer $\frac{d\sigma}{d(Q^...
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Integral convergence in scattering problem

Consider the scattering of a particle by a central time-independent potential $V$, that is limited to a finite region in the space. the hamiltonian is $H = H_{0} + V$. Using the Moller operators, we ...
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Maximum scattering angle for relativistic elastic collision

In Landau Classical theory of fields, in the section of elastic collision(chapter 2, section 13), he mentions that for $m_1>m_2$, the scattering angle $\theta_i$ cannot exceed a maximum value, and ...
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A Question about In/Out States in Quantum Field Theory

When I was reading the lecture notes Advanced Quantum Field Theory by Jorge Crispim Romao, I accidentally found the following thing that I don't understand. On page 56, section 2.2, the author ...
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Polarized structure functions and Bjorken sum rule

I'm trying to understand what the Bjorken sum rule and the polarized structure functions entering it are. I will use equation (2.3) here as a reference for asking the question. In Peskin, I've only ...
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Calculating the charge density from a form factor

For an atomic form factor $F(\textbf q)$, the corresponding charge density distribution is given by $$ \rho(\textbf r) = \frac{1}{(2\pi)^3}\int\text{d}^3 \textbf q \,F(\textbf q)\,\text{e}^{-\text{i}\...
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How do we see if light scatters in all directions?

This may be a silly question, but I'm not sure how we see an object in front of us. If light hits the points of the object and scatters in all directions, how come we are able to form an image of the ...
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S-matrix branch cuts properties

I'm trying to formally understand some non-perturbative results in scattering theory but the material available on the topic are not too friendly, so there are some very simple and essential facts I ...
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Why are number changing interactions inelastic?

Inelastic processes are those in which the kinetic energy of the initial particles and final particles are not the same. Is this true also for number changing processes such as pair creation or pair ...
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Example of calculating phase shifts in scattering theory

I have an extended question to this post: Phase shifts in scattering theory I have read it and also went over the formalism in Sakurai's, Shankar's, and Griffith's. I am now trying to look for ...
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Neutrino scattering cross-section in high energy limit

I've come across a problem in out particle physics lecture notes that I have been unable to resolve on my own. I've paraphrased the bits of the notes that are giving me so much trouble: The notes ...
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How to evaluate the Feynman gauge photon propogator in coordinate space?

In coordinate space the Feynman gauge looks like: $$\frac{g_{\mu\nu}}{\partial^2} .$$ Without fourier transforming, how does this operator act on currents? In general for inverse derivative operators ...
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Direction of propagating wave in quantum barrier

Consider a step potential $V(x)$ where \begin{align} V(x) & = 0; \quad x\leq 0 \\ V(x) & = V_0; \quad x> 0 \end{align} Now consider the case where $E_0<V_0$. The solutions of the ...