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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Second born amplitude for the electron-hydrogen scattering

can someone explain how could they got the result of the second born formula written in equation 2.36 from 2.32 I failed to demonstrate it. The image from Byron 1973 here the link enter link ...
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Transfer mechanism of two particles in laboratory coordinate [closed]

There is two particles' collision with angles theta for M1 and phi for M2. The initial velocity of M1 is V0 and of M2 is 0. The collision follows the conservation of energy and momentum. Three ...
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Peskin & Schroeder Chapter 16.1 derivation

I am trying to derive the term shown in chapter 16.1 in Peskin & Schroeder. We have defined our polarisation vectors as $$ \epsilon^+_\mu(k)=\left(\frac{k^0}{\sqrt{2}|\vec{k}|},\frac{\vec{k}}{\...
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Question about quantum scattering theory (elastic) [closed]

I tried to solve this question and reach to this: J1=ħ/m Im[ψ*(incident)dψ/dz]=ħk/m J2=ħ/m Im[ψ*(scattered)(gradient ψ)] =ħ/m Im[f*(θ) (e^-ikr)/r (d/dr +1/r d/dθ+1/rsinθ d/dφ) (f(θ) e^ikr)] =ħ/m Im[|...
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Ratio between Stokes and anti-Stokes scattering amplitudes in Raman scattering

I'm trying to understand the amplitudes and the ratio between those of Stokes and anti-Stokes scattering in Raman scattering. I understand that from a Boltzmann distribution point of view, the ratio ...
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Calculate the transition amplitude and the differential cross section [closed]

Calculate the transition amplitude and the differential cross section for the lowest order process in perturbation theory in which a photon strikes an electric charge core Ze and the heavy core ...
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Photoelectric emission at frequency less then threshold frequency

If I shine an EM radiation of frequency $\nu$ on a metal surface which has threshold frequency of $\nu_o$, where $\nu < \nu_o$ then, will the emission occur by multi photon absorption? My reasoning ...
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Running of the fine structure constant: meaning of $\alpha(Q^2=0)$?

In Measurement of the Running of the Fine-Structure Constant, the L3 collaborations writes At zero momentum transfer, the QED fine structure constant $\alpha(0)$ is very accurately known from the ...
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Why lead plate was used in Rutherford's gold foil experiment?

I have read that lead plate is used to concentrate the beam of alpha particles which are being directed towards the gold foil as it is a heavy metal. But there are other heavy metals like manganese, ...
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Energy and Momentum conservation in Bhabha scattering

I came across this question here which was asking my exact initial question (I even came from Griffiths problem 2.4 too!). But the given answer gave me a lot more questions which I think constitute ...
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Discrete Spectrum vs Continuous Spectrum and Bounded, Scattering States

Apolgies in advance if this is a confusing ramble and multitude of questions, I'm not quite sure how to articulate myself. I am currently reading up on quantum mechanics and seem to have confused ...
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Validity of defining Effective Permittivity in Dielectric Mixture

I am a optics-major student currently studying the topic of line-of-sight propagation of wave in scattering medium. I recently noticed some interesting articles about microwave propagation in mixtures,...
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Gell-Mann Low formula vs time independent perturbation

Consider a nonperturbed Hamiltonain $H_0$ and an eigenstate $|\Psi\rangle$ satisfying $$H_0|\Psi\rangle=E_0|\Psi\rangle.$$ Now consider the perturbed Hamiltonian $H=H_0+\lambda H_1$ and let $H_\...
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Phase shift in square potential barrier when $E>V$

I'm trying to understand what happens to the phase of the wave reflected by a potential barrier when the energy $E$ is greater than the height of the barrier (i.e. $E>V0$) in the region $0<x<...
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$S$-Matrix and Relation to Phase Shifts

Given some potential $V(x)$, we can describe the amplitude of incoming and outgoing waves through the scattering matrix $S$ whereby $$\begin{pmatrix} B \\ F \end{pmatrix}= \begin{pmatrix} S_{11} & ...
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In and out states of scattering in Asymptotically flat spacetimes

I am reading a paper called "New symmetries of massless QED", written by Temple He, Prahar Mitra, Achilleas P. Porfyriadis and Andrew Strominger (https://arxiv.org/abs/1407.3789). At some ...
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Questions on the Zakharov-Shabat inverse scattering paper

I am trying to work through the Zakharov and Shabat paper on inverse scattering for the nonlinear Schrodinger equation (PDF). I am stuck on section 2. Problem 1. I need to know how to reconstruct $\...
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How to derive Sommerfeld radiation conditions from Limiting Absorption Principle?

For the Helmholtz equation $$ -(\Delta + k ^2) u = f, \tag{1} $$ imposing the Sommerfeld radiation condition $$ \lim_{r\to\infty} r ^{\frac{m-1}2} \left( u_r - i k u\right) = 0 $$ on $u$ allows us to ...
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Is there a physical interpretation of the connection between the scattering matrix and bound states?

The square integrability condition of a scattering wavefunction can be written for imaginary wavenumber $k = -\mathrm{i}\kappa$ as $$\int_0^\infty \mathrm{d}r\left|(-1)^l \mathrm{e}^{-\kappa r} - S_l(-...
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How does the intensity of scattered light depend on the intensity of incident light?

Let's say I shine an infrared laser beam on a particle in the first scenario, and white light or visible light on the same particle, in the second scenario. The particle scatters the light rays in ...
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What is the relation between phonon anharmonicity and thermal conductivity?

The textbook says that: if the vibration of the lattice were harmonic, then the states of phonons would be orthogonal to each other. As a result, there would be no interaction between phonons, hence ...
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$S$-matrix commutation with Hamiltonian

I know from scattering theory that $S$-matrix and the free Hamiltonian $H_{0}$ commute due to energy conservation of incident and outgoing asymptotic states, but can the $S$-matrix and $H = H_{0} + V$,...
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Unfamiliar notations about $\pi\pi\rightarrow\pi\pi$ scattering amplitudes in Weinberg’s QFT?

I’m reading section 19.5 of Weinberg’s second volume of QFT, and confused about some notations. In that chapter, he introduce the non linear sigma model as an low energy effective theory of 2-flavor ...
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First derivative boundary condition for scattering phase shift

My understanding is that in the partial-wave approximation we can solve for the phase shifts $\delta_{\ell}$ by (in my case, numerically) integrating the radial equation $$\frac{d^2 u_\ell}{dr^2} + \...
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Wave function of a real scalar field in interacting quantum field theory

In interacting real scalar field theory, if I intuitively define the "wave function" of a state as $$\Psi(x)\equiv\langle\Omega|\hat{\phi}(x)|\Psi\rangle.$$ Does this wave function satisfy ...
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Conceptual meaning of differential cross section with respect to theta

By doing a seminar paper about Compton scattering I came across two different differential cross-sections: $\frac{d\sigma}{d\Omega}$ and $\frac{d\sigma}{d\theta}$ where $\theta$ is the scattering ...
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How can recombination lead to photon decoupling if scattering can still occur with neutral particles?

During the recombination era, two things happened: Electrons and protons bonded to form neutral hydrogen atoms. As a result of #1, Compton scattering is no longer efficient enough to keep photons and ...
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Definition of transmission and reflection coefficients for a particle

Quick intro: A 1D quantum particle is subject to the potential $$ V(x) = \begin{cases} 0 \;\;\;\;\; x\leq 0\\ V_0 \;\;\; x > 0 \end{cases} $$ I am trying to understand the definition of ...
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Mott-Bethe electron scattering factor at g=0

I am a non-physicist, but am doing some calculations related to electron diffraction in (crystalline) solids. Generally, electron scattering factors $f_\text{e}(s)$ can be estimated from the xray ...
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LSZ reduction formula relation

LSZ formula gives a relation between the scattering amplitudes and correlators as $$\langle f |i \rangle = (-i)^{m+n}\int \Pi_{i=1}^m d^4x_, e^{ik_i'x_i (\Box_{x_i} -m^2)}\Pi_{j=1}^n d^4x_, e^{ik_j ...
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Differences in interactions of light with different mediums

I am trying to figure out this problem, I apologize in advance if the question is silly. If i am correct sunsets are red because red light doesnt get diffounded as much as blue light, which eventually ...
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1 vote
1 answer
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Can Compton scattering occur between a photon and a neutrally charged particle?

Compton scattering occurs because of the particle-like nature of light, but does it occur between photons and charged particles only? Is it impossible for Compton scattering to occur between a photon ...
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Any details on deep inelastic scattering? [closed]

The article on Wikipedia is rather scanty and I couldn't find more info in previous questions. I hope you will cot consider this as a multiple question since all queries are details of a single issue. ...
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More general propagator of a real scalar field

I have some Lagrangian containing a real scalar field $\phi$ with mass $m$. Let $A \in \mathbb{R}$ be some constant. The Lagrangian takes the form: \begin{equation} \mathcal{L} = -\frac{A}{2} (\...
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Doubt in the bound states which we get through Levinson's Theorem

Levinson's theorem gives us the relationship between the bound states of a potential and phase difference between the scattered wave for $V\neq 0$ and $V=0$. $N_b=\frac{\delta(0)-\delta(\infty)}{\pi}$....
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What decides that a light will excite something?

Are there any conditions on when an absorption and reemission process will happen Are the atoms in my bottle getting excited and re-emitting the light bouncing around in my well lit room? Irrespective ...
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Lorentz invariance, locality and unitarity of the S-matrix

I am reading these notes on cosmological bootstrap by Baumann and found the following statement, which I am trying to understand / see where it comes from [page 2 of the linked notes]: "[...] S-...
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Running of the fine structure constant

In Measurement of the Running of the Fine-Structure Constant, the L3 collaboration reports their fine structure constant data for various values of momentum transfer which they call $Q^2$. This is ...
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Conservation of flux in scattering problem

Consider a localised potential which becomes 0 after some distance $a$. So, we are considering a wave coming from infinity along z direction, so for $r>>a$, $\psi_{incoming}=e^{ikz}$ Now for ...
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Why does the LSZ reduction formula only give the connected part of the $S$ matrix?

As an example, using the LSZ reduction formula, the $S$ matrix element for $2\rightarrow 2$ scattering is found in Peskin and Schroeder to be $$\langle \boldsymbol{p}_1 \boldsymbol{p}_2\rvert S \lvert ...
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Can an observer visible distinguish between Rayleigh and Mie scattering of monochromatic light by a medium?

Is there a way to visually determine that monochromatic scattered light by a medium is Rayleigh or Mie scattered by this medium? And if there is no way to tell the difference by just looking at it, ...
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In compton scattering, is the emitted photon the same as the incident one? [closed]

In Compton scattering (you can extend to Raylegh and Rutherford light scattering if you wish to), is the emitted photon the same as the incident one? In other words, should we consider one photon as ...
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Closest approach as a function of scattering potential and impact parameter

I'm trying to express the relation of the scattering angle $\theta$ as a function of the impact parameter $b$ in the case of the scattering through a potential of the form $V(r) = \frac{k}{r^2}$. I'm ...
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On Mandelstam variables

Citing Wikipedia: $[\dots]$ the Mandelstam variables are numerical quantities that encode the energy, momentum, and angles of particles in a scattering process in a Lorentz-invariant fashion. They ...
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Is there a formula for probability of Compton Scattering?

I am making a Monte Carlo simulation of an X-ray detector and trying to account for Compton Scattering, but cannot find anywhere a formula for the probability that Compton Scattering occurs, only that ...
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3 votes
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How can daylight have a higher colour temperature (e.g. 6500 K or D65) than sunlight in space?

Supposedly, daylight at midday has a colour temperature of 6500 K. This reference is also the standard for calibrating computer screens (that's how I fell into this). However, outside the atmosphere ...
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Calculating the Feshbach resonances between carbon atoms

From my understanding, Feshbach resonance is a scattering resonance that occurs when the energy of an atom pair coincides with the energy of a molecular bound state. Feshbach resonances are ...
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Dielectric susceptibility and scattering intensity

I am currently reading a paper about Resonant Soft X-ray Scattering and they mentioned that the resultant scattering intensity can be found from the dielectric susceptibility of the thin film, with ...
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How does wavelength affect scattering?

Let's say that I have a detector and a few sources of light (think lightbulbs). The sources are all the same power and emit different colours of light. We're on the surface of Earth. As I walk further ...
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SAXS vs. X-ray diffraction?

Both small-angle X-ray scattering and X-ray diffraction can be used to obtain structure factors, though I imagine the wave vectors accessible to each are different (?). What are the main differences ...
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