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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The radiation power of an electromagnetic wave scatter due to the magnetic field
In studying the scattering of an electromagnetic wave by a single charge, it seems typically we consider the motion driven only by the electric field, as is presented in Section 32-5 Scattering of ...
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How many relativistically invariant degrees of freedom in $n$-particle scattering?
Suppose we have a scattering process with $n$ external legs with four-momenta $p_1, \cdots, p_n$. Naively there are $4n$ degrees of freedom, however most of these putative degrees of freedom are not ...
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Meaning of Scattering-Amplitudes "time-volume"
I've been reading this book by Schwichtenberg as I re-learn QFT. My question is general, but applies easiest to the scattering amplitude at first order in the $\phi^4$-theory for $k_1,k_2\rightarrow ...
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Step Potential versus Free particle [duplicate]
In the step potential
\begin{equation}
V=
\begin{cases}
0 &, \text{x<0}\\
V_0 &, \text{x>0}
\end{cases}
\end{equation}
for the scattering states$(E>V_0)$, the states on the right and ...
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Scattering off spherical well - thermal neutron absorption and $1/v$ behaviour
I am attempting to describe the $\sigma_{abs} \sim 1/v$ behaviour for thermal neutron absorption by heavy nuclei. In Krane's "Introductory Nuclear Physics" he first computes the cross-...
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Compton scattering but not quite
Is it possible that for a gamma ray, of around $3$ MeV, when scattering off a nucleus of oxygen (which undergoes mostly Compton scattering), does not always eject a loosely bound electron? If so, what ...
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Compton Scattering - On the equivalence of the Klein-Nishina formula (and on the demonstration to go from one to the other)
A stupid question about the Compton scattering and in particular the Klein Nishina formula.
I'm not sure I can find, if it exists, an equivalence between the three following formulas. (and what's the ...
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Scattering of entangled states
Recently, I became interested in scattering processes which involve an initial and final state that consists of entangled states (lets say $\left|e^{-}\right\rangle \times\left|e^{+}\right\rangle $ or ...
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Why do the 'colors' of liquids in differently sized glass cylinders appear similar despite varying absorption rates?
For some liquids, such as cooking oil, I have observed that when filling two glass cylinders (with lids) of different diameters (e.g., one with a 5 cm diameter and another with a 10 cm diameter) with ...
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Scattering Differential Cross Section Laboratory Frame
Let the differential cross section of a scattering experiment given by $\frac{\text{d}\sigma_{c}}{\text{d}\Omega_{c}}(\vartheta_{c})$, where $\vartheta_{c}$ describes the scattering angle in the ...
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Explanation for an atmospheric optical phenomenon
Consider the atmospheric optical phenomenon appearing in this video. A screenshot at the appropriate time is shown below:
The video is footage from a drone flying just above a low-lying, thin layer ...
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Amplitude of the process $q \bar q \rightarrow \tau^+ \tau^-H$
I want calculate the cross section of the process $q \bar q \rightarrow \tau^+ \tau^-H$, where the Higgs takes the $vev$. My question is: if the Higgs takes the $vev$ the amplitude of the process is ...
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I think deriving $E_f=\gamma^2E_i$ of the inverse Compton scattering is unreasonable
https://casper.astro.berkeley.edu/astrobaki/index.php/Inverse_Compton_Scattering
I have two questions on the above site's table of contents 1.1.
$\space$
Can $\theta_i\approx\theta'_f\approx\pi/2$ be ...
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Can we compute tree-level amplitudes in string theory using the fundamental domain of $SL(2; \mathbb{C})$?
I am not a specialist in string theory. I understand the computation of tree-level string amplitudes (Veneziano or Virasoro-Shapiro), where three variables are fixed using the symmetry $SL(2;\mathbb{C}...
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What is the mass dimension of scattering amplitudes in string and membrane theories?
It's all in the title: I am interested in the mass dimension (in natural units) of scattering amplitudes in string and membrane theories. For particles in $d=4$, it seems to be
$$[ \mathcal{A}^{(n)} ] ...
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Relate form factor and differential cross section in case of nuclear scattering
In the case of nuclear scattering, we very often discuss form factors. How can I relate this to the Differential cross-section?
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How to calculate the amplitude for emission of a gravitino in unbroken supersymmetry?
I am studying supersymmetry and supergravity, and I have encountered the following problem:
Suppose that supersymmetry is unbroken. Show how to calculate the amplitude for emission of a gravitino of ...
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Can we say that amplitude of light scattered by air molecules is inversely proportional to the square of wavelength of incident light?
As per Rayleigh's criteria of scattering of light by air molecules the intensity of scattered light is inversely proportional to the forth power of wavelength.
AND WE ALSO SAY :
Intensity of a wave ...
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Integral on phase space
I'd like to integrate the square amplitude in the phase space( in $d^3k/(2\pi)^3 2E_k$ and $d^3k'/(2\pi)^3 2E_k$) where $p$ and $p'$ are the 4-momentum of the input particles, $k$ and $k'$ 4-momentum ...
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Are intermediate states just mathematical constructs?
In the vacuum state, particles and antiparticles can spontaneously emerge as virtual pairs due to the uncertainty principle. These virtual particles have a brief existence before they annihilate each ...
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Scattering off an extended collection of scatterers
Scattering from a single scattering centre can be described by the (differential) cross section, which tells us the proportion of particles scattered into a given solid angle.
However, what if the ...
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Fourier transform of electric quadrupole potential
I'm struggling to find the scattering amplitude by the first Born approximation (Fourier transform) given by
$$
f(\vec{k}_f,\vec{k}_i)= -\frac{1}{2\pi}\langle \vec{k}_f | {V}| \vec{k}_i\rangle = -\...
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Proving that the interference current integrated over a small cone does not depend on the angle of the cone
I'm studying quantum mechanical scattering and I have gotten to $$\psi=\psi_{in}+\psi_{scattering}=e^{ikrcos\theta}+f(\theta,\phi)\frac{e^{ikr}}{r}$$ and when calculating the current, i get three ...
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Effective field theory of massive spin-1 and spin-2
I'd like to understand what could be the use of an effective field theory (EFT) of a single massive particle of spin 1 or 2, or simple modification of these (see below). By EFT, I mean the most ...
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What exactly does the quantity $\sigma(\theta)$ represent in scattering problems? What is the interpretation of the differential cross section?
So I don’t understand intuitively what the scattering cross section is. The equation also seems quite random to me. I have looked at derivations but I cannot wrap my head around. I am looking for some ...
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Compton Scattering Angle Distribution, and the Klein-Nishina Model
I have a Geant4 simulation where 662keV photons are going into a detecting volume (Germanium). As expected, when I look at the output of the simulation, these photons undergo Compton scattering and ...
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Discontinuities in the $u$ channel
if we consider a 2-to-2 scattering, we have normally an $s$ channel a $t$ channel and $u$ channel. In CMS frame $s$ is positive and $t$ and $u$ negative, by crossing symmetry there are kinematics ...
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Relation between matrix element of a process with its crossed processes
Consider a process in particle physics denoted by, $$(1) \quad a+b\to c+d$$ which is related to the reverse process $$(2)\quad c+d\to a+b.$$ By virtue of the hermiticity of the interaction Hamiltonian,...
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Details in the derivation of the Lippmann-Schwinger equation
So the argument goes that for a slightly perturbed Hamiltonian
$$
H = H_0 + V,
$$
there will be some exactly known states, $\left|\phi\right>$, solving
$$
H_0\left|\phi\right> = E\left|\phi\...
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Why differential scattering cross sectional area is same for Lab frame and centre of mass frame
Differential scattering cross section is denoted by:
$\frac{{d\sigma}}{{d\Omega}}$
Here, "$d\sigma$" represents the infinitesimal differential scattering cross-sectional area, which is not a ...
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Solving QED Feynman diagram with one vertex
I'm new to Feynman diagrams and I want to calculate the probability of electron and positron anihilating into one photon to show it is impossible. I know this can be shown easier with special ...
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How is it possible to collide particles with specific momentum in microscopic scale?
Quantum theory says particles with almost specific momentum are spatially spreaded. (have relatively large spatial scales). Then how is possible to collide them very effectively in microscopic scale? (...
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Why would this light beam look different from different directions?
I noticed a weird phenomena while in a particulate-filled restaurant with a sunbeam through a window. While facing the sun, the light beam was quite visible, but as you rotated towards facing away ...
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Is it possible to have colorful foams?
As we know foam is white regardless of the color of the soap or shampoo.
... the foam in its entirety looks white because when light enters the soap solution, it must pass through a number of tiny ...
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About Compton scattering in QED
Consider the Compton scattering
$$e^{-}(p,s)+\gamma(k,\lambda)\rightarrow \gamma(k',\lambda')+e^{-}(p',s')$$
To calculate the process' amplitude one has to compute the matrix element
$$S_{fi}=<f|\...
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CPT invariance and Soft Theorems
I am reading the paper IR Dynamics and Entanglement Entropy, written by Toumbas and Tomaras and I have a question on using the CPT invariance of the QED $S$-matrix elements in order to derive the ...
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Understanding the potential step for a particle in 1D
In an exercise, I consider a particle moving from $x=-\infty$ towards a potential step, where $V(x)=0$ for $x\leq 0$ and $V(x)=V_0$ for $x>0$.
If we consider the case of $0<E<V_0$, we have;
$$...
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The relation between charge distribution and form factor
In Peskin and Schroeder Eq.(6.33), they introduced the concept of form factor
\begin{equation}
\Gamma^\mu\left(p^{\prime}, p\right)=\gamma^\mu F_1\left(q^2\right)+\frac{i \sigma^{\mu \nu} q_\nu}{2 m} ...
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Rayleigh law contradicting tyndall effect
Sir, we have been taught that according to Rayleigh, the amount of scattering of light is inversely proportional to the fourth power of its wavelength and this law only occurs when the size of a ...
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Boundary conditions required to get a unique solution to Schrodinger Equation
If we are considering the scattering of an electron plane wave from a crystal specimen, we could start with the time-independent Schrodinger equation (TISE) as our governing equation:
$$ \{\nabla^2 + ...
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Rutherford's experiment
I have read everywhere that the gold foil experiment performed by Rutherford was done hoping that the alpha particles face only a little deflection/no deflection however this doesn't sit right with me,...
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Making sense of Scattering of Impulsive Gravitational Waves
Consider the space-time diagram of KP-wave as shown below:
We see that two transverse plane fronted GW waves intersect at the point ($u,v$)=(0,0). The curvature comes with a delta function, except in ...
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How an autocorrelation function is calculated experimentally in a Dynamic Light Scattering experiment
As said in the title, I would like to know how an autocorrelation function of scattered light intensities defined as $G(\tau)=\langle I(t)I(t+\tau)\rangle$ is computed experimentally. Let's say we ...
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The blue sky — is the simple Rayleigh explanation wrong?
Reading various answers here ([1], [2], [3]), Wikipedia, nasa.gov, and other places, the common explanation of our blue sky is Rayleigh Scattering due to gases and particles in the air, maybe with ...
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First EXPERIMENTAL proof of indistinguishability of electrons
Fairly early on in Thermodynamics there was a suggestion that particles are generally indistinguishable because of entropy paradoxes. Later on, my recollection is that somebody in the 1920's shot ...
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How to calculate a scattering matrix numerically for 1D localized potential?
I want to calculate a scattering matrix numerically for an arbitrary localized potential for the 1D Schrödinger equation. I want to do this to get a better feel for the scattering matrix.
I can solve ...
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How can I calculate the reflectivity of an electron gas with Thomson scattering?
I have to do a seminar presentation about the topic of using relativistic mirrors in integrated laser ion accelerator systems.
The idea is (for context sake) to accelerate an electron bunch to ...
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Order of fields in scattering amplitude
Given the lagrangian
$$\mathcal L=-\dfrac{1}{4}F_{\mu\nu}F^{\mu\nu}+(D_{\mu}\phi)^*(D^{\mu}\phi)-M^2|\phi|^2+\bar\psi(i\gamma^{\mu}D_{\mu}-m)\psi.$$
I tried to compute some first order scattering ...
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Confusion about scattering in QFT
When it comes to scattering in QED it seems only scattering cross sections and decay rates are calculated. Why is that does anyone calculate the actual evolution of the fields themselves like how the ...
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Is it possible to Compton scatter from delocalised pi-electrons in liquid scintillator?
I am wondering if an incident gamma could compton scatter from the delocalised pi-electrons in an aromatic compound (e.g. liquid scintillator).
I understand that compton scattering is valid for free ...
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