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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Cross section normalization in $2 \to 2$ scattering
Consider Compton scattering $$p_1 + p_2 \to p_3 + p_4$$ in the laboratory frame. According to Quantum Field Theory and the Standard Model by Schwartz, the relation between the differential cross ...
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Scattering probability distribution for $2 \rightarrow 2$ scattering
Consider a 2-to-2 particles scattering process (treated in second quantization) of particles with the following $4$-momenta:
$$p_1 + p_2 \rightarrow p_3 + p_4.$$
The probability measure associated ...
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Positive values of Mandelstam variable $t$
Is it possible for the Mandelstam variable $t$ to reach positive values in the quasielastic charged current neutrino-neutron scattering?:
$$\nu_{\mu} + n \rightarrow \mu^- + p$$
(don't assume that ...
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Computation of scattering cross section using Dirac equation
The differential cross section formula of the scattering of an electron on a nucleus are known to coincide when computed using either classical mechanics approach (Rutherford) or the Schroedinger ...
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Understanding derivation of quantum differential scattering cross-section [duplicate]
I've been trying to understand quantum scattering, but I think I am not very clear about the full picture in the derivation of differential cross-section below. In Modern Quantum Mechanics by Sakurai, ...
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When is the 3D Dirac delta function a good approximation for scattering?
When discussing X-ray or neutron scattering, it is usually assumed that the scattering potential is of the form
$$V_{\mathrm{eff}}(\mathbf{r}) = \sum_i b_i \delta^3(\mathbf{r}-\mathbf{r}_i)$$
with $...
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Confused about derivation - electron gas with binary collisions and impurities scattering
I am confused about a derivation for the behaviour of electrons in a conductor with binary collisions, and scattering due to static impurities. The derivation begins as follows:
The distribution ...
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Formula for a moving Schrodinger gaussian wave packet in three space dimensions [closed]
I am trying to time evolve quantum systems in the presence of a gravitational potential. To do this I need a free localised 3+1 dimensional wave packet with velocity so that I can perturb with a weak ...
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Why rainbow appears only after rainfall? [duplicate]
This is a silly question I know but I need a good logical scientific answer for this to quench my thirst of this doubt
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Why do discussions of classical EM scattering use scattering cross-sections instead of scattering amplitudes?
In every discussion of classical electromagnetic scattering that I've read - e.g. Jackson and Wikipedia (1 and 2) - the primary quantity that is used to quantify EM scattering is the differential ...
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General formula of glancing collision to classical scattering theory?
I encountered this . It takes some time for me to find that it is called glancing collision, well my language doesn’t has. What i interest isn’t the solution of the picture, but generalized ...
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Conventions in spinor-helicity formalism: are Elvang & Huang using angle brackets for left or right-handed Weyl spinors?
So, I'm reading about the spinor helicity formalism. In some references, I see angle brackets referring to left-handed (dotless) spinors. For example, Cheung writes (equation numbers in this post ...
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QFT Scattering: Perturbation Theory v.s. LSZ Reduction Formula
Context
It is well known that $S$-matrix could be computed in the following two ways:
Calculate in interaction picture Perturbatively.
Use the LSZ reduction.
To be specific, we have the math ...
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Fermi's Golden Rule in Two-Body Decay (Thompson)
I don't have enough reputation to add a comment to the original thread Interpretation of the lorentz-invarient transition rates (LI Fermi's Golden Rule), so I hope it's okay to ask a related ...
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Why does the straight-line approximation work for X-rays but not for waves with larger wavelengths?
In many imaging methods, such as X-ray CT, wave propagation is often modeled using the straight-line (ray) approximation. This works well for X-rays, partly because their refractive index is extremely ...
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What is the difference between diffraction and scattering?
In the context of acoustic waves interacting with small particles (for example, in medical ultrasound imaging of biological samples) I often read that when a wave encounters a particle whose size is ...
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Spin dependent interaction for alkali-metal atom
When studying ultracold atomic quantum gas, we encounter the problem where two alkali-metal atom with spin(hyperfine spin), for example, when two $f = 1$ atom scatter, the zero-range pseudo-potential ...
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Can we derive laws of reflection by treating reflection as a form of wave scattering theory?
My professor once told me that reflection of light is fundamentally a form of the scattering of (electromagnetic) waves. When I asked him to explain it a bit his response was the following. When light ...
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Correlation between position and momentum after reflection from a barrier [duplicate]
Consider a particle's wave function that has reflected from a square barrier.
If I then measure the particle to be to the left of the barrier, it will have negative momentum (reflected - runs toward ...
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Physical terminology for multiplying a wave by a negative number
In physics, given a function $f: \mathbb{R} \to \mathbb{R}$ representing some wave, if we multiply $f$ by a large positive number this might be called amplifying the wave, and if we multiply $f$ by a ...
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Rayleigh scattering not weakening light
Usually everyone describes Raleigh scattering from thermal fluctuations the same way they describe scattering from molecules or random cloud of similar particles, but I found this explanation wrong.
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Why doesn't Rayleigh scattered light amplify intensity?
Let's consider some linear ideal infinite medium where infinite plane monochromatic wave is propagating.
Fluctuations of density cause relative permitivity to fluctuate and proportionally create ...
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Why is the kinetic energy not a Hermitian operator in the scattering state?
In quantum mechanics, we know that the operator of a physical observable satisfies
\begin{equation}
\langle \phi_1|\hat O\phi_2\rangle =\langle\hat O\phi_1|\phi_2\rangle.
\end{equation}
But this ...
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Optical theorem and forward scattering in weak interactions
The optical theorem (for the case of $2\to 2$ scatterings) is the statement that the imaginary part of the forward scattering amplitude is related to the total cross section through $$ \sigma(\text{...
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Circuit scattering: energy balance
I was studying how a pure resistive circuit behaves when radiation effects are taken into account. In particular, I considered a circuit made by an ohmic resistance R, and an alternate voltage ...
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Are photons affected by wind? (visible-light)
Observatory is in an area of gentle wind. What is the effect, if any, on quality of image?
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Extracting decay rates and cross sections from finite time correlation functions
Is it possible to extract decay rates or cross sections from finite volume lattice QFT in minkowski space time? (Suppose i have simulated such a system, and i have correlation functions available)
...
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Fourier Transform for sinusoidal number-density to obtain the structure function
I was reading chapter 2 of Chaikin and Lubensky, where I got stuck at this derivation of structure function. While talking about Smectics-A liquid crystal, it was mentioned that the molecules are ...
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Rayleigh phase function formula concretization
I am in the process of writing a Master's thesis in Computer Graphics and it is tightly related to the physics field in order for the model to be physically-based, but sadly I am not a physicist.
I ...
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Do we need to match the UV theory with the IR one always computing physical processes?
I am studying EFT and as far as I understand one usually (in the TD approach) start from an $\mathcal{L}_{UV}(\phi,H,c'_{j})$ and derive the IR theory $\mathcal{L}_{IR}(\phi,c_{i})$ by simply ...
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One-Particle States and Time Evolution in Interacting Scalar Field Theory: Clarifications on Equations 4.87 and 4.88 in Peskin & Schroeder
In equation 4.87 of Peskin & Schroeder it states,
$$\langle p_{1}p_{2}...|S\left|k_{A}k_{B}\right\rangle = \lim_{T\rightarrow \infty}\langle p_{1}p_{2}...|e^{-iH(2T)}\left|k_{A}k_{B}\right\rangle\...
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Behavior of Radiative Transfer in Homogeneous Plane-Parallel Scattering Media
Coakley and Chylek (1975) provide a formulation of the plane-parallel equation of radiative transfer:
$$
\mu \frac{dI^{+}(\tau,\mu)}{d\tau}
= I^{+}(\tau,\mu)
- \frac{1}{2} \int_{0}^{1} d\mu'\, p(\mu,\...
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Relativistic Central Force Problem and Scattering
I derived the relativistic Binet-equation for a particle of charge $q$ subject to electromagnetic interaction due to a fixd point charge $Q$ ($Qq>0$) held at the origin. Let $u=1/r$.
The result I ...
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What is the probability in classical field theory?
I am studying domain walls. In Vilenkin's book on topological defects (p. 382) a classical field $\phi(z)$ forms a domain wall, while the field $\chi(x,y,z,t)$ of a particle interacts (scatters) with ...
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Impact parameter $b$ in the formula used in the Eddington experiment
According to Wikipedia the formula used to predict gravitational lensing of the Sun during the Eddington experiment is $4GM/c^2b$. It says
"$b$ can be interpreted as the distance of closest ...
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Differential Inelastic Cross section and Optical Theorem
Context
For a single channel scattering problem, it is well known that we have to solve the wave function from the Schrodinger equation:
\begin{equation}
\left( -\frac{1}{2m} \nabla^2 + V(r) \right) \...
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What is $s$-wave sector in the context of black holes?
Can someone explain the terminology $s$-wave sector that appears here?
Let us begin by reviewing the derivation of Hawking radiation in the $s$-wave sector,.....
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Is there a change in the light beam coming from an object that allows us to view it?
When light hits objects it is scattered and those light beams that hit our eyes make us see the objects.
But how does this allow us to see the objects?
Does that mean that the light beam going towards ...
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Density of state for scattering states
For a typical one-particle Hamiltonian $$H=\frac{1}{2}p^2+V(x)$$ the spectrum generally has some discrete bound states and continuous scattering states above that.
The density of states of such a ...
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Scattering states and 2nd-order perturbation theory of a bound state
It is known that, in quantum mechanics, the standard 2nd-order perturbation theory (and beyond) depends on summing over intermediate states. My question is over the range of this sum: for systems ...
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Where do eigenstates go when they pass the continuum threshold?
Consider the quantum mechanics of a massive particle subject to a finite potential $V(\mathbf r)$ which has a well in it. This could be in 1D/2D/3D, and the well could be finite and square, or some ...
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Two-particle phase space integral for a fixed target: No kinematic limit?
I have a fairly basic question concerning a Lorentz Invariant phase space for a 2 particle final state in a fixed-target experiment lab frame. For some reason, in my derivation, I do not see that that ...
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Effect of particle charge on scattering amplitude
In QED, consider for example the scattering process $e^-\mu^- \to e^-\mu^-$, with the leading order Feynman diagram
(time flows from bottom to top).
The scattering amplitude is, using standard ...
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Quantum scattering states [duplicate]
While studying about scattering states in quantum mechanics we come up with terms like Transmission coefficient and Reflection coefficient in consequence of Obtaining two solutions for x<0 and x>...
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Modelling chaos with Edward scattering
A typical chaotic Hamiltonian, such as those from the GUE/GOE ensembles, is often considered unphysical because it involves non-local many-body interactions. Now, consider the Edwards model, which ...
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Help with understanding scattering in CM reference frame
I'm studying Introduction to Elementary Particles by Giffiths, and in Unit 6 (scattering), he presents the following system: let us study the scattering process $A+A\to B+B$ in the center of mass (CM) ...
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Confusion on Combinatorics in Feynman diagrams in QED
I want to study the interaction
$$e^-(p_1)+e^+(p_2)\rightarrow \gamma(k_1)+\gamma(k_2)+\gamma(k)$$
where in the parentheses I write down the momenta of the respective particles. I want to obtain the ...
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Rutherford scattering angle
Good morning. IN David Tong's theoretical physics notes, at page 66
https://www.damtp.cam.ac.uk/user/tong/relativity.html
we find a derivation of the impact parameter - deflection angle relationship. ...
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One-point functions and single particle states in QFT
In Ch 5 of Srednicki's book on QFT, he states the definition of a single particle state $|\textbf{k}\rangle = a_{\textbf{k}}|0\rangle$ as the action of the creation operator on the ground state. Then, ...
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Why we have only planar diagram in the cyclic ordered Feynman rules of Yang-Mills?
I'm studying the $SU(N)$ YM theory, particularly the scattering amplitudes at tree level.
I have understand that the Feynman rules give a huge proliferation of terms because of three-point verices and ...
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