What is Scattering: Definition and 916 Discussions
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, is forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, a pioneer in light scattering research, noted the connection between light scattering and acoustic scattering in the 1870s. Near the end of the 19th century, the scattering of cathode rays (electron beams) and X-rays was observed and discussed. With the discovery of subatomic particles (e.g. Ernest Rutherford in 1911) and the development of quantum theory in the 20th century, the sense of the term became broader as it was recognized that the same mathematical frameworks used in light scattering could be applied to many other phenomena.
Scattering thus refers to particle-particle collisions between molecules, atoms, electrons, photons and other particles. Examples include: cosmic ray scattering in the Earth's upper atmosphere; particle collisions inside particle accelerators; electron scattering by gas atoms in fluorescent lamps; and neutron scattering inside nuclear reactors.The types of non-uniformities which can cause scattering, sometimes known as scatterers or scattering centers, are too numerous to list, but a small sample includes particles, bubbles, droplets, density fluctuations in fluids, crystallites in polycrystalline solids, defects in monocrystalline solids, surface roughness, cells in organisms, and textile fibers in clothing. The effects of such features on the path of almost any type of propagating wave or moving particle can be described in the framework of scattering theory.
Some areas where scattering and scattering theory are significant include radar sensing, medical ultrasound, semiconductor wafer inspection, polymerization process monitoring, acoustic tiling, free-space communications and computer-generated imagery. Particle-particle scattering theory is important in areas such as particle physics, atomic, molecular, and optical physics, nuclear physics and astrophysics. In Particle Physics the quantum interaction and scattering of fundamental particles is described by the Scattering Matrix or S-Matrix, introduced and developed by John Archibald Wheeler and Werner Heisenberg.Scattering is quantified using many different concepts, including scattering cross section (σ), attenuation coefficients, the bidirectional scattering distribution function (BSDF), S-matrices, and mean free path.
From posts like this I get that the color of the sky is explained by Rayleigh scattering, but needs density fluctuations. However as atoms are not uniform and are localized, the density is
$$\rho(\mathbf r)=\sum_i \delta(\mathbf r-\mathbf r_i)$$
where ##i## sums over all the atom positions...
For part one, my energy conservation equation is nhf0 + mc2 = nhf' + E
my momentum conservation in x-axis is nhf0= nhf' cos(theta) + c𝒑 cos(fi)
My momentum conservation in y-axis is nhf' sin(theta) = c𝒑 sin(fi)
For part 2 I understand that I am supposed to get a qudratic equation in terms of...
Stuck on (c), part (i). Any ideas about what is the most elegant way to prove it, maybe using Mandelstam variables since this exercise is supposed to be about them?
Seeking to leave academia for industry and am seeking help identifying non-defense jobs where one can solve scattering / wave-like problems.
I enjoy both numerical and analytic solutions partial differential equations where I have worked on parallel solutions to the TDSE in fortran and analytic...
So my first thought was that I can just use Fourier trick and integrate:
$$ F(q^2) = \int_V \rho(r) \cdot e^{ i \frac{ \vec{q} \cdot \vec{r} }{h} } d^3r $$
$$ F(q^2) = 2\pi \rho_0 \int_0^{\infty} r^2 \cdot e^\frac{-r}{R} dr \cdot \int_0^{\pi} \sin{\theta} \cdot e^{ -i \frac{q \cdot r...
From the Born Approximation, you can relate the potential to the scattering amplitude. So it follows that a potential can be derived from the scattering amplitude from Delbruck scattering. I tried to solve this myself, and get a scattering amplitude with only angular dependence, no momentum...
In scattering theory, the quantity of interest is the amplitude for the system—initially prepared as a collection of (approximate) momentum eigenstates—to evolve into some other collection of momentum eigenstates. For example, for ##m\to n## scattering, the amplitude we're interested in is...
To whom it concerns,
Would it be possible to reopen the thread "Confusion about scattering in QED". I think I might have some helpful pointers for the OP.
If not would it be better to start a new thread?
Thanks.
When it comes to scattering in QED it seems only scattering cross sections and decay rates are calculated. Why is that does anyone calculate the actual evolution of the field states or operators themselves like how the particles and fields evolve throughout a scattering process not just...
Looking to calculate the amplitude and cross section of the process: electron + positron to photon + Z boson.
Basically the annihilation resulting in Z + gamma rather than gamma +gamma.
My question is mainly about how to deal with the polarization states with the Z boson, since there are 3 and...
Consider a source emitting a beam of photons. These photons pass through x thickness of material. The attenuation coefficient of the beam \mu is known.
We can write this formula
If I'm not wrong, this formula tells us the number of photons that passed through the material of thickness x...
We have the three-phonon interactions Hamiltonian $$H_{\mathrm{ph}-\mathrm{ph}}=\sum_{i j k} M_{i j k}\left(b_{-i}^{\dagger}+b_i\right)\left(b_{-j}^{\dagger}+b_j\right)\left(b_{-k}^{\dagger}+b_k\right).$$
We will not need the explicit expression for the $$M_{ijk}$$
here, but only note that it is...
Teacher described the Thomson scattering effect through the lens of the electric field changing as a moving particle is accelerated. The changing electric field of the electron accelerating carries with it an amount of energy, and this energy radiates out from the acceleration event. (there were...
I am looking for experimental nucleon form factors from electron-nucleus scattering. Is there any compliations or tables?
In 'The proton charge radius ', H. Gao and M. Vanderhaeghen, Rev. Mod. Phys. 94, 015002 (2022), p. 24, there is 'world data on the proton and also the neutron'.
In 'Form...
Greetings,
in one of the exercise sheets we were given by our Prof, we were supposed to draw the trajectory of a patricle that moves toward a bounded spherical potential that satisfies
##
V(\vec{r}) = \begin{cases}
V_0 & | \vec{r} | \leq a \\
0 & else \\
\end{cases}
##
for...
In Chapter 5.4b of Ballentine, a discussion ensues about the analysis of a particle scattering off of a (Bravais lattice) periodic array. I attach pictures here of the full discussion in case anyone wants/needs to refer to it, but I am particularly baffled by the discussion on page 135. In...
How is it treated or what Feymann's rule applies to a virtual photon in an external leg? I would like to calculate the modulus of squared amplitude for the process
e-γ*→e-γ
where the * indicates that the photon is virtual. I've never dealt with virtual particles on a external leg and would...
There is a video, where the author shows the interference of laser beam on a strand of human’s hair:
I bought a laser pointer and reproduced this experiment. Indeed, when a single hair is placed on the way of the laser beam, I see the “scattering” picture (a series of points with intervals of...
I think I read somewhere that the trajectories of particles in the De Broglie–Bohm theory do not cross, is that true?
If true, then in the case of Rutherford scattering the trajectories below can't be those of the De Broglie-Bohm theory?
Thanks.
In Compton's 1923 paper on X-rays scattering from light elements, he presents the following diagram:
Here, ## h\nu_0/c ## is the momentum of the incident photon, ## h\nu_\theta/c ## is that of the scattered photon and ## mv/(1-\beta^2)^{1/2} ## is that of the recoiled electron. He uses this to...
I was reading about Compton scattering. I have a question I did not find an answer for it in the book (Concepts of Modern Physics-Sixth Edition-Arthur Beiser) or in the internet search. My question is:
Is the incident X-ray beam, with the original wavelength, detected at different scattering...
Hi,
the task is as follows
Unfortunately, I am not getting anywhere at all with task c. I have now proceeded as follows:
I assume that the calculation takes place in the reference system of the sun. In the task the following is valid, $$\vec{v}_{si}=-s\vec{v}_p$$ I have now simply assumed...
In electron microscopy of thin solid specimens elastic scattering is treated as the main process responsible for formation of (phase contrast) images and diffraction patterns.
However, if an electron changes direction it should lose energy by producing a breaking radiation photon.
How can it be...
Dear friends,
I will be grateful if anyone can help me
I study electromagnetic scattering by rough surfaces for a certain case. Each rough surface can be specified with the statistical parameters sigma (σ) and correlation length (lc). while writing my manuscript I drew a schematic...
I have seen the term "conventional scattering lens" being used (see https://arxiv.org/pdf/2112.08144) and I was wondering whether the term scattering lens is accurate? I always envisioned a lens as a refractive element, and wondering if the reference means refracting rather than scattering...
I have a little question about Rayleigh scattering: I know that Rayleigh cross section is proportional to the inverse of the fourth power of the wavelenght of the incident light and that it is so even the intensity of the scattered beam of light, now:
1. What is the color of the sky due to...
Hi,
Is there a more general equation than the Compton equation that allows one to determine whether an electron will Compton scatter or inverse Compton scatter? If so, where can I find it (or what is it?)
Thanks.
If you have γ+γ→γ+γ what would the Feynman diagram look like (time-ordering implied).
I think it will be a square with four photons on each vertex but is this all there is to it or am I missing something?
Hi, I'm reading Chapter 2-II of of Duderstadt & Hamilton's "Nuclear Reactor analysis". In the section "Differential scattering cross sections with upscattering" it is discussed the situation in which neutrons suffers elastic scattering collisions in a hydrogen gas at finite temperature T and the...
I recently thought it might be interesting to see if there were any online simulations or videos of Compton Scattering experiments. The search result yielded following:
Given the standard equation: $$1-\cos\theta_d=\frac{E_0 \Delta E}{E_1 E_2} ,$$ we should get a straight line with gradient...
If I have a material with some thickness , say 0.5 meters and I have an incoming gamma photon that undergoes Compton scattering. The gamma ray loses some energy and is shifted in angle with respect to it's original trajectory and leaves the material. The electron gaining KE in the interaction is...
Hello,
I am wondering why in all X-ray diffraction experiments used to probe or know the crystal structure of the solid they assume that the scattering process is elastic, e.g, if an X-ray with wave vector ##k\vec{n}## is incident on a sample, it will diffract with a wave vector ##k\vec{n}'## of...
Homework Statement:: Mathematics to understand Quantum Scattering Theory
Relevant Equations:: Suitable math book to understand Quantum Scattering Theory
I need to study Scattering theory from Introduction to Quantum Mechanics by David Griffith. But I think I need to study mathematics first...
Hello,
I plan to run an experiment using SAXS for in-situ solution phase reaction analysis. We will use a glass micro-fluidic chip due to experimental limitation reasons. I am looking for the optimal path length for these channels (fluid channel depth).
My understanding is that we need to...
I am just wondering how best to visualise a Compton scattering event. Since a photon has no mass, we can't exactly presume it's the same as two masses colliding even if at relativistic speeds.
Does the photon encounter some kind of force field as it approaches the stationary electron ? If so...
How can we understand T-matrix in two-body scattering? Especially term "leading order" in the text. In addition, how to understand the connection between fig2.3 and equation 2.24-2.26?
Thanks.
I came across the term scattering time in Simon's "The Oxford Solid State Physics".
Apparently it's supposed to be obvious because I can't find a definition anywhere but what is it? Why is so much stuff left undefined in solid state physics?
I have been studying scattering process in QFT, but i am stuck now because i can't understand how this integral was evaluated:
$$\int dp\space \frac{1}{\sqrt{p^2+c²}}\frac{1}{\sqrt{p^2+k²}}\space p² \space d\Omega \space \delta(E_{cm}-E_{1}-E_{2})$$$
Where Ecm = c + k, E1 is the factor in the...
When we learn about the scattering of a particle, the context is usually a charge shooting towards a Coulomb potential. With some assumptions, we can derive the scattering cross-section pretty reasonably. Therefore, the scattering cross-section of different elements in X-ray spectroscopy is...
Maybe we could use
(1) uncertainty principle
$\Delta E \Delta t = \hbar$
and get $\Delta E$ from the spetrum.
Or
(2) forced vibration model, then get the damping factor $\gamma$，
and get $Delta t = frac{1}{\gamma}$
So I can find the initial momentum using p=h/wave = 4.98 x 10-23. Now my problem is that I don't know the final momentum of the photon nor electron, I just know the photon is scattered at an angle of 34 degrees.
I know how to solve this problem if I was given the final wavelength of the light...
So the initial wavelength gives the total momentum, p=h/11.2p. Which is 59.161y.
Then I tried to substract the momentum from the scattered light to get the momentum of the electron.
59.161y-h/13.6p, which ends up being 0.4872 as the final answer, but the answer is supposed to be 0.77?
Hello everybody at the forum
I'm from Ukraine, I have Chemistry degree, and last year I began to self studying Quantum Mechanics.
I'm reading this article:
R. Garcia, A. Zozulya, and J. Stickney, “MATLAB codes for teaching quantum physics: Part 1,” [Online]. Available...
It is an open question. The professor asked us to find a suitable method to solve it with the help of a computer.
When I learned the Mie scattering, the equations are given for particles in homogenous medium. But now half of the particle is surrounded by glass while the other half by air...
Hello ,
Why does an incoming photon can only scatter from an electron if the electron is not bound top an atom ?
Because from what I know a bound electron can absorb a photon then be excited to a higher energy level and then re-emit a photon while transitioning back to it's previous energy...