What is Scattering: Definition and 915 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.

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  1. Wrichik Basu

    B What am I missing here? (QFT: ##e^- - p## scattering)

    I am currently reading Particle Physics by Palash Pal. In one place, the author shows the Feynman diagram for the electron-proton scattering: Then, he writes the Feynman amplitude for the process: $$i \mathcal{M} \ = \ \left[ \bar{u}(\vec{k'}) i e \gamma^\mu u(\vec{k}) \right]...
  2. jim421616

    I Can Compton scattering increase the energy of photons?

    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..." I thought Compton scattering could only decrease a photon's energy. What am I missing?
  3. JD_PM

    Nucleon-nucleon scattering; why can we assume ##l=0##?

    I have found the following explanation: Isn't ##l \hbar = mvR## (semi-classical argument) wrong? I'd state ##mvR = \sqrt{l(l+1)} \hbar## instead. Text is coming from Introduction to Nuclear Physics; Krane, pages 87 and 88.
  4. dRic2

    Scattering direction and probability

    Hi, I'm having some trouble understanding the following result. Let's immagine a collision of two point particles in which one can be considered at rest and suppose the scattering process viewed in center of mass frame is isotropic. Then the probability of one particles to be scattered in one...
  5. W

    I 1D scattering: Taylor expansion

    Hi all, I'm having a problem understanding a step in an arxiv paper (https://arxiv.org/pdf/0808.3566.pdf) and would like a bit of help. In equation (29) the authors have $$R = \frac{\sigma}{\sqrt{\pi}} \int dk \ e^{-(k - k_0)^2 \sigma^2} \ \Big( \frac{ k - \kappa}{ k+ \kappa} \Big)^2$$ where...
  6. W

    A Questions from Peskin & Schroeder 5.5 about Compton Scattering

    Hi! Just a couple questions on the Compton scattering calculation in P&S. I feel like I'm missing something very simple here but can't quite figure out what it is. On page 166, the amplitude to be evaluated is $$ i\mathcal M = -ie^2 \epsilon_\mu(k)\epsilon^*_\nu(k^\prime) u_R^\dagger(p^\prime)...
  7. W

    Work Check: Neutron Scattering

    Homework Statement Hi all, could someone assist me in checking through my work? Many thanks in advance! An image of the problem is attached below (problem 1b) Homework Equations Far field approximation of a scattered wavefunction: $$\psi_s (\vec{r}) \approx \Psi_i \ r^{\frac{1-d}{2} } \...
  8. JD_PM

    A What is the Vector Manipulation Formula for Elastic Scattering Angle?

    I was reading *Introduction to Nuclear Physics* by Krane and stumbled on the following (page 47): In Elastic scattering, the initial electron wave function is of the form ##e^{i k_i r}## (free particle of momentum ##p_i = \hbar k_i##). The scattered electron can also be regarded as a free...
  9. Rafiki

    [Compton scattering] Solving for wavelength

    Homework Statement Question: Determine the energy of the incident photon when the recoiled electrons energy is measured to 3 MeV. The angle between the incident photon and the scattered photon is 60°. Given and knowns: θ=60° (Angle between incident photon ##\gamma## and scattered photon...
  10. brotherbobby

    Alpha Particle Scattering and angular momentum

    Statement of the problem : "Using the definition L = r ##\times## p, prove that the direction of L is constant for an alpha (##\alpha##) particle whose scattering is shown in the diagram below. " Relevant equations : We are aware that the scattering takes place via a central force F = F(r)...
  11. dRic2

    Neutron moderation in a Hydrogen medium and scattering

    Hi, I'm reading chapter 6-3 of Lamarsh's book "Introduction to Nuclear Reactor Theory". Here it is discussed the very idealistic case of Hydrogen being used as a Moderator (without adsorption). The moderator is: - infinte - homogeneous - with uniformly distributed source emitting at constant...
  12. W

    I Assumptions made in stationary-state scattering

    Hi all, I recently started learning about quantum scattering in school and came across a few things I find confusing. Thanks in advance for any assistance! 1. Plane wave approximation to incident waves. In past QM courses, I kept reading that plane waves were not "physical" since they do not...
  13. JD_PM

    Size resolution limitation on Dynamic Light Scattering

    I have been looking online and it is stated to be 1nm, but these are posts around 6 years old: https://www.azonano.com/article.aspx?ArticleID=3662 https://www.researchgate.net/post/Whats_the_measurement_limit_of_dynamic_light_scattering I am wondering if the limiting resolution has improved...
  14. dRic2

    Questions about Neutron scattering theory

    Hi, I'm reading Lamarsh's book "Introduction to nuclear reactor theory" and in chapter two there is a brief description of neutron scattering theory. I have a few questions about it. 1) In the book the author says that it is easier to analyze the interaction process in the center of mass frame...
  15. G

    Conservation of angular momentum in scattering processes

    Greetings. So... let us consider a particle moving in the yz plane, coming from the infinite towards a region were a gravitational potential is appreciable. The Lagrangian of the system is \mathcal{L} = \frac{1}{2}\mu (\dot{r}^2+r^2{\dot \phi}^2) + \frac{G\,m\,M}{r} where \mu is the reduced...
  16. Dipra Irham

    Why Does a Prism Periscope Focus Light Instead of Scattering It?

    a prism is supposed to scatter light rays and separate it into rainbow,then why in a prism periscope the prism send light rays to a particular direction instead of scattering?
  17. M

    Form Factor for Scattering (like muons off of protons)

    Homework Statement Homework Equations N/A The Attempt at a Solution I am trying to complete the last part of this question, part 5(c). My professor has told me that the form factor $$F(q)\rightarrow1$$ as $$q\rightarrow0$$ but I am unsure how to show this. I believe that $$\lim_{{q...
  18. M

    On Rayleigh Scattering and UV Light Absorption

    I've read that UV light cannot "penetrate" the atmosphere as easily during winter. But what does this exactly mean? My hypothesis is that due to rayleigh scattering, since light with smaller wave lengths scatter more, the UV light doesn't end up reaching the surface of the Earth (i.e. gets...
  19. nomadreid

    I Compton scattering in a Feynman diagram

    Attempting to understand the following: Compton scattering can happen either (a) an electron could absorb a photon and later emit a photon, or (b) an electron could emit a photon and later absorb a photon. OK, the maths works out, but I am trying to get intuition on track. These two are...
  20. PlasMav

    E' vs. E_2 Neutron Scattering and Logarithmic Energy Loss

    Hello, I just had a little debate with my professor after taking my final exam. He had given us an additional formula sheet at the last second (hand written on the projector) which confused me. The question was a 7 MeV neutron collides with several U-238 atoms before reaching 2 MeV. How many...
  21. M

    B Electron scattering off of a nucleus

    If I'm scattering electrons off of an atomic nucleus, can I infer any information about the duration of time the electron was accelerating by looking at the wavelength of the emitted bremsstrahlung radiation? I am wondering if it would be possible to derive a time interval between electron...
  22. Radwan Parvez

    A Neutrino Electron Scattering In The Standard Model Approach

    Previously I posted a problem concerning Electron-neutrino scattering, but as I couldn't describe the problem clearly, so I am trying to post the problem using latex codes to present it in the correct way. For a couple of months, I am trying to calculate the invariant amplitude of the Neutrino...
  23. Radwan Parvez

    A Neutrino Electron Scattering In The Standard Model Approach

    For a couple of months, I am trying to calculate the invariant amplitude of the Neutrino electron scattering in the standard model (SM) approach where I am not considering any kind of approximation and using the SM propagator for W Boson and Z Boson. I tried to do as following, find out the...
  24. T

    How does the size between scatterers affect reflection?

    If a sound wave hits multiple scatterers spaced closer than the wavelength and moving fast but at different velocities how is the reflective beam is affected?
  25. YMMMA

    What are the frequency and speed of a photon after scattering

    Homework Statement Photons incident upon free electrons that are essen- tially at rest are scattered by the electrons. As a consequence, the electrons gain kinetic energy. How do the frequency and speed of the photons present after the scattering compare to those present before the scattering...
  26. C

    Quantum Books on scattering experiments

    I’ve been self-studying quantum mechanics for a while, and currently looking at scattering theory, using chapters in books by Shankar, Sakurai, and John R. Taylor’s Scattering Theory text. But was wondering if there are any good sources that relate the theory in these books to actual experiments...
  27. Javier Lopez

    I How can I use the NIST XCOM online tool to calculate X and Gamma shielding?

    In order to calculate X and Gamma shielding of I should like use the NIST XCOM online at https://physics.nist.gov/PhysRefData/Xcom/html/xcom1.html In the Xcom tool it is obtained a graph and table of scattering in cm2/g. In order to calculate as example the shielding from 1e19 gamma rays of...
  28. B

    Scattering Gel Effect on Velocity/Frequency of Light

    How would a gel with index of refraction 1.33 (~same as water) effect the velocity/frequency of incoming light assuming the material is a scattering medium with a scattering coefficient greater than zero?
  29. S

    Scattering from lossy medium whose refractive index is unity

    Consider a thin transparent plate surrounded by air. The plate's refractive index is exactly the same as the air's, but it does have a small loss (say of the order of 1%). Let the plate be vertical and normal to our "page" or your computer screen. A laser beam passes through the plate at an...
  30. nmsurobert

    Rayleigh Scattering calculation

    I've been trying to find a proof or a paper that goes into calculating why the sky is blue as opposed to the "the sky is blue because of scattering" explanation that all over the internet. I (think) understand the concept but I would like to see some numbers. I'm aware of the I = 1/lambda^4...
  31. P

    Compton Scattering- finding photon wavelength

    Homework Statement An electron moving to the left at 0.8c collides with an incoming photon moving to the right. After the collision, the electron is moving to the right at 0.6c and an outgoing photon moves to the left. What was the wavelength of the incoming photon? Homework Equations p=γmv...
  32. itoero

    Light propagation in water -- Is the scattering Rayleigh scattering?

    When light enters an ocean, the photons scatter elastic with water molecules yet the presence of opaque particles causes the depth to be limited. Is this scattering Rayleigh scattering? (like the scattering in our atmosphere) https://en.wikipedia.org/wiki/Rayleigh_scattering
  33. K

    Tree-level diagram Moller scattering

    Homework Statement If the electron and photon were spinless, in the non-relativistic limit we can write the Lagrangian as: $$L=-\frac{1}{2}\phi_e(\Box+m_e^2)\phi_e-\frac{1}{2}A_0\Box A_0+em_eA_0\phi_e\phi_e$$ For Moller scattering $$e^-e^- \to e^-e^- $$ Draw the three tree level diagrams...
  34. D

    Compton Scattering and Recoil Velocity

    Homework Statement A photon of wavelength ##\lambda_i = 200## pm hits an electron at rest, and is scattered exactly backwards. Find the approximate recoil velocity v of the electron using momentum conservation. Homework Equations Comptons Scattering: $$\lambda_f = \lambda_i...
  35. S

    I Massless Electron Compton Scattering: Energy of Outgoing Photon

    Hello! I found this problem where we are asked what happens to the energy of the outgoing photon in a Compton interaction, if the mass of the electron goes to zero and what is the physical intuition of it. So the formula is this: $$\lambda - \lambda_0 = \frac{h}{m_0 c}(1-cos \theta)$$ So when...
  36. L

    I Question about orbits and Kepler's problem

    I've been looking at the Kepler's problem, and it looks like your orbit (elliptic, parabolic or hyperbolic) are given in terms of energy and angular momentum. I was wondering: if I have a central attractive potential (such as the Sun) and a projectile starting from an infinite distance at a...
  37. amjad-sh

    Solving scattering problem including spin flip

    Homework Statement The Hamiltonian is given below: ##H=\frac {\mathbf p^2}{2m} -\frac {\partial^2_z}{2m} +V(z) +\gamma V'(z)(\hat{\mathbf z} \times \mathbf p)\cdot \vec{\sigma}## Where this term ## \gamma V'(z)(\hat{\mathbf z} \times \mathbf p)\cdot \vec{\sigma}## represents the spin orbit...
  38. A

    A Pp and pBARp scattering amplitudes

    Is A_pp(s,t)=A_pBARp(t,s) true based on crossing symmetry? Consider pp and pBARp elastic colissions (p + p -> p + p and p + BAR(p) -> p + BAR(p)). The scattering amplitudes are related by crossing in the following way: 1) A_pp(s,t)=A_pBARp(u,t) \simeq A_pBARp(-s-t,t) (energy large compared to...
  39. Glenn Rowe

    A Scalar-scalar scattering Feynman diagram

    I'm trying to work out the Feynman diagrams for scalar-scalar scattering using the Yukawa interaction, as given in Chapter 6 of Lahiri & Pal's A First Book of Quantum Field Theory. The interaction hamiltonian is $$\mathscr{H}_{I}=h:\overline{\psi}\psi\phi:$$ where ##\psi## is a fermion field and...
  40. K

    I Compton Scattering w/Moving Electron: Turner's Eq 5.29

    I beg your pardon for not writing out the math explicitly in the following. I started to do so, and realized that it would take me hours to debug my attemps at Latex! And I hope that the my explanation is clear enough that it's not needed. I've been working through R.E. Turner's "Relativity...
  41. R

    Rutherford scattering with Coulomb cutoff

    Hello, I am reading a section in Jackson discussing classical Rutherford scattering, and he mentions incorporating a cutoff in the Coulomb interaction in order to model electric screening. I am trying to understand how he applies this, as described below. The set up is basically the classic...
  42. C

    I Are resonances formed in the scattering of a baryon and a meson?

    Consider the following reaction of strong interaction (in a scattering process) $$n+\pi^+\to \Lambda_0+K^+\tag{1}$$ Then the particle ##\Lambda_0## formed decays with weak interaction $$\Lambda_0\to \pi^+ +p\tag{2}$$ For each decay process I measure the four momenta of ##K^+##, ##\pi^+##...
  43. A

    Scattering dynamics and viscosity

    I have been studying the statistical mechanics' viewpoint of fluid dynamics by considering the derivation of Navier-Stokes' equations from the Boltzmann equation involving the whole Chapman-Enskog expansion. It is clear that through this process, it is possible to account for the dependence of...
  44. CDL

    Determining a Scattering Cross Section (Quantum Mechanics)

    Homework Statement Consider scattering of a particle of mass ##m## on the potential $$U(r) = \begin{cases} 0, & r \geq b\\ W, & r < b \\ \end{cases}$$ Where ##W## is some arbitrary chosen constant, and the radius ##b## is considered a small parameter. Find the cross section ##\sigma## in the...
  45. CDL

    I Quantum Scattering Differential Probability

    I am reading Griffiths' Introduction to Quantum Mechanics, specifically the chapter on scattering. He is discussing the scenario where an incoming beam of particles scatter off an azimuthally symmetric target. At large separation ##r## from the scattering centre, the wavefunction for incoming...
  46. T

    Finite well scattering in the Born approximation

    I'm preparing for an exam and I expect this or a similar question to be on it, but I'm running into problems with using the Born approximation and optical theorem for scattering off of a finite well. 1. Homework Statement Calculate the cross sectional area σ for low energy scattering off of a...
  47. M

    A Fredholm scattering theory to quantum dissipative system

    Dear Community, I am trying to figure out what is happening in this article (https://journals.aps.org/prb/abstract/10.1103/PhysRevB.29.130) when they are calculating the Fredholm Determinant (Section IV). The basic idea is that you want to solve $$ k = |\frac{det(1+h_0)}{det'(1+h_0+v)}| $$...
  48. Soffie

    I What can elastic e-p scattering tell us about the proton?

    I'm already aware that deep inelastic scattering, when an electron of high energy is scattered from a proton, shows us that the proton consists of point-like particles (quarks). However, what does elastic electron proton scattering tell us about the proton? Presumably elastic proton scattering...
  49. R

    X-ray Flux density and a differential equation for photon scattering

    Homework Statement Consider interactions of a X-ray beam at a depth, x, within a material. The flux density is: density flux = $$\frac{I}{A}$$ where I is the intensity of the beam that cross a unit area A at right angles to the beam. Let dx be a small slice at the depth x and let dI(x) be the...
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