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.
Our condition for scattering is based on the idea that the amplitude of the outcoming wave is maximal, when all atoms contribute to a constructive interference. By using the attached drawing a simple relationship between the phase change of the two beams are derived. But my, maybe stupid...
Bee Hossenfelder has proposed a new approach to QG phenomenology, involving new ways to look for signs that space-time arises from a fundamentally non-geometric theory.
The basic hypothesis is that if what looks like a geometric continuum actually arose from myriad nongeometric entities then...
Hi,
I am slightly confused regarding the termenology elastic and inelastic. My focus is on the interactions, Rayleigh, photoelectric, comptonscattering and pair production. I have read around the internet and have some question I did not fully got answered.
1) Is Elastic = Coherent and...
Hi All,
Following on from the last dumb question I asked...
Suppose you calculate the tree-level approximation to the elastic scattering of two charged fermions
to find that the result varies as ##\sim 1/t##, where t is the Mandelstam variable describing the squared momentum transfer in...
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I'm currently in a crash course on X-ray Diffraction and Scattering Theory, and I've reached a point where I have to learn about Bessel Functions, and how they can be used as solutions to integrals of certain functions which have no solution. Or at least, that's as much as I...
Homework Statement
In a Compton scattering experiment, a photon is scattered through an angle of 90.0deg, and the electron is scattered through an angle of 21.4deg. Determine the wavelength of the scattered photon
Homework Equations
Conservation of momentum and energy. p = h/lambda, E =...
Hello. I'm reviewing background information on Raman scattering and I've noticed that the polarizability scales with v+1 for Stokes transitions and v for anti-Stokes. Why is this and what assumptions are used in the derivation? An explanation or pointing me to a good reference would be...
I've been reading Coleman's notes and the book on QFT by Ticciati. There they both place a lot of emphasis on computing the scattering matrix S. I can follow their computations (using Wick's theorem etc.) but I don't really have a good understanding of what S actually tells you. Ticciati even...
Homework Statement
Incomming photon gives half of its energy to an electron during scatering. After scattering, photon is headed ##\phi=120^\circ## according to the original direction. What is the ##\lambda## of the incomming photon?
Homework Equations
\begin{align}
\Delta \lambda &=...
Homework Statement
The length of the photon waves which are under Compton scattering ( compton scattering is applied on them) is measured in the angle =90 degree.If ΔΛ/Λ is 1.5 %,what is the length of the waves of the falling photons?
Homework Equations
The Attempt at a Solution...
Hi there,
I am trying to calculate diffraction efficiencies of a lattice with the coupled wave theory. As material parameters the programm I got needs the atomic scattering factor f1 and f2. (see http://henke.lbl.gov/optical_constants/asf.html for elements)
I understood this seems to...
Hi there, I'm learning about solitons and chanced upon this pdf talking about the inverse scattering method. However, I'm stuck trying to derive the coefficients using the LAX method (pg 5 of the attached pdf or from http://arxiv.org/pdf/0905.4746.pdf). Hope that someone can help shed some light...
Hi All,
So the photoelectric effect is the phenomenon where an orbital electron fully absorbs an incoming photon (assuming the energy of the photon is greater than the binding energy of the electron) and is ejected from its shell. The electron can then undergo its own interactions in the...
Provide one of the following answers: PE,CS, BOTH, OR NEITHER.
PE if the statement applies only to Photoelectric Effect.
CS if the statement applies only to Compton Scattering
BOTH if the statement applies only to both the Photoelectric Effect and Compton Scattering.
NEITHER if the...
Hello.
I am currently studying scattering theory in detail for my BSc thesis, and I'm starting with Rayleigh scattering. I'm following Scattering of electromagnetic waves: theories and applications by L Tsang, J A Kong and K-H Ding, which is pretty much what I like in a science textbook...
I have been watching Susskind's lectures on Cosmology which are great. There is something that I can't wrap my head around.
I know that if we look far away enough into the past (about 100,000 years after the big bang I think he said) , the radiation that is being emitted comes from plasma and...
first question, would there be more rayleigh scattering on neon gas vs air?
im wondering if you have a tube of neon gas, and shine a laser through it, will the laser beam become visible? as opposed to shining a laser pointer around and only seeing the dot.
Homework Statement
Asked to calculate the relativistic correction, to the differential scattering cross section which is given by the equation below in terms of E, E0 and θ where E0= .511 MeV.
with 100MeV electrons from an Au nuclei at certain angles θ.
Homework Equations
Relativistic...
Hello!
Reading up on simulations of electromagnetic scattering with DG-FEM and trying some myself, I got stuck.
In some of papers I have read, a scattering field formulation is used, in which the total field is linearly decomposed in incident field and scattering field...
Has anyone read or seen any articles that might highlight the techniques of Stimulated Raman Scattering Spectroscopy? Or just any knowledge on the process they would be able to share? I am having a tough time getting a hold on the process and if anyone has any useful information or articles that...
I've got a question that asks what the maximum scattering angle in \nu_\mu e \rightarrow \nu_\mu e is. The electron is stationary in the lab frame and after the collision has E >> m_e.
The answer given is
\sqrt{\frac{2 m_e}{E_e}},
independent of the neutrino's energy. How can I get...
Homework Statement
What relations can you derive from isospin conservation for the cross sections of the following scattering processes:
K^{+} + p → K^{+} + p
K^{+} + n → K^{0} + p
K^{0} + n → K^{0} + n
The Attempt at a Solution
I do not really have my own solution as I've...
Homework Statement
Show that, for low energy photons scattered by ultrarelativistic electrons, the cange in frequency of the photon is given by
(v'-v) / v = [(Ω'-Ω).β] / [1-Ω'.β]
Homework Equations
The full/general form of Compton scattering is given by
v'/v = (1-Ω.β) /...
Homework Statement
Consider the spherical well such that V(r<a) = -V0 and V(r≥a) = 0. Calculate the l = 0 partial wave scattering cross section in the low energy limit for this potential.
Homework Equations
σ = \frac{4 \pi}{k^2} * \Sigma (2l+1)*sin^2(\delta_l)
The Attempt at a...
Hi Guys,
I am doing a bit of work with dynamic light scattering (DLS) data. It is one of the many areas of science where we encounter an inverse problem.
The forward problem is: For a known sized particle, calculate its scattered spectrum (that is easy). The inverse problem is: from the...
Homework Statement
Use the boundary conditions to show that
\frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}=\frac{k^2_1}{k^2_2}
Homework Equations
A+B=C+D and k_{1}A- k_{1}B = k_{2}C- k_{2}D
C e^{i k_{2}L}+D e^{- ik_{2}L} = F e^{i k_{1}L} and k_{2}C e^{ ik_{2}L}- k_{2}D e^{-i...
Homework Statement
In the non-relativistic limit, the equation for Compton scattering is
v' / v = 1 / (1+x) where x = (hv/mc2)(1-Ω.Ω')
Show that the change in frequency Δv = v' - v is given by
Δv / v = -x
Homework Equations
The Attempt at a Solution
I rearranged the...
Homework Statement
A two-dimensional rectangular crystal has a unit cell with sides a 6.28Å and
b 3.14Å. A beam of monochromatic neutrons of wavelength 5.0 Å is used to
examine the crystal.
Using either the Laue condition for diffraction or Bragg's Law, determine
whether it would be...
Homework Statement
Reading a textbook, I come across a situation where an electron is scattered off a nucleus. The book says p.P = p'.P', where p is the momentum of the electron and P is the momentum of the nucleus.
I don't understand how it gets the conservation of scalar product.
It's steps...
Well I am sure this is a lame question, but I am stuck over it for hours. I'm working on Bjorken, Drell book, and I'm trying to calculate the extreme relativistic differential cross section for electron-positron scattering.
Well, I have evaluated the cross section up to my attachment's...
Homework Statement
Given that the scattering amplitude off of a single atom is f_{1}(\vec{q}), find the scattering amplitude for 1) four atoms each placed in the corner of a square of length a, and 2) two atoms a distance d apart
Homework Equations
The total scattering amplitude can...
Hi all!
I have been told that if an unpolarized photon hits an electron in a Thomson scattering the outcoming photon will be polarized because of the electron's spin. I didn't understand what it means, nor do I get how an electron reacts to an unpolarized photon: in Classical Electrodynamics...
I'm testing my faith in the photon. I understand that energy levels are quantized, and I understand that the EM field carries momentum. I want to make sure the idea of a photon is necessary to intuitively understand the observations.
I am focused on compton scattering of a photon and an...
Hello PF people,
Homework Statement
In a Compton scattering event, after the collision, the Photon has an energy of 0.12 MeV
and the Electron has an energy of 0.04 MeV. Find the following:
i) The Wavelength of the photon before the collision.
ii) The scattering angle for the photon...
I was reading Wikipedia article on Rayleigh scattering and came upon this:
"...the major constituent of the atmosphere, nitrogen, has a Rayleigh cross section of 5.1×10^(−31) m^2 at a wavelength of 532 nm (green light). This means that at atmospheric pressure, about a fraction 10^(−5) of...
Consider a plane sound wave (\varphi^i) incident up on a solid object . The object will scatter this incident wave. Let this scattered wave pass through an interface separating two different fluids (say with sound speeds c1 and c2). Now at the interface, is the scattered velocity potential...
Homework Statement
A photon carrying energy of 40keV scatters from an electron initially at rest. what is the maximum energy the electron can have?
Homework Equations
The Attempt at a Solution
I tried using conservation of energy
Initial: 40keV (energy of photon) + mc^2...
I'm looking at scattering theory and eventually the Born approximation... In the notes I am reading it says we want to solve the Schrodinger equation written in the form:
##\left(\nabla ^2+k^2\right)\psi =V \psi##
Of which there are two solutions, the homogeneous solution which tends to...
Homework Statement
Consider a blackbody contain atoms that typically produce photons with energy of about 7eV. Estimate the number of photon-electron collision each photon undergoes before it escape the object. Assume the blackbody has a temperature of 1000K.
Homework Equations
λ2 - λ1...
I apologize for not following the template, but it doesn't really fit. I would have posted it elsewhere but as it's for academic purposes I think it has to be here. Please excuse me if I'm wrong.
I'm a high schooler working on a project, and I was planning to send ≈3 cm microwaves through an...
Homework Statement
I need to give scattering amplitude f(θ) in Born approximation to the first order in the case of delta function scattering potential δ(r). The problem is in spherical coordinate and I'll give major equation concerned.Homework Equations
The equation for scattering amplitude is...
I understand that in elastic scattering, the incident particle leaves the interaction with the same magnitude of momentum it had initially. But, can there also be a target particle recoil in this case? If the kinetic energy of the incident particle is conserved, how does the target particle...
Homework Statement
Okay, so here's the problem:
In a Compton scattering experiment, a photon is scattered through an angle of 90.0 and the
electron is set into motion in a direction at an angle of 20.0 to the original direction of the
photon.
(a) Explain how this information is...
Hey all,
Anyone know if there is a δt to Compton scattering or is it an instantaneous event, entertaining classical physics...billiard balls colliding in an elastic collision.
Cheers
What is the difference between the two ?
Maybe that in the photoelectric effect all of the energy of a photon is absorbed by the electrons ? Is that it ?
In Compton scattering, only part of the energy is absorbed hence there is a photon of lower frequency emitted !
OR
Maybe in the...
Homework Statement
Determine the mass of the virtual photon in each of the lowest-order diagrams for Bhabha scattering (assume the electron and positron are at rest). What is its velocity? (Note that these answers would be impossible for real photons)
Note: You can "just write down" the...
I am looking at a 1-d quantum system with a delta-potential barrier in the centre (at x = 0) and an infinitely high wall on one side of this barrier (at x = -a), while the system is open on the other side.
So the potential V is equal to:
V = κ\delta(x) at x = 0, κ being some constant and δ...
Homework Statement
The scattering amplidtude, F, of a, by a crystal, diffracted beam is defined to be:
(1) F=\sum{_\vec{G}}\int n_{\vec{G}}e^{i(\vec{G}-\delta\vec{k})\cdot \vec{r}}\mathrm{d}V
The integral is over all the volumeelements, dV, of the crystal.
n_{\vec{G}} is the local...
I have a very trivial question to ask and it would be great if someone could
help me in this.
The statement that '3-point amplitudes' and the location of poles are sufficient to
determine any n-point amplitude at tree level is confusing to me. Don't I also need to know
4-point amlitudes, for...