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.
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...
If we were to consider a nucleon-nucleon interaction:
We know that the incident wave (plane wave) is ψ= Ae^{ikz}, propagating in z direction
But for some mathematical facilities, we tend to use spherical coordinates, the wave becomes = \frac{A}{2ik}[e^{ikr}/r - e^{-ikr}/r]
How come...
hi All,
We know from QM that black bodies at temperature T emits light in a well stabilished patern.
Now what if the body has color? Which is the emission patern of a green snooker ball for example, at temperature T?
When scattering white light we see this ball green because it absorbs...
Hello everyone
I have been supplied with this eqn
n=\frac{Nat}{16r^2}(\frac{2Ze^2}{4\pi\epsilon_0E_K})^2cosec^4(\frac{\phi}{2})
for Rutherford scattering.
N is the number of alpha particles incident on a unit area of foil
t is the thickness of the foil
a is the number of atoms...
ee --->e+e+ scattering
Homework Statement
I have come across the following scattering : e-e- ---->e+e+
Does anyone know the name of this scattering ?
Do you know of any book describing simililar lepton scatterings?
Thank you
Homework Equations
The Attempt at a Solution
Hello,
I am trying to understand the idea of using analytic continuation to find bound states in a scattering problem. What do the poles of the reflection coefficent have to do with bound states? In a problem that my quantum professor did in class (from a previous final), we looked at the 1D...
Why Thomson scattering calls for a "size-changing" electron?
From my limited understanding of Thomson scattering, it only works for wavelengths comparable to the size of the electron. Because scattering was observed at a variety of wavelengths, it was assumed that the size of the electron must...
Hi,
I can't seem to find any straightforward information on this. I know wave transmission does not change the incident wave's phase, and wave reflection shifts it by $\pi$ if the wave is reflected by a denser medium than the one it is in...
But what happens to the phase when the wave undergoes...
I'm learning scattering theory from Griffiths' book, and I don't really understand the meaning of differential cross section; it's one of those things that I find hard to conceptualize and give a physical meaning to. The most intuitive description he gives is "the proportionality factor between...
Homework Statement
In the Compton scattering, a photon of wavelength λ collides with an electron at rest, and a new photon of wavelength λ' emerges at an angle θ. Find λ' y θ.
Energy of incident photon Ei = 1 MeV
Energy of scattered electron Ee = 0.32 MeV
Homework Equations
E =...
Homework Statement
The atmopshere allows all the colours of white light except the blue one and instead absorbs it. It is then scattered as blue light. However, I don't get why we would see it as blue. Won't the scattered light overlap all the other colours that were not refracted? So...
Homework Statement
It is desired to study the low-lying excited states of 35Cl (1.219, 1.763, 2.646, 2.694, 3.003, 3.163 MeV) through the 32S (alpha,proton) reaction. a) With incident alpha particles of 5.000 MeV, which of these excited states can be reached? b) Again with 5.000 MeV incident...
Homework Statement
I'm studying scattering from a rough surface, and my textbook defines h(x,y) as a small vertical deviation from a flat surface. Then they proceed calculations by assuming that the height difference between two points h(x,y)-h(x',y')=some f(x-x', y-y'), i.e. it depends only...
Hello again,
My question is on determining the scattering amplitude via time-dependent perturbation theory (first-order) for a given potential - I believe the perturbation potential is modeled due to some interaction between two scalar particles and has form:
\delta V=\lambda...
Homework Statement
The problem is to get the classical turning point as a function of the impact parameter b for the Lennard-Jones potential.
Homework Equations
The Lennard-Jones potential is given as [itex]V(r)=4\epsilon[(\frac{\sigma}{r})^{12}-(\frac{\sigma}{r})^6][\itex].
The effective...
Homework Statement
A certain crystal has a set of planes 0.33 nm apart. A beam of neutrons strikes the crystal at normal incidence and the first maximum of the diffraction pattern occurs at ∅= 38°. What is the de Broglie wavelength of the neutrons?
Homework Equations
nλ = Dsin∅ where D...
Hi. I am new to the forum, If I am missing something, please kindly remind me.
Homework Statement
Given/Known:
- A photon with Energy Eγ, momentum pγ hit an atom with mass M.
- The photon is perfectly elastic scattered at angle \theta
Problem: Find recoil energy
Homework Equations...
Homework Statement
Given variables and data: flux of alpha particles;Z; T-kinetic energy of the flux;
t-thickness of the target.I have to calculate the number of alpha particles which are
scattered in angle θ>60 degrees.
Homework Equations
1) Is my formula correct ( see below) if I am...
Hi everyone,
Really struggling to find anything on the internet to solve this problem. I really thought it would be an easy plug and chug equation..but I can't find it anywhere.
Basically, I was asked to find what the maximum and average energy of secondary electrons produced by 2 MeV...
So during neutron scattering in a crystal, a neutron can interact with 0, 1, or more phonons. First of all, what is the actual mechanism by which they interact? My textbook just kind of glosses over that.
Second of all, when a neutron goes in it can absorb a phonon and come out with more...
Determine scattering amplitude for atomic charge which is "spread" as wavefunction
Homework Statement
Derive the scattering amplitude and differential cross section for Rutherford scattering (done this). Now rederive the same quantities for the atomic charge which is "spread" with the...
Homework Statement
Consider the 1D potential V(x) such that V(x)=0 for x<0 and V(x) = V for x>0 and assume that a wave packet with energy E0=p20/2m<V is incident on the barrier from the left. Calculate in terms of E0 and V the difference in time between the arrival of the incident packet at...
I'm trying to learn scattering theory in quantum mechanics. and I'm trying to decide between Sakurai, Merzbacher and Landau.
I heard good things about Landau's books but I never looked at them.
any advice?
Homework Statement
I'm taking a graduate level course in classical mechanics that uses Goldstein's book. We are currently discussing scattering in a central field in chapter 3. Here are two problems that might be very basic/standard scattering problems, yet I'm not how to proceed or get...
Homework Statement
In Compton scattering,how much energy must the photon have in order for
the scattered electron to achieve relativistic velocity?
Homework Equations
Compton scattering formula: $$λ'-λ=\frac{h}{mc}(1-cosθ)$$
##E=\frac{h}{λ}##,conservation of mass and momentum,possibly...
Homework Statement
X-ray photons of wavelength 0.02480 nm are incident on a target and the compton-scattered photons are observed at 90 degrees.(a) What is the wavelength of the scattered photons?(b) What is the momentum of the incident photon and scattered photon? (c) What is the kinetic...
Homework Statement
Consider Compton scattering of a photon by a moving electron. Before the collision the photon has a wavelength λ and is moving in the positive x direction. The electron is moving in the negative x direction with a total energy E ( including rest energy mc^2). The photon and...
Dear all,
I just started learning about the Monte-Carlo methods of simulating particle interactions. I would like to ask a question about simulating potential scattering. In particular I think that the simulating scattering by Coulomb potential, and writing a corresponding MC test program might...
Homework Statement
Low-energy (s-wave) neutrons are scattered from protons, and the distribution of recoil
protons is observed and analyzed. Let the neutron scattering angle be \Theta in the laboratory
coordinate system, and let the incident neutron kinetic energy be Tn. Assume that mp =...
I have some basic doubts in the alpha ray scattering experiment by Rutherford and his students way back in 1909.
1.In the formula for the distance of the closest approach, the term velocity of the alpha particle and the charge of the gold nucleus appears. How did they measure the velocity of...
Homework Statement
Hello everyone,
I've been struggling to understand the relationship between two algebraic forms of the scattering function used in the Mie solution for light scattered by (transparent) spheres. I think there's some use being made of Legendre function identities, but I've...
In field theory:
[H,P]=0
So shouldn't that mean there can be no scattering? If you have momentum state |p1p2> then it is an eigenvalue of P with eigenvalue p1+p2. But it should be a simultaneous eigenstate of H too, so
e^(-iHt)|p1p2>= |p1p2> up to a phase factor.
But in general...
Hi everyone, I'm trying to get my head around scattering still. The books I've been looking at derive it, but then kind of skip some steps when they actually do problems with it. This is long but I'd really love it if someone could help me understand!
From what I can tell, this seems to be the...
Hi, I'm reading about the partial wave expansion in Shankar. In his method, we expand the incident plane wave (he chooses it such that it's coming in along the z axis, and using spherical coordinates) using the Legendre polynomials:
e^{ikr cos(\theta)} = \sum _{l = 0} ^\infty i^l (2l + 1)...
Hi,everyone!I have a problem!As known to us all,in Rutherford scattering experiment α rays are used to bomb gold foil, and most of them pass through the gold foil.But today I read something about the characteristics of α particles,the book says that you can stop α rays with a piece of paper...
Hi,
Those of you familar with dynamic light scattering (DLS), will know that a common method used to obtain a particle size distribution is via a laplace inversion of the autocorrelation function.
What I want to know is why? What does Laplace space have to do with DLS (I've only learned...
Homework Statement
By extrapolating the Fricdmann equations back in time, they discovered that the energy density of this radiation field must have initially considerably exceeded that of matter (as defined by E = mc^2). Radiation density is the amount of energy in a given volume of space...
Homework Statement
Take the case of elastic scattering (A+B -> A+B); if particle A carries energy EA', and scatters at an angle θ, in the CM (center of mass/momentum frame), what is its energy in the Breit* frame? Find the velocity of the Breit frame (magnitude and direction) relative to the...
I am trying to understand why radio waves are not greatly attenuated by the atmosphere due to scattering or absorption? I have tried searching the internet and can't find any satisfactory answers. Please help.
Oh and does this property somehow relate to why they are used to transmit information...
Elastic scattering from a bound electron is classically described by considering the driven, damped harmonic oscillator model for the motion of a bound electron in a classical em-wave. The (non-relativistic) equation of motion is written as...
Hi all. I'm studying deep inelastic cross section in parton model. In particular I'm referring to Halzen-Martin's "Quarks and leptons" section 8.5, but I think this is a quite generale procedure.
In studying the deep inelastic scattering by e- on proton it cuts off the electron part and work...
To calculate the intensity of the scattered radiation from a crystal after irradiating with X-rays, one can add up all electromagnetic fields of the oscillating electrons (calculated using the Liénard–Wiechert potential). Taking the time-average of the norm of the Poynting vector of the...
Inelastic scattering of Xray photons from electrons give them a wavelength shift, the Compton effect. The shift is inverse proportional with the mass of the electron. Now, if visible light scatters inelastic from electrons in graphene what will be the wavelength shift? The electrons in graphene...
I was studying Rayleigh Scattering.
The theory says that Rayleigh Scattering is approximated to x<<1 where x=(2*pi*r)/lambda
where r is the radius of the particle scattering light and
lambda is relative scattering wavelength of light.
lambda = wavelength of light / refractive index of...
I understand that in photoelectric effect, the energy of the whole photon is absorbed, freeing an electron. I don't understand why in the case of Compton scattering, the higher energy photon lost part of its energy instead of transferring the whole of its energy to the electron as in...
I've been reading a few books on scattering of light from particles, in particular mie scattering of cylinders. At first I want to look at infinite cylinders, then finite cylinders once I understand a bit better.
The problem is that all of the books I've looked at treat the problem where...
Homework Statement
Evaluate the triplet S-wave (l = 0) phase shift in n-p scattering at low energy assuming the interaction potential is given by a square well of depth V0 = 38.5 MeV and width b = 1.73 fm. Deduce also the value of the triplet scattering length.
Homework Equations...
How do particle scattering cross sections scale with energy in colliders?
Particularly photons, electrons, protons, and gold or lead nucleii?
(If necessary, break this into four separate questions.)
It is stated that due to the Heisenberg uncertainty principle, it takes more energy to...