What is Scattering cross section: Definition and 23 Discussions
In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). For example, the Rutherford cross-section is a measure of probability that an alpha-particle will be deflected by a given angle during a collision with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of transverse area. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.
In classical physics, this probability often converges to a deterministic proportion of excitation energy involved in the process, so that, for example, with light scattering off of a particle, the cross section specifies the amount of optical power scattered from light of a given irradiance (power per area). It is important to note that although the cross section has the same units as area, the cross section may not necessarily correspond to the actual physical size of the target given by other forms of measurement. It is not uncommon for the actual cross-sectional area of a scattering object to be much larger or smaller than the cross section relative to some physical process. For example, plasmonic nanoparticles can have light scattering cross sections for particular frequencies that are much larger than their actual cross-sectional areas.
When two discrete particles interact in classical physics, their mutual cross section is the area transverse to their relative motion within which they must meet in order to scatter from each other. If the particles are hard inelastic spheres that interact only upon contact, their scattering cross section is related to their geometric size. If the particles interact through some action-at-a-distance force, such as electromagnetism or gravity, their scattering cross section is generally larger than their geometric size.
When a cross section is specified as the differential limit of a function of some final-state variable, such as particle angle or energy, it is called a differential cross section (see detailed discussion below). When a cross section is integrated over all scattering angles (and possibly other variables), it is called a total cross section or integrated total cross section. For example, in Rayleigh scattering, the intensity scattered at the forward and backward angles is greater than the intensity scattered sideways, so the forward differential scattering cross section is greater than the perpendicular differential cross section, and by adding all of the infinitesimal cross sections over the whole range of angles with integral calculus, we can find the total cross section.
Scattering cross sections may be defined in nuclear, atomic, and particle physics for collisions of accelerated beams of one type of particle with targets (either stationary or moving) of a second type of particle. The probability for any given reaction to occur is in proportion to its cross section. Thus, specifying the cross section for a given reaction is a proxy for stating the probability that a given scattering process will occur.
The measured reaction rate of a given process depends strongly on experimental variables such as the density of the target material, the intensity of the beam, the detection efficiency of the apparatus, or the angle setting of the detection apparatus. However, these quantities can be factored away, allowing measurement of the underlying two-particle collisional cross section.
Differential and total scattering cross sections are among the most important measurable quantities in nuclear, atomic, and particle physics.
Hi there. I'm trying to solve the problem mentioned above, the thing is I'm truly lost and I don't know how to start solving this problem. Sorry if I don't have a concrete attempt at a solution. How do I derive the Feynman rules for this Lagrangian? What I think happens is that in momentum...
a) I have $$d\sigma=-\beta sin(\theta)d(\theta)+2\gamma sin(\theta)cos(\theta) d\theta$$
and $$d \Omega=2\pi sin(\theta) d \theta$$
so $$\frac{d\sigma}{d \Omega}=-\frac{\beta}{2\pi}+2\gamma cos(\theta)=|f(\theta)|^2$$
b) $$\sigma(\theta)=\alpha+\beta cos(\theta)+\gamma...
Homework Statement
Consider scattering of a particle of mass ##m## on the potential
$$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...
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...
Homework Statement
In an experiment carried out with a beam of thermal neutrons it is found that on traversing a 2mm thick foil of 197Au, some 70% of the neutrons are removed. What is the total thermal neutron cross-section for this isotope of gold? Comment on the result of the cross-section...
Hi. I'm trying to model the attenuation (extinction) of a weak laser through a gas sample using the Beer-Lambert law. I've found that the attenuation cross section can be written as the sum of both a scattering and absorption cross section, however I'm having difficulty finding a source that...
Hi All,
I am designing an optical solid phantom to represent tissue optical properties (scattering and absorption coefficients).
I know what should be the optical properties of tissue but I don't how much absorbing agent should I add to the mixture so that the phantom exhibit my desired...
The Lawson criterion suggests that a chain fusion reaction will only occur in a confined plasma. Since it's a product of temperature and pressure (or density) a chain reaction would be virtually impossible in a cold target at pressures attainable in a lab.
Likewise, the Coulomb barrier makes it...
Homework Statement
[/B]
(a) Find the ratio of cross sections.
(b) Find the cross section for electron-neutrino scattering by first writing down relevant factors.
Homework EquationsThe Attempt at a Solution
Part (a)[/B]
These represent the neutral current scattering for the muon-neutrino and...
I was studying my notes and specifically for the ##e^+e^- \rightarrow \mu^+ \mu^-## process, cross section is given by
\sigma = \frac{4\pi}{3} \left( \frac{\alpha \hbar c}{W} \right)^2
where ##\alpha = \frac{g_{EM}^2}{4\pi}## and ##W## is the centre of mass energy.
Is this the same for...
Homework Statement
I am making an old exam of a particle physics course, and i know how to calculate the cross section for example for
bhabha or moller scattering.
now one of the questions on the old exam is:
Explain why e-+ e+ -> γ is zero, but i am not sure why this is, can someone explain...
Homework Statement
Why does ## \frac{ e^+ + e^- \rightarrow \mu^+ + \mu^- }{e^+ + e^- \rightarrow \tau^+ + \tau^- } \rightarrow 1## at high energies?
Would it be the same if it was ## \frac{ e^+ + e^- \rightarrow \mu^+ + \mu^- }{e^+ + e^- \rightarrow e^+ + e^- }##?
Homework EquationsThe...
Homework Statement
Using the Eikonal approximation
(1) Determine the expression for the total scattering cross section of a particle in a potential V(r)
(2) Using this result, compute the total scattered cross section for the following potential.
V(r)=
\begin{cases}
V_0, \text{for } r < a \\...
Hi,
I am self-teaching Quantum Elctrodynamics, and have come across something which I do not understand. I would appreciate feedback from anyone on this specific issue from Atchison & Hey, "Guage Theories in Particle Physics" pg 238-239:
In calculating the u-channel electron-muon...
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...
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...
I'm just wondering what the difference is between a cross section and a scattering cross section? Or is there any? I can't seem to find anywhere that clears it up, in fact there's a whole section on scattering cross sections in Kibble and Berkshire but they don't define it once :P
I do not understand the interpretation of the http://hyperphysics.phy-astr.gsu.edu/hbase/rutsca.html" .
To me, that equation says:
(1) for a given θ, the proportion of particles exiting at θ does NOT depend on mass or charge;
(2) if you integrated over all possible scattering angles, you...
hi
how to calculate the traces of product of Dirac matrices in QED.
i want caculate crossection of process scattering in QED. a program to calculate it
Homework Statement
Integrate the rutherford cross section over the backward hemisphere to get 4pi(sigma0(E))
Homework Equations
Rutherford cross section is sigma0(E)/sin^4(theta/2)
The Attempt at a Solution
When I integrate this with the limits pi/2 to pi i get sigma0(E)*(8/3) i...
Not technically homework, just something I wanted to see if I could do.
Homework Statement
Find the differential cross section for the interaction between an electron and a photon via compton scattering. Basically, I'm just after calculating the matrix (s-matrix?/amplitude?) for the s-channel...