# Scattering cross section Definition and 11 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.

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1. ### Feynman rules and the tree level cross section of two scalar fields

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...

4. ### 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...
5. ### Finding the scattering cross section

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...
6. ### I Difference between absorption and scattering cross sections

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...
7. ### How to calculate required concentration of absorbing agent

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...
8. ### Do supersolids or BECs have higher fusion cross sections?

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...
9. ### What is the cross section?

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 Equations The Attempt at a Solution Part (a)[/B] These represent the neutral current scattering for the muon-neutrino...
10. ### Cross Section for e+e- in EM interaction - Is it the same?

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...
11. ### Zero cross section

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...