# What is Cross-section: Definition and 76 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.

View More On Wikipedia.org
1. ### Double differential cross section in Fluka

Dear experts, I would like to do a double differential cross section calculation for iron at 90 degrees and at 22 MeV in Fluka. What changes should I make in the input and output files of the application and what transformations should I make in order to see the double differential cross section...
2. ### Magnetic field in a solenoid with rectangular cross-sectional area

I was thinking of using magnetic monopoles, but I don't know how to do. I tried to calculate the magnetic flux through the cross section of the solenoid if a current ##I## flows through it. Magnetic induction inside can be given as ##B = \mu_0 n I##, whereas magnetic induction at a distance...
3. ### Product Cross Section For Zn66 in Geant4

Dear experts, I want to calculate the cross section (Product Crosssection) of the Ga66 element produced by sending deuteron to the Zn 66 element, which is my target in Geant 4.Is there a Geant4 sample file where I can do this calculation, so in which sample file can I calculate it? Do I need to...
4. ### A Differential cross section, double differential cross section, triple...

There are differential cross section, double differential cross section, triple DCS. What are the difference, and why is the names? Thanks.
5. ### I have a problem on my MCNP5 cross-section library

I have a problem with my MCNP5 cross-section library. Se and Te elements with atomic numbers; 34000 and 52000, respectively, have no neutron cross-section stored, either neutron contentious or neutron other, in the library, and so I can't run any input file that has any material of them because...
6. ### A cylinder with cross-section area A floats with its long axis vertical

Summary: A 5.0- cm -diameter cylinder floats in water. How much work must be done to push the cylinder 11 cm deeper into the water? F =Aρgx A 5.0- cm -diameter cylinder floats in water. How much work must be done to push the cylinder 11 cm deeper into the water? F =Aρgx x being the...
7. ### A "Cross-section" and "half-life" of excited states

Hello, I work with a spectrometer that does ionizations through laser 2+1 photons resonant ionization (a high power narrow bandwidth laser is tuned to a precise wavelenght so that it allows reaching an excited energy level of a particular element with the sum of two photons absorbed...
8. ### I Where does the Sol system lie in the cross-section of the Orion Spur?

So, I know that Sol lies roughly in the 25 000 light years from the core and from the edge of the galaxy and thus the approximate the position when seen from "above." But what a search today has not given me any idea of is where Sol is (thought/estimated to be) in relation to, well...
9. ### Electron moles present in wire cross-section

So I know current is just coulombs/second. Electrons are also in the unit of coulombs, so I can get coulombs to cancel. 7.9C/s/1.602E-29C = 4.93133E29 1/s Now I just need to get mol on top. There are 6.022E23 electron in a mol so 4.93133E29 1/s / 6.022E23 atoms/mol = 8.1889E5 mol/s. Now my...
10. ### Maximum shear stress in an assymetric cross-section

Hi, the formula for average shear stress in cross-section due to bending is simple: $$\tau=\frac{V}{A}$$ There’s also a formula for maximum shear stress in cross-section: $$\tau_{max}=\frac{VQ}{Ib}$$ But, from what I know, this equation is limited to symmetric cross-sections (rectangular, I...
11. ### Software for nuclear cross-section measurement and Irradiation yield

I work in research paper on medical isotope production. I need a software where i can measure the cross section and Irradiation Yield like TALYS and EMPIRE. If you ask me why i don't use TALYS then the reply is I can't install it on my PC. so i am looking for alternate software where i can do...
12. ### QED, Electron-Proton Scattering: Rosenbluth cross-section

Hello, this problem is causing headaches, it would be very helpful if you could tell me if you know of a book where you can solve it. Maybe my English is lousy because I use a translator. Thank you very much.

39. ### MHB Find Equation for Parabolic Mic Cross-Section | Miguel's Yahoo Q

Here is the question: I have posted a link there to this thread so the OP can see my work.
40. ### Torsion of a non-circular cross-section with more than one material

I am trying to understand how to tackle torsion of bars that are non-circular and two-material composites. I understand the process of finding the torsion constant for non-circular sections but I am not sure how the warping function changes across a material interface. For example, if I have...
41. ### Cross-section for elastic scattering?

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...
42. ### Torsion in a hollow beam cross-section

Homework Statement The problem is regarding the question on the attached file called 'QUESTION3.png' This is urgent so please reply if you can. Homework Equations The attempt is in the file attached. Is my procedure correct? Am I missing something or is something wrong? Also, how do...
43. ### MHB Ale's question at Yahoo Answers regarding a tunnel with parabolic cross-section

Here is the question: Here is a link to the question: This is another question about parabola? - Yahoo! Answers I have posted a link there so the OP can find my response.
44. ### Calculating EM field using only cross-section of past light cone?

If you want to know the value of the electromagnetic field at some point in space P at time t1, I assume that since EM is a relativistic theory, it should be possible to derive it using only the value of the field (along with charges, but let's say we are dealing with fields in free space) at an...
45. ### Solenoid geometry question: circular cross-section or rectangular?

Some Background I am working on a soccer robotics project called RoboCup (perhaps people here have heard of it), which revolves around building a fleet of autonomous soccer robots that play against each other (league website - http://small-size.informatik.uni-bremen.de/ [Broken]). The kicking...
46. ### Prove cross-section of elliptic paraboloid is a ellipse

Homework Statement a elliptic paraboloid is x^2/a^2+y^2/b^2<=(h-z)/h, 0<=z<=h, show that the horizontal cross-section at height z, is an ellipse Homework Equations The Attempt at a Solution i don't know how to prove this, i only know that the standard ellipse is...
47. B

### Bremstrahlung cross-section for nucleus and electrons

Homework Statement Explain what is meant by Bremsstrahlung. Which cross-section is higher for atoms with Z>1: Bremsstrahlung on the atomic nucleus or on the atomic electrons? Why? The Attempt at a Solution I explained what Bremsstrahlung was just by copying from the notes. I am not...
48. ### Mott's scattering cross-section formula

Homework Statement We were asked to derive the Mott's scattering cross section. Given by \sigma(\theta)=(\frac{1}{4k^{4}}) (\frac{1}{(\sin\frac{\theta}{2})^{4}} - \frac{1}{(\cos\frac{\theta}{2})^{4}}\cos[\frac{2}{k}\ln(\cot\frac{\theta}{2})]) I get it into this form (that was easy, lengthy...
49. ### Cross-Section in Nuclear Reactions: Explained by Iorfus

Hi! I need an help on short thesis I'm writing for an exam. It is about artificial radioactivitiy, and my professor has told me to treat the partial waves formalisms to calculate the cross-section of nuclear reactions. He told me to start that section with: "Cross section is the most...
50. ### Toroid of Circular Cross-section

Homework Statement A toroid of circular cross-section of radius a and mean radius r_{m}. Show that the inductance of this coil is given by L = μ_{r}μ_{o}N^{2}[r_{m}-(r_{m}^2-a^{2})^{1/2}]. Homework Equations The B-field of a toroid: B = μNI/2πr (phi-direction)The Attempt at a Solution Total...