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.

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  1. emilmammadzada

    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. Hak

    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. emilmammadzada

    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. qnach

    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. Islam Nabil

    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. BlackPhysics

    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. D

    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. AotrsCommander

    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. J

    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. FEAnalyst

    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. Rifat amin

    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. L

    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.
  13. JD_PM

    I Understanding how to derive the cross-section formula in the CoM frame

    We work in natural units. Let's assume in this post that the differential cross-section of two particles that, after collision, yield ##N## particles is given by the following formula: $$d \sigma = (2\pi)^4 \delta^{(4)} (\sum p'_f - \sum p_i) \frac{1}{4 E_1 E_2 v_{rel}} \Pi_l (2m_l) \Pi_f...
  14. JD_PM

    A Understanding how to derive the differential cross-section formula

    Please let me make questions after showing what I am studying. We first consider two particles (they may be either leptons or photons) with initial (i.e. before collision) four momentum ##p_i = (E_i, \mathbf p_i)##, ##i=1,2##. These two collide and produce ##N## final particles with momentum...
  15. Joe3502

    Buoyancy with the Cross-Sectional Area of a Rectangle

    Hi all, My teacher assigned us a problem to do a few days ago and have attempted it many times, often leaving and coming back to see if I could figure it out. I imagine that you would take the cross-sectional area and multiply it by how far under the surface of the water the rectangular object...
  16. S

    Springy wire with custom cross-section

    This potato masher youtu.be/j5IXRT3uxbA?t=170 would be easier to use if the spring wire had a tear-drop shaped cross section, with the pointy edge facing downwards. But how much would it add to the cost and feasibility? Can standard machines be easily rejigged to make non-circular wire?
  17. A

    A Could the Odderon intercept be ##\alpha_\mathbb {O}(0)=0.813##?

    The directed percolation dynamical universality class is characterized by just three independent critical exponents. These exponents are (in a 3d space): $$\beta=\beta'=0.813(9)$$ $$\nu_\perp=0.584(5)$$ $$\nu_\parallel=1.110(10)$$ The latter two numbers are in close agreement with the (soft)...
  18. A

    MCNPX - problem in cross-section

    Why does mcnpx not recognize the shell when I crop the cell in half? I put on a lead shield. I put everything (covering everything) and it worked. I cut half and the shield stop of work, but the cell is there. 10 2 -0.9500 (-1 2 -3) #20 imp:p=1 VOL=149.2256511 $ espessura / thickness...
  19. Vigardo

    Wind loads for circular cross-section lattice structures?

    Dear experts, How should I compute the wind loads for a Shukhow tower, i.e. a circular cross-section steel lattice structure? The structural members should be rectangular or circular. I´ve been checking EUROCODEs EN 1991-1-4 (2005) and EN 1993-3-1 (2006) without success. Is there any other...
  20. A

    Area of Airfoil cross-section

    Not really sure if this thread belongs here but I am supposed to figure out the radius of gyration, section modulus, and Q values at the neutral axis for this symmetric wing cross section. The only problem is that I am not even really sure how to find the area of the cross section. i know that...
  21. O

    Where can I find d-d reaction cross-section data for higher energies?

    Hi, I have been searching d-d reaction cross-section at higher energies up to 10 MeV. I checked ENDF database, however, I could not find any data. Do anyone offer a source from which I can get d-d cross-section data? thanks in advance.
  22. Abhishek11235

    A Penrose paragraph on Bundle Cross-section?

    I am reading "Road to Reality" by Rogen Penrose. In chapter 15, Fibre and Gauge Connection ,while going through Clifford Bundle, he says: .""""...Of course, this in itself does not tell us why the Clifford bundle has no continuous cross-sections. To understand this it will be helpful to look at...
  23. S

    I Calculating E+e- -> μ+ μ- Cross Section

    Hello! When calculating the matrix element for (let's say) ##e^+e^- \to \mu^+ \mu^-##we have to average over initial spins and sum over final spins. I understand the motivation of this, but when the calculation is done, the sum is done for 2 cases: spin up and spin down, so you have to add 8...
  24. LeInvertedPenguine

    I Antiproton flux and cross-sections in antideuterium production

    Hello! I`m currently reading an article about antideuterium production and dark matter detection. The article often uses the term cross-section, like for example: “Assuming an annihilation cross section into a particular Standard Model Channel” and “Probe scattering cross sections through the...
  25. O

    Effective cross-section of catching a comet with the Sun

    Hello. 1. Homework Statement I have to find formula for effective cross-section (σ) of catching a comet with the Sun. I know mass of the Sun (M), radious of the Sun (R) and initial velocity (v) of the comet (at a big distance from the Sun). Homework Equations σ=πb^2, where b is on the...
  26. O

    Effective cross-section of catching a comet with the Sun

    Hello. 1. Homework Statement I have to find formula for effective cross-section (σ) of catching a comet with the Sun. I know mass of the Sun (M), radious of the Sun (R) and initial velocity (v) of the comet (at a big distance from the Sun). Homework Equations σ=πb^2, where b is on the...
  27. Dileep Ramisetty

    Tank outlet velocity exit pipe cross-section area dependence

    Sir, actually in a tank by the toricelli's law and also from bernoulli equation, we have outlet velocity as V= (2*g*H)^(1/2). In the case 2, I have closed the pipe exit partially with hand and observed a higher velocity than case 1, in practical. but when I applied the bernoulli...
  28. J

    I Cross-Section from Lab Frame to C-O-M Frame

    Dear Forum, I am searching for a good explanation and worked example that shows how to convert a inelastic cross-section from the lab frame to the center-of-mass frame. I need to first convert the energy (x-axis) from the lab frame to the COM frame. In addition, I need to convert the...
  29. sk1105

    Why is the electroweak cross-section zero at Z boson mass?

    The Standard Model formula for the cross-section of ##e^+e^-\rightarrow\mu^+\mu^-## is made up of 3 components: QED interactions, weak interactions, and electroweak interference. I understand the behaviour of the QED part, and the resonance that occurs in the weak part at ##\sqrt{s}=M_Z##, but...
  30. Destroxia

    Current through a bound cross-section

    Homework Statement [/B] The magnitude J of the current density in a certain wire with a circular cross section of radius R = 2.20 mm is given by J = (3.07 × 108)r2, with J in amperes per square meter and radial distance r in meters. What is the current through the outer section bounded by r =...
  31. binbagsss

    E+e- collison Resonance peaks cross-section partial widths

    Question: The Breit-Wigner cross-section for a resonance R is ## \sigma_{i \to f} =12\pi\frac{\Gamma_{R\to i} \Gamma_{R\to f}}{(s-M^{2})^{2}+M^{2}_{R}\Gamma^{2}_{R total}}## [1], where ##s## is the com energy squared, ##M_{R}## is the mass of the resonance , ##\Gamma_{R total}## is the total...
  32. Andropov

    D-shape cross-section of plasma in fusion reactors

    I was curious about why the plasma inside a modern fusion reactor (ITER, DIII-D) is modeled with a D-shaped cross section. From what I've read, it is more stable that way, but WHY is it more stable than a similar plasma flow with a circular cross-section? Thanks in advance (and sorry if I...
  33. W

    Differential cross-section for partonic collisions

    I am trying to calculate differential cross-section for partonic collisions (QCD) like q + q \rightarrow q +q q + \bar{q}\rightarrow q + q g + g \rightarrow g + g I can't find those calculations done anywhere, just the results and maybe some middle tips, that's all. As you may know those...
  34. C

    Scattering Cross-Section from a Central Force

    Homework Statement An object from space (like an asteroid) approaches Earth. A collision will occur if the scattering cross-section is less than π*Re2. If the distance of closest approach is much greater than Re, no collision would occur. Find an implicit expression for the cross-section in...
  35. J

    Differential Cross-Section

    Hello guys! I was wondering if you can help me out with the differential cross section. We set up an experiment to measure the DCS in gold of the bremsstrahlung emission by electrons. The goal is to determine: ## \frac{d\sigma}{dW d\Omega} ## (1) for a 1.9 MeV electron beam at an angle of...
  36. S

    Mutual-Inductance of Rogowski Coil (Toroid of Circular Cross-section)

    Homework Statement Calculate Mutual-inductance of a circular cross section toroid. circular cross-section radius :a toroid mean radius :R Previous attempt for self inductance :https://www.physicsforums.com/showthread.php?t=537149 Homework Equations B=μNI/(2pi(R+y))...
  37. G

    How cross-section area of single E-M wave looks like?

    This question has been asked probably many times, and is inspired by area that appears in denominator of energy flux unit [W/m^2]. From what i have read so far, i come to conclusion, that this post should, first of all, try to explain that this question makes some sense. First thing that...
  38. Einj

    Rutherford cross-section from QED

    Hi everyone. I have a question about the calculation of Rutherford cross section in the context of QED. I know how to compute it using the usual four potential: $$ A_\mu(q)=(\frac{e}{q^2},0,0,0) $$ and taking the matrix element to be: $$ \mathcal{M}=\bar u_{s'}(p')\gamma_\mu...
  39. MarkFL

    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. V

    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. M

    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. B

    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. MarkFL

    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. J

    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. H

    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. C

    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. Demon117

    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. I

    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. R

    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...
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