What is Cross section: Definition and 315 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. leVanw

    Conductor Cross Section: Small vs Large Copper Wire in 9V Battery Experiment

    I connected the small copper wire and the light to a 9V battery, the light came on, but when I changed to the large copper wire, the light did not light up.
  2. Rayan

    I Neutrino-atom interaction

    What happens generally when a neutrino/anti-neutrino collides with a light vs heavy atom? My guess is, since neutrinos have very low cross section, their interaction is weak and therefore it will be an elastic scattering! For example: $$ \overline{\nu} + He^3 \rightarrow \overline{\nu} + He^3...
  3. P

    This integration appeared in the reconstruction of cross section

    I am reading the Horatiu Nastase's Introduction to quantum field theory (https://professores.ift.unesp.br/ricardo.matheus/files/courses/2014tqc1/QFT1notes.pdf ) ( Attached file ) or Peskin, Schroeder's quantum field theory book, p.105, (4.77). Through p.176 ~ p. 177 in the Nastase's Note, he...
  4. DuckAmuck

    I Calc Ampl & Cross Sec: Electron + Positron to Photon + Z Boson

    Looking to calculate the amplitude and cross section of the process: electron + positron to photon + Z boson. Basically the annihilation resulting in Z + gamma rather than gamma +gamma. My question is mainly about how to deal with the polarization states with the Z boson, since there are 3 and...
  5. 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.
  6. Ranku

    I Cross Section & Mass: Is There a Relation?

    In the sentence "WIMP-nucleon cross sections of 1.2x10-47cm2 at 1 TeV/c2 WIMPs", there is a relationship between cross section and mass. Is there a general formula that relates the two quantities, in that if there is a certain cross section that means it will be associated with a certain mass?
  7. simonjech

    I Lorentz invariant phase space and cross section

    Can someone please explain to me how can we obtain this integral in eq. 5.27 from eq. 5.26? I quite do not understand how is it possible to make this adjustment and why the (p_(f))^2 appeared there in the numerator and also why a solid angle appeared there suddenly.
  8. greg_rack

    Engineering Analyzing Shear & Bending on Idealized Cross Section

    As you can see from the picture, the cross section to analyze is idealized and the boom areas resulting from this are given. For POINT A) all I did was: for determining the shear forces, integrating the shear flows over the sides to compute the vertical and horizontal contribution of each side...
  9. LUFER

    What is the Electromagnetic Cross Section in this plasma deposition process?

    What is Electromagnetic Cross Section? (shock section) Hello, I have a question regarding the manufacturing process of electronic components in the case of the silicon deposition and corrosion process. My biggest doubt is the behavior of the plasma interacting in the reactor, I don't know if...
  10. karmion

    A Cross section-temperature equivalence

    It's assumed that interaction rate between a species of particule m and l is expressed as: Γm=<nlσv>, where nl is the density of the species l, σ the cross-section of species m (=probability of interaction) and v the relative velocity between the two particles. It's also assumed that...
  11. Anava1001

    A Normalized differential cross section

    Hello, I know that this question might be a bit silly but I am confused about plotting a normalized differential cross section. Suppose that I have a histogram with the x-axis representing some observable X and the y-axis the number of events per bin. I want the y-axis to show the normalized...
  12. neilparker62

    B Cross section (?) of Great Pyramid from drone footage

    Following is a frame carefully chosen from this drone footage. At about 0:29 into the video the drone is directly in front of one of the four faces (if you know Cairo, you will know which one) and moving from left to right. At that point I have paused and 'frame-stepped' till the moment before...
  13. M

    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...
  14. M

    I Dependency of phase space generator to differential distributions

    I attatched an example plot where I created the histogram for the differential distribution with respect to the energy of the d-quark produced in the scattering process. My conception is that the phase space generator can "decide" how much of the available energy it assigns to the respective...
  15. grotiare

    Engineering Question about max stress on circular cross section with two moments

    I couldn't fit in the title, but this is with a hollow circular cross section So currently I am trying to figure what occurs when two, perpendicular bending moments are applied to a hollow circular cross section (one about the z axis, and the other about y). I know that if I was dealing with a...
  16. Johnstonator

    What would be the ideal cross section of an axially loaded cantilever beam?

    Pretty much the title. Just some brain teasers I'm trying to figure out. I can't think of how a cross section would come into play when it comes to axial loading. Buckling? Since the critical force for buckling is proportional to moment of inertia, so theoretically if I have a high moment of...
  17. B

    Round vs Square cross section tubing

    I want to make some beaching legs for my 30ft, 9T yacht... these are supports either side of the yacht that keep it upright when the tide goes out and it sits on its keel without falling from one side or the other. My question is this, would it be stronger to use sguare or round tube to do this...
  18. Amy_93

    I Statistic uncertainties in cross section plots - how to calculate?

    Hi there, I hope I chose the right forum for my question. So, basically, I'm doing an analysis measuring the number of signal particles in a certain momentum bin i, and doing two corrections: Nsig, i=M*(Nmeas, i-Nbkg, i) Here, M is a matrix covering PID correction and PID efficiencies, and...
  19. D

    I The 1/v law for U-235 cross section

    The cross section for fission of U-235 is much higher for slow, thermal neutrons than for fast neutrons, for which it is similar to the geometric area. The cross section for slow neutrons seems to decrease empirically like 1/v where v is the velocity of the neutron. What is the qualitative...
  20. Haorong Wu

    I Where does this formula for absorption cross section come from?

    My professor gave us a formula for absorption cross section, but he said he did not remember where he found it. The formula is given by $$\sigma_a =\frac {1} {| \mathbf E_i|^2} \int_V k \epsilon^{''}_r | \mathbf {E} |^2 dV = k \epsilon^{''}_r |\frac 3 {\epsilon_r +2}|^2 V.$$ Where does...
  21. R

    A Compton Recoil and the Electron Differential Cross Section

    Hi folks, My understanding of the Compton Effect is that maximum energy transfer to the electron takes place when the photon scattering angle is 180 degrees. For the following please reference Evans "The Atomic Nucleus" ...
  22. I

    Connecting Two 30x10mm2 Earth Busbars: Min. Conductor Cross Section

    I have two 30x10mm2 Earth busbars in switchboard, both are placed on insulators, but connected through various parts of switchboard (ground terminal, rails, door, mounting plate...) What is the minimal conductor cross section allowed for connecting this two busbars directly?
  23. B

    I Understanding Nuclear Fusion Cross Section Diagrams

    I'm working on programming a particle simulation that visually shows the nuclear fusion reaction rate of deuterium at different densities and temperatures, but I'm having trouble understanding exactly how nuclear fusion cross section diagrams are supposed to be interpreted. (The simulation...
  24. JD_PM

    I Understanding the (polarized) cross section for Compton Scattering by electrons

    I have specific questions, but let's first give context. Initially we have an electron with momentum ##p=(E, \vec p)## and spin state ##u_r (\vec p)## and a photon with momentum ##k=(\omega, \vec k)## and polarization state ##\epsilon_s (\vec k)##. Finally we have ##p'=(E', \vec p')##, ##u_r'...
  25. qnach

    A Software for cross section calculations using .cif files

    Is there any software available to calculate cross section using .cif file?
  26. H

    Matrix and cross section of the Xf -> Xf process

    The attempt at a solution follows as an attachment. If you are only interested in the solution without the derivation, look at page 1 and page 9.
  27. imselva

    Conduction heat transfer with varying cross section

    How to modify this Formula? and arrive at the solution. Q = -K(Th-Tc)A/thickness
  28. Adesh

    I How can generatrices be parallel to the y-axis?

    CONTEXT: We are finding the the buoyancy force on a boat which is upright in a still water (Fluid at rest) and the only gravity is acting as the external force. So, first we go for imaging a proper geometry of our boat. See this figure : For this figure the book writes: Fig 8 represents...
  29. K

    I Simple explanation for cross section ratio

    Hello! Is there any simple (i.e. using some physics arguments, without actually doing the math) explanation for why $$\sigma(pp \to \pi^+d)/\sigma(np\to\pi^0d)=2$$ where d is the deuteron? Thank you!
  30. P

    Easy tool to see a cross section?

    I need to visualize what the cross section is of an oval tube is at angles of 10 degrees, 20, 30 up to 60. Is there an easy way to do this online somewhere or is there a mechanical drawing trick that can be done to see this result?
  31. A

    Solving Cross Section Confusion: Adding Positive and Negative Ions

    ik that i have to add the positive and negative ions but the cross section (surface) confuses me how do i resolve this?
  32. W

    I Cross Section Formula in Peskin and Schroeder

    On page 105 of Peskin and Schroeder's book it says that the integral over ##d^2b## in the expression: $$d\sigma = \left(\Pi_f \frac{d^3 p_f}{(2\pi)^3}\frac{1}{2E_f}\right) \int d^2b\left(\Pi_{i=A,B} \int \frac{d^3 k_i}{(2\pi)^3}\frac{\phi_i(k_i)}{\sqrt{2E_i}} \int \frac{d^3...
  33. Diracobama2181

    How Do I Solve These Scattering Cross Section Problems?

    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...
  34. weningth

    A Cross section from subgraph in electron-proton DIS

    I am currently following R.K. Ellis et al.: QCD and Collider Physics, pp. 99 to understand how to arrive at the parton density functions starting from the matrix elements in electron-proton deep inelastic scattering (see figure below). But there seems to be a very fundamental concept that I...
  35. E

    A WW Cross section calculation

    Can anyone help me about cross section calculation of W+W->gamma>l+ l- (leptons), at the tree level? I am stuck to writing amplitude,after written Feynman rules, because of massive vector boson polarization states. How should I do?
  36. M

    Biology What are the vascular structures of this cucumber cross section?

    We were asked to label the vasculature structures of a cucumber cross section (complex tissue). I just wanted to know if my labels were accurate. Image attached 1. Xylem 2.— 3. Sieve elements 4. Phloem
  37. Arman777

    I Cross Section of DM: What Are the Particle Candidates?

    What are the cross sections of the DM particle candidates ?
  38. dRic2

    I Wave function of a scattered particle and cross section

    In Landau-Lifsits's book about non relativistic QM it is said that if I have a particle described by a plane wave ##\phi = e^{ikz}## (I think he choses the ##z## direction for simplicity) the wave function after the scattering event is (far from the scattering event) $$\psi \approx e^{ikz} +...
  39. U

    Radar Cross Section simulation with CST

    I'm trying to understand how CST measures the RCS of an object. If not specified by me, it gives me (with a very brief simulation even for complex objects) graphs, both 3D and 2D, entitled 'Bistatic RCS'. With this wording I think that there is an antenna in a different direction than the one...
  40. S

    Use of an Impact Test in the cross section design of a component

    If I have impact test data showing energy absorbed by notched specimen, how do I utilize this data while designing. In my case, i am trying to design the valve which closes by striking on valve seat, how do i use the impact test results for this design?
  41. S

    Automotive Design of a Valve stem cross section in a Steam turbine emergency valve

    I want to design cross section area required for valve stem when valve is closed under spring force. Valve stem should be designed for buckling load but I am unable to calculate buckling load coming due to impact force coming when valve bangs on valve seat. Valve is having concentric spring. Is...
  42. A

    A How do soft Pomerons become hard?

    The exchange of soft Pomerons (and Reggeons) (##\alpha_R(0)=0.55## and ##\alpha_P(0)=1.08##) seem to describe total hadron-hadron cross sections pretty well in the Regge limit. See, for example: https://arxiv.org/abs/hep-ph/9209205 In this limit, QCD is of very little use since the exchanged...
  43. Clara Chung

    Question about differential cross section

    I have attached the two pages in my notes and I have the following question. 1. Where have the n_t*l gone in 9.9? (According to 9.5 why do they disappear?) 2. Why J_s=sigma_tot J_i? The dimension of flux is per m^2 and sigma is per area too, the dimension is not right...
  44. A

    B Differential cross sections in Pythia

    Dear Users, I would like to ask you how can I plot d_sigma/d_omega and d_sigma/d_theta for any collision (for instance, proton and proton) using pythia event generator. I would be greatful if you could tell me how make it. Any ideas would be appreciated. Kind regards.
  45. C

    Effect of cross section shape of an iron core in a solenoid?

    I know the basic equations of a solenoid carrying a current, the consequences of having an iron core inside one, and how that derives from Ampere's law. But these suggest that the only figure of merit is the cross section area of an iron core and the solenoid, not their shape. Thinking in more...
  46. rpthomps

    I Interpretation of a cross section vs energy graph

    Hello. I am reading DeAngelis - Introduction to particle and astroparticle physics and I have come across a plot showing proton proton cross section vs energy. I am trying to reconcile the statement in the book that says cross section total = cross section elastic whenever there is no available...
  47. K

    I What is the cross section of a graviton?

    In particle physics there is usually a cross section for a particular particle . I came up with a cross section of 1.07 x 10^-42 m^2 for a graviton.
  48. K

    A Why does the cross section for Dark Matter decrease with increasing mass?

    Hello! In most papers that present exclusion plots as cross section versus mass, the plot has a specific shape in which mostly the cross section decreases with mass. I am a bit confused why. If you assume that the density and speed of DM is constant, shouldn't a higher mass (and hence a higher...
  49. Ajdin Palavric

    Using PDFs to Compute the Total Cross Section

    Homework Statement I would like to compute the total cross section of a lepton pair production using parton distribution functions. The main problem I am having is the numerical computation and the order of magnitude I am getting as a final answer, which so far definitely indicates that...
  50. parazit

    I The Maxwellian Averaged Cross Section

    Hi, Please forgive my ignorance but, can somebody please explain the Maxwellian Averaged Cross Section briefly and basically? Thank you in advance.