Cross section Definition and 315 Threads

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. E

    What is the connection between path integrals and cross sections?

    Hey folks, i am currently making myself familiar with the path integral in high energy physics by reading Lewis Ryder's QFT book. I do have a question however, since i do not really understand the connection between the path integral and the cross section of a process. Are they only related...
  2. E

    Calculating Radar Cross Section

    I am trying to write a program to numerically calculate RCS using geometrical optics (or some form of it). Basically my idea was to cast a bunch of rays from an emitting object (in my code it is a 1 m^2 plate), find where they intersect a surface, reflect the rays off of this surface and see if...
  3. Q_Goest

    Seeing Double: Superimposing a Real Cross Section onto a CAD Model

    This was pretty cool. I had to draw the cross section of a quad seal (on CAD). It’s basically an O-ring with a cross section that looks like a deformed square with these lobes on the corners. It looks like this: http://www.daemar.com/images/Quad-Ring-PartingLine.jpg But I don’t have...
  4. D

    Finding the shear centre of a non-homogeneous cross section cross

    for the following cross section the ratio Eb/Ep=30 find the shear centre of the cross section ------------------------------------------- first of all i need to find the equivalent cross section, which will be the same except that the horizontal parts will be of length n*L=30*1=30cm...
  5. S

    Rutherford Scattering cross section

    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...
  6. I

    What does dσ/dΩ represent in terms of particle scattering?

    What is physically meant by: \frac{d \sigma}{d \Omega} Where \sigma is the cross section and \Omega is solid angle. I can't really picture it.
  7. P

    Neutron microscopic cross section data

    Hi guys, I am trying to calculate the macroscopic cross section (scattering and absorption) for high energy neutrons between 1 MeV and 10^7 MeV in Silicon. I am using the macroscopic cross section to determine the mean free path. To calculate the macroscopic cross section, i need to know the...
  8. K

    Singularity in Rutherford cross section

    The Rutherford differential cross section \frac{d\sigma}{d\Omega} goes like cosec(\vartheta)^4 which means at \vartheta=0 the differential cross section is infinite, which is ok. My question is, given that the differential cross section is proportional to the probability per unit solid...
  9. N

    Reactor Neutrons: Seeing Surface Area not Projected Cross Section?

    My professor told me that the neutrons in a reactor see the surface area of nuclei, and not the the projected cross section. That really doesn't make intuitive sense. Is he right?
  10. D

    Transverse loading with varing cross section

    i know that τ=VQ/(Ib) now I am looking for the maximum stress so i will find that at the point at the centre of the rectangle Q=A*\bar{y} A=0.5*d*b \bar{y}=0.25*d ===> Q=0.125d2b I=(b*d3)/12 τ=VQ/(Ib) τ=V*0.125d2b*12/((b2*d3) τ=1.5V/(bd) now d changes as a function...
  11. H

    Finding Volume by Cross Section Area

    I need to find the volume of this figure y=sinx, y=sinx + 2, x=4, x=-4 using the area of triangular cross sections. i don't really know where to start...how to find the formula for area of cross section etc. HELP!
  12. D

    Finding stress in non symetric cross section

    in a given shaft with a circular cross section, the radius changes linearly find the maximum shear stress i used T*r/J and since J is dependant on r^4, i found that the cross section with the smallest radius will feel the largest stress. find the angle of twist at the end of the...
  13. D

    What Are the Shear Stress and Angle of Twist for a Steel Member Under Torque?

    A 3.5 m long steel member with a W310 x 143 cross- section is subjected to 4.5KNm torque. Knowing that G=77GPa, determine (a) the maximum shearing stress along the line a-a, (b) the maximum shearing stress along the line b-b, (c) the angle of twist...
  14. K

    Cross section for two identical particles in the final state

    I was calculating the cross section for a particular decay and saw that I was off by a factor of half from the known value.. Now, the decay has two identical particles in the final state and I seem to remember having read somewhere that this requires a factor of half...but I am not able to...
  15. C

    Another volume by cross section.

    The base of a solid is the triangular region bounded by the y-axis and the lines x + 2y = 4, x - 2y =4. Find the volume of the solid given that the cross sections perpendicular to the x-axis are isosceles right triangles with hypotenuse on the xy-plane. So what I did is: 2\int_{x=0}^2...
  16. naima

    Why does the amplitude <p |T| p'> have the dimension of a volume?

    Hello I am reading this book: "[URL and the appearance of a classical word&f=false"]decoherence[/URL] I hope someone could help me. Please go to Appendix A1 Joos introduces the notation f(q,q'). What is the dimension of f from his notation? Next page he writes that \int f^2 d\Omega...
  17. G

    Infinite cross section in scattering

    Hi For example in e-e- -> e-e- scattering (electron-electron scattering) the differential cross section goes to infinity as theta goes to zero. Consequently the cross section is infinite. But how can we measure and interpret the cross section/differential cross section and interpret it as a...
  18. S

    Cross section of the photodissociation of CH

    Does anybody know how to calculate cross section of the photodissociation of CH?
  19. naima

    Understanding Cross Section in Physics: Dimension and Formula Explanation

    Hi all I found http://en.wikipedia.org/wiki/Cross_section_(physics)#Relation_to_the_S_matrix" on wikipedia: {d\sigma \over d\Omega} = (2\pi)^4 m_i m_f {p_f \over p_i} |T_{fi}|^2 Has it the dimension of a surface? (I only see M*M) It is the first time I read this formula about...
  20. K

    Please suggest a book including cross section

    I am reading some material on laser physics and quantum physics, there involes something called absorption cross section, collision cross section, differential cross section and so on quite often. I try to google the definition online but many website or book just give the formula instead of...
  21. R

    Varying cross section superconductor

    Here's the question: How can we describe a sudden change in the cross sectional area of a super conductor carying a current i from bigger A1 to smaller A2, such that the current density J after change is higher than Jc ? I have one scenario in my mind, the tempreture rises in the...
  22. M

    Nuclear Collsions fusion cross section

    Hello, I am curious about fusion reaction cross sections, and fusion power in general, and have been trying to self-teach myself in this area. I saw some emprical data for cross section curves in a paper that I read recently, and thought I understood enough of what made the curve (cross...
  23. D

    Photodetachment Cross Section Formulas: Explained

    I know the formulas for the length and velocity forms of the photodetachment cross section for an electron with energy \hbar\omega are, respectively, \sigma_{L}(\omega)=\frac{4\pi^{2}\alpha a_{0}^{2}\omega}{3}\sum_{f}|\langle\Psi_{f}|\sum_{j=1}^{n}z_{j}|\Psi_{i}\rangle|^{2} and...
  24. V

    How to deal with non uniform cross section bending?

    How to deal with non uniform cross section bending? How does one approach a solution for bending of a shaft having multiple diameters. I have one particular shaft in mind that has 11 diameters to get to the midpoint. I know the deflection at the midpoint, and I would like to calculate...
  25. D

    Compton Scattering cross section calculation

    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...
  26. R

    Find the Moment Inertia of a Cross Section: y = 30 & 35

    Hi.. I've got a problem about moment inertia. I don't understand about looking the distance of centroid (y). I am still confucing about the formula of "y" in Moment Inertia. Can you shows me about the formula of y or if any thread for this before, I am glad to see it too.Thanx's for your help...
  27. P

    Cross Section Difference Bhabha Scattering and Muon Pair Production

    Hello, how do the angular distributions of Bhabha Scattering e^+ e^- \Rightarrow e^+ e^- and Muon pair production e+ e- \Rightarrow \mu^+ \mu^- differ? Regards, Phileas Fogg
  28. K

    Approximate cross section calculations

    Hello Ive come across some approximate cross section formulas during a course of particle physics. And in a reaction like A + B --> R --> C + D the cross section should be something like \sigma = K\frac{\Gamma_R^{AB}\Gamma_R^{CD}}{(s-m_R^2)^2+m_R^2\Gamma_R^2} Where K is a constant (depending...
  29. Lisa!

    MATLAB Draw Thomson cross section in polar plot by matlab

    Well I'm supposed to draw Thomson cross section in polar plot by MATLAB software. Have I done it right? I mean does this figure that I got seem to be in polar plot or not? t = 0:.01:2*pi; r = 2.8179e-13 x = t,0.5*power(r,2)*(1+power(cos(t),2)) polar(t,x) Thanks
  30. F

    Bending a laser beam's cross section possible?

    So here's a crazy question...I was trying to think it through and have come up with nothing. Is it possible to bend a laser beam's cross section? For instance, if you are using a diode bar (which has a beam cross section resembling a line) is there a simple way to bend it into a...
  31. N

    How to determine the darcy friction factor for irregular cross section ducts

    How to determine the darcy friction factor for irregular cross section tunnels hi, I needed to calculate the f value for tunnels with these cross section area but I am not sure what are method available to calculate these shapes. Two of those cross section areas are already provided as...
  32. T

    How to Determine Neutron Interaction Time for a Given Nucleus?

    Suppose we consider a beam of neutrons incident upon a thin target with an intensity of 10^12 neutrons/(cm^2.s). Suppose further that the total cross section for the nuclei in this target is 4 b. Using this information, determine how long one would have to wait, on the average, for a given...
  33. M

    Neutron absorption cross section

    Does anyone know anywhere where I can find reliable up-to-date cross section infromation? In particular I'm looking for the absorption cross section of Gadolinium-157 for thermal neutrons. Everywhere I look seems to give a different value ranging fro 70000barns up to 450000barns.
  34. R

    Photon-Proton Cross Section vs Electron-Photon

    why is the cross section of photon - proton less than the electron- photon cross section for the same photon energy??
  35. I

    Calculating Cross Section: Is (1-\gamma^5) Same as (1-\gamma_5)?

    Is there a difference between (1-\gamma^5) and (1-\gamma_5) ? I see the two used interchangeably when calculating cross section.
  36. M

    (Neutron capture) cross section

    Cross section means the effective size of a nucleus for capturing a neutron, am I right? But what makes the cross sections for different nucleus different? I am a bit puzzled, why the cross section for Boron(for example) is so high?
  37. B

    Benchmark of high temperature cross section libraries in MCNP

    I need to use this libraries with confidence. Any articles that involves benchmarking of these cross sections?
  38. I

    Calculating Cross Section with 4-Fermi Interaction

    Hi all, I'm trying to teach myself high energy physics and was wondering if anyone knew a good reference site on calculating cross sections. I'm specifically trying to calculate the cross section for \nu _{\mu} + e^- \rightarrow \mu ^- + \nu_e using the 4-fermi interaction. Are there any good...
  39. L

    Differential Cross Section for scattering by Hard Sphere

    Problem Determine the differential and total cross sections for scattering from a "hard sphere" of radius R ("hard" means impenetrable). Relevant Formulae \sigma (\Omega) d \Omega = \frac{number \ of \ particles \ scattered \ into \ solid \ angle \ per \ unit \ time}{incident \ intensity}...
  40. T

    S- and P-Wave Cross Section Explained

    What does it mean when they say s wave cross section, p wave cross section .. ?
  41. J

    What is the Cross Section of a Hydrogen Atom in Thermal Equilibrium at 6000K?

    Homework Statement I've been asked to find the cross section of a hydrogen atom in thermal equalibrum at 6000K for a photon which induces a transition from the ground state to the first excited state. The density of states for n=2 is 4x the density of states for n=1 i.e. g(E2) = 4*g(E1)...
  42. P

    Mean free path and collisional cross section in Na due to impurities

    Let's say that we have Na at room temperature. The concentration of Na becomes plus one percent due to impurities. I'm interested in finding the mean free path and collisional cross section due to these impurities. I'm not sure on how Matheissen's rule could be applied, if we don't know what the...
  43. G

    Cross Section Large Hadron Collider

    Homework Statement b) The Large Hadron Collider (LHC), a 14 TeV proton-proton collider, will produce about a million Z0 per year. Explain why the cross section of such a process can be approximately written as: d\sigma / d\Omega = F_{q/p}(X_{1})F_{q'/p}(X_{2})d\sigma '(qq' \rightarrow...
  44. N

    Differential cross section w.r.t rapidity

    I'm extracting data from a Monte Carlo sim. and i need to extract the differential cross-sections of the resultant protons and neutrons in momentum and rapidity space. ie \frac{d\sigma}{dy} ; \frac{d\sigma}{dp} and \frac{d^2\sigma}{dydp} where I know the values of y and p...
  45. H

    How to find neutron capture and fission cross section

    I'm writing a paper on Thorium utilization in nuclear reactors. In this connection I'm looking for figures which describe the neutron capture and neutron fission cross sections over a wide energy range (not only thermal). There are probably some online resources unbeknown to me, any hints?
  46. J

    Electron-impact ionization cross section

    I'm calculating an ionization cross section in partially ionized plasma, with taking into account of correlation effects. I'm trying to do it with help of variation phase method. Please, help me to find some link to useful articles.
  47. Z

    How to prove the width of a resonance using the cross section of a S wave?

    Homework Statement The total cross section of a S wave is given by the following equation Sigma=(pi/k)*(b^2)/((E-En)^2+(b/2)^2)) prove that b is the width of the resonance. Homework Equations Nothing that is the only thing The Attempt at a Solution I already solved the question...
  48. D

    Cross section for scattering of gauge bosons and Majorana neutrinos

    For my diploma thesis I must provide a calculation that reproduces the results given on page 46 of the paper hep-ph/0309342 . For those who do not want to look it up, I briefly explain what it is about: It concerns the two-body scattering processes (1) N + V => L + H, (2) N + L => V + H, (3) N...
  49. M

    Hard nuclear physics cross section problem

    In a scattering experiment, an aluminium foil of thickness L = 10E-6 m is placed in a beam of intensity of 6E12 particles per second. The differential scattering crosss section is known to be of the form. \frac{d\sigma}{d\Omega} = A + Bcos^2 (\theta) where \theta is the...
  50. A

    Is cross section is proportional

    If I show something that a cross section is proportional to: 1 / (16p^2 sin^4( x) + 8mpsin^2 (x) + m^2) does it imply that the cross section is proportional to 1 / sin^4 (x) as well?
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