Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Need some help with cross sections

  1. Mar 29, 2006 #1
    Hello all,

    I have a fellow grad student who is convinced that the differential cross section:
    [tex] \frac{d\sigma}{d\Omega}[/tex]
    is truly a ratio of differentials. That is you have an infinitesimal cross section divided by an infinitesimal solid angle.

    I contend that when we write
    [tex] \frac{d\sigma}{d\Omega}[/tex]
    we really mean
    [tex] \sigma(\Omega) [/tex] and that we only call it the differential cross section because the integral of the differential cross section over the physical range of the variable gives the total cross section.
    I stated this along with the fact that the total cross section is simply a number. You sample an event (lets say pp->pp is the event in question) at different energies and record the number of particles that come out of the reaction at the energy. This gives you a number.
    The derivative of the number with respect to any variable is zero. So the differential cross section- is not the derivative of the cross section.
    He contends this is not true because when you do the "experiment" you have a finite width detector and this smears out the solid angle so it is no longer an infinitesimal.

    Can anyone find a very clear discussion somewhere about this fact? Or maybe present one? Or am I simply wrong and it truly can be thought of as a ratio of differentials?
  2. jcsd
  3. Mar 29, 2006 #2


    User Avatar
    Science Advisor
    Gold Member

    Mathematics answer. There is no such concept as a ratio of differentials. What you have is a derivative, defined in the usual way, and it is the cross section as a function of direction.

    Physics contribution. The numbers that are used for the cross sections are obtained by experiments as described.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Need some help with cross sections
  1. Need Some Help (Replies: 1)

  2. Need some help (Replies: 2)