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Structure functions in electron-proton scattering

  1. Nov 22, 2016 #1
    1. The problem statement, all variables and given/known data
    In electron proton scattering,

    ##\int_0^{1} F^p_2(x)dx = 0.18##

    For the neutron in electron deuteron scattering,

    ##\int_0^1F^n_2(x)dx = 0.12##

    Therefore determine the ratio ##\frac{\int_0^1xu^p_v(x)dx}{\int_0^1xd^p_v(x)dx}##.

    2. Relevant equations


    3. The attempt at a solution
    The answer is 2. Unfortunately, I don't know how to show that.
    I know that ##F_2^{ep}(x) = x(\frac{4}{9}u^p(x)+\frac{1}{9}d^p(x)+\frac{4}{9}\overline{u}^p(x)+\frac{1}{9}\overline{d}^p(x))##.

    Based on that, I think
    ##F_2^{n}(x) = x(\frac{4}{9}u^n(x)+\frac{1}{9}d^n(x)+\frac{4}{9}\overline{u}^n(x)+\frac{1}{9}\overline{d}^n(x))##
    And because a proton is essentially a neutron with up and down swapped, ##u^n(x) = d^p(x)##, so that can be substituted in:
    ##F_2^{n}(x) = x(\frac{4}{9}d^p(x)+\frac{1}{9}u^p(x)+\frac{4}{9}\overline{d}^p(x)+\frac{1}{9}\overline{u}^p(x))##

    ##= x(\frac{4}{9}d(x)+\frac{1}{9}u^p(x)+\frac{4}{9}\overline{d}^p(x)+\frac{1}{9}\overline{u}^p(x))##

    But I couldn't explain why, I've just replaced the superscript from the first expression with n. I've tried using the above expressions to get a ratio of the integrands but it doesn't work, and I don't know what the subscript ##v## means in the ratio I'm supposed to calculate. Any help is much appreciated, I really have no idea what to do!
     
  2. jcsd
  3. Nov 27, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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