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Nuclear Transport

  1. Feb 6, 2015 #1
    Show by direct calculation that Eqs. (4-134) and (4-137) in the textbook by Duderstadt and Hamilton hold, i.e.:


    (a) ∫ dΩΩiΩj= 4π/3 δij; i,j = x,y,z;



    (b) ∫ dΩΩxΩyΩz = 0, if l, m, or n is odd.


    The integrals are over 4π.

    This is part of the derivation of the diffusion equation from the neutron transport equation. Part (b) from D&H Next note that the integral of the product of any odd number of components of OMEGA vanishes by symmetry.

    (a) I think that 4π/3 comes from the volume of the sphere and δij is the kronecker delta. I don't know how to show this mathematically.
    (b)
    I think that this has to do with the sin or cos function.
     
  2. jcsd
  3. Feb 6, 2015 #2

    DEvens

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    Not volume. Omega is solid angle.

    http://en.wikipedia.org/wiki/Solid_angle

    I don't have the textbook you cite. So it's a little difficult to follow the question. You should read back in the text to see if they don't do something on solid angle and how to manipulate it.
     
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