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Homework Help: Introductory Particle Physics - Form factor, charge distribution?

  1. Oct 5, 2009 #1
    Here is the problem. I've been messing around with it for a while but I'm not sure if what I'm trying to do is the right way to approach this.

    The form factor F(q) = [tex]\int\rho(\vec{r})e^{i\vec{q}.\vec{r}/\hbar}d^{3}\vec{r}[/tex] is the 3D Fourier Transform of the normalised charge distribution [tex]\rho[/tex]([tex]\vec{r}[/tex]).

    For a simplified model of a proton's charge distribution, [tex]\rho(r)\propto[/tex] (e[tex]^{-r/R}[/tex])/r.

    R can be considered as some characteristic "size" of the proton, setting the rate at which the charge dies away, but does not constitute a hard edge to the proton.

    i) Find the constant of proportionality required to normalise [tex]\rho[/tex] correctly.
    ii) something else that presumably needs the answer to i) first.

    I am new to all this particle physics business, so I am in unfamiliar territory and I'm not sure how to approach this question. I've so far just aimlessly waded into this and ended up with a couple of sides of mindless mathematical messing around. This could be a simple question or a complicated one for all I know, so I thought i'd post it here before I bother my busy lecturer...

    Anyway, my closest attempted solution:

    -what I thought was that I should assume the proton has its highest charge density at its centre and it gradually fades away, uniformly in all directions.

    -I'm also thinking that r must be the distance from the centre of the proton, so that as r tends to infinity, the charge density [tex]\rho(r)[/tex] approaches zero.

    -I'm trying to find some constant of proportionality here, lets call it A, so that [tex]\rho(r) =[/tex] A(e[tex]^{-r/R}[/tex])/r.

    -I'm thinking that if I do [tex]\int \rho(r) dV = 1[/tex] then I can solve for A, but this is as far as I have got, I'm struggling with how to take this integral any further.

    Am I on the right lines, has anyone got any suggestions that would make my life easier?

  2. jcsd
  3. Oct 5, 2009 #2


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    Homework Helper
    Gold Member

    Looks fine so far, now just compute the volume integral using spherical coordinates, centered on the proton's center (r=0)....you should know how to do that.
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