# Structure functions in electron-proton scattering

1. Nov 22, 2016

### Kara386

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. Nov 27, 2016