We are a group of undergraduate students currently doing a lab work to measure the Compton Cross-section, using a radioactive ${}^{22}$Na source. The setup simply has the ${}^{22}$Na source decaying $\beta$ which sends 2 photons at opposite directions. One photon is captured by a gate detector and the other one interacts with an Aluminum target, we then place a detector at a certain angle $\theta$ to measure the energy spectrum of the outgoing photon.
The experimental cross section is measured via: $$ \frac{d\sigma}{d\Omega} = \frac{1}{\Delta \Omega} \frac{N_S}{N_I} \frac{1}{\mathcal{N} dx} $$ where $N_S$ are the counts in the detector for the scattered photons and $N_I$ are the incident photons (aka the number of times the gate detector "is opened"). In addition $\mathcal{N} =N_{A} \frac{\rho}{M}$ and $dx$ is the target's thickness.
For values of $\theta$ = 30,45,60,90 we get decent results, however when evaluating the spectrum for $\theta=0$ we get a result $10^2$ higher. (meaning the parameters outside of $N_S/N_I$ are decent).
The underlying suggestion is that there are additional counts in the spectrum ($N_S$ must be "too high").
Questions: Is there actually a point in measuring the cross section at 0 degrees? If so, how do we evaluate the additional counts we should not be expecting?
If there is no point in using counts how do we evaluate experimentally the cross section at 0 deg?
The first thought we had (likely not a good one) was that the additional counts come from photons that are able to pass through the target without interacting , which could be evaluated via $I(t) = I_0 e^{-\mu dx}$: but the idea of a cross section at 0 degress is that the particles don't interact at all, right?
