# How to calculate angular momentum given angular distribution

I have recently attended a colloquium on transfer reactions. At one point, the speaker was talking about calculating the angular momentum of a nuclear transfer reaction from an angular distribution plot. The angular distribution plot is a differential cross section ($$d\sigma / d\Omega$$) vs. lab angle ($$\theta_l$$) plot. On the plot, there were a set of data points which are then fitted with different fitting of different values of $$l$$ (orbital angular momentum?).

From what I gather, it seems like you can get the $$J^\pi$$ value of the heavy product by using that angular distribution plot, but I am not sure how. It seems like this is common knowledge in the nuclear astrophysics community, but I have not taken any advance course in nuclear phyiscs yet, so this method is very new to me.

So my questions are:

What is the differential cross section? And how does plotting it against the lab angle yield gives you the orbital angular momentum? Once you got the the value of orbital angular momentum, how do you get the angular momentum?

Note: So, I understand that you get the spin by looking at what value of $$l$$ gives you the best fit since $$\pi = (-1)^l$$, but how does the value of $$l$$ give you angular momentum?