Differential cross section signature

[ryanwilk]

1. The problem statement, all variables and given/known data

Hi, I'm currently carrying out a computing project on Resonant Scattering and when I have identified a resonant state, I need to examine whether it has a "particular signature". However, I'm not really sure what this means...

2. Relevant equations

The differential cross section for a specific scattering angle is:

\frac{d \sigma}{d \Omega} = |f(\theta)|^2 = \mathrm{Re}[f(\theta)]^2+\mathrm{Im}[f(\theta)]^2,

where \mathrm{Re}[f(\theta)] = \frac{1}{2k} \sum_{l=0}^{\infty} (2l+1) \mathrm{sin} (2 \delta_l) P_l(\mathrm{cos} \theta),

and \mathrm{Im}[f(\theta)] = \frac{1}{k} \sum_{l=0}^{\infty} (2l+1) \mathrm{sin}^2 (\delta_l) P_l(\mathrm{cos} \theta).

3. The attempt at a solution

So, plotting differential cross section as a function of scattering angle, i get graphs which look like:

http://i159.photobucket.com/albums/t136/ryanwilk/resonant_state_uranium_227-1.png

(e.g. for a neutron scattering from a 238U nucleus)

However, I'm not really sure what information this shows other than the fact that the graph is symmetrical about \theta = \pi .

Any help would be appreciated,

Thanks.