Differential cross section signature

[ryanwilk]

Homework Statement

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...

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

The Attempt at a Solution

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

(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.

 

[mark726]

Hello, thank you for your question. A "particular signature" in the context of resonant scattering refers to a distinct pattern or shape in the differential cross section plot. This signature can indicate the presence of a resonance state, which is a temporary energy state of a system that is formed by the interaction of particles. In order to identify this signature, you can compare your plot to theoretical models or experimental data of known resonance states. The shape and position of the resonance peak in the plot can provide information about the energy and properties of the resonance state. Additionally, you can also examine the behavior of the differential cross section at different scattering angles to further analyze the resonance signature. I hope this helps clarify the concept for you. Good luck with your project!