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    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...

    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).

    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,

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Updated: March 20, 2011
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