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My question is simple, and I'm hoping the answer is also simple!

Lets say I have a neutron and I scatter it off of an iron nucleus. Lets say that this is non-relativistic elastic scattering and I model the potential of the iron using Wood-Saxon potential:

$$V(r)=-\frac{V_{0}}{1+\exp \left(\frac{r-R}{a}\right)}.$$

I am using partial waves to calculate the total cross-section which has the form:

$$\sigma=\frac{4 \pi}{k^{2}} \sum_{l=0}^{\infty}(2 l+1) \sin ^{2} \delta_{l}$$

where $\delta_l$ are the phase shifts. I am solving this problem numerically and I find there are 2 resonant states when I plot the cross-section as a function of the energy of the neutron.

I am wondering the following: can I analytically find where the resonances are and how many resonances there are for a given potential?

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