Nuclear wave function in function of for the proton state, obtained by diagonalizing the self energy in the exact continuum used above. The first eigenvalue at -23.97 MeV (solid red line) is compared by the corresponding harmonic oscillator state multiplied by the square root of the spectroscopic factor (dashed red line), the second eigenvalue at -2.85 MeV (solid blue line) is similarly compared with harmonic oscillator state (dashed blue line). The spectroscopic factors are 0.78 and 0.21 respectively

A IMHO good picture to didactically illustrate the effect of many-body dynamics on nuclei.

I post it here since that it did not make it to the final version of the Proceeding for Pisa conference, but I think it illustrate nicely how, from the combination of several base state wavefunctions we build many-body wavefunctions which have different properties (are quenched, so posses spectroscopic factors, and have a completely different tail) from the harmonic oscillator starting point (dashed).

This is also why reaction dynamics are way different calculated with a complete set of many-body relation instead of a simple mean field picture.

IMHO would also be difficult to reproduce the richness of these wavefunctions with a single Wood Saxon, let alone an harmonic oscillator potential (you can notice that the decay of the is quite fat respect to the exponential of an harmonic oscillator eigenfunction).

Non-local optical potentials are the way to go! 😉

(absolutely objective and no conflict of interest there), more info here: arXiv:1612.01478 [nucl-th], and soon-to-be publication.