Abstract
With the explicit example of α + α scattering we emphasize the incompleteness of using just the on-shell properties in any inversion procedure. A deep, energy-independent and angular-momentum-independent effective local potential is constructed to reproduce the phase shifts from a single-configuration microscopic resonating-group method (RGM) calculation for α + α scattering up to E = 16 MeV. From this we derive its phase-shift-equivalent shallow supersymmetric partner-potentials by eliminating the bound states which are unphysical due to the Pauli principle. These deep and shallow potentials are used to calculate bremsstrahlung emission in α + α collision and compared with the results from RGM as a means to investigate their wave functions. While the bremsstrahlung cross sections from RGM and the deep potential resemble each other, those of the shallow potentials are distinctly different.
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