Inverse Potentials for α-α Scattering using Gaussian Interaction

Alpha-alpha scattering phase shifts (SPS) have been determined using phase function method (PFM) with local nuclear interaction between two alpha clusters modeled as double Gaussian potential and Coulomb repulsion in the form of $erf()$ function. The obtained SPS for various -channels have been compared with experimental ones with mean absolute percentage error (MAPE) as a measure. The model parameters have been optimised by suitable optimisation technique by looking for minimum value of MAPE. The results for =0⁺, 2⁺ and 4⁺ partial waves have been obtained, to match with experimental SPS, with MAPE values of $7.6$, $2.7$ and $6.5$ respectively for data up to $120$ MeV, while for higher states 6⁺, 8⁺ and 10⁺ has MAPE of $1.7, 7.4$ and $10.4$ respectively for data from $53-120$ MeV. On extrapolation for data in range Eab. = $23-120$ MeV, using the optimised parameters, the SPS are found to be in close agreement with experimental ones for first three channels.