Algorithm to obtain inverse potentials for $\alpha$–$\alpha$ scattering using variable phase approach

An algorithm has been developed with the purpose of obtaining inverse potentials, where the Riccati-type non-linear differential equation, also called phase equation, has been kept in tandem with the Variational Monte Carlo method. The optimization of Gaussian function parameters is achieved such that the experimental phase shifts are reproduced. The obtained SPS for various $l$ channels has been compared with experimental ones with mean absolute percentage error (MAPE) as a measure. The model parameters have been optimized by suitable optimization technique by looking for minimum value of MAPE. The results for $l$= 0$^+$, 2$^+$, and 4$^+$ partial waves have been obtained, to match with experimental SPS, with MAPE values of 2.9, 4.6, and 6.2, respectively, for data up to 23 MeV, while for higher states 6$^+$, 8$^+$, and 10+ has MAPE of 3.2, 4.5, and 5.9, respectively, for data from 53–120 MeV. On extrapolation for data in range $E_{lab}$ = 23–120 MeV, using the optimised parameters, the SPS are found to be in close agreement with experimental ones for the first three channels.