  Background: An accurate way to incorporate long range Coulomb interaction
alongside short-range nuclear interaction has been a challenge for theoretical
physicists. Purpose: In this paper, we propose a methodology based on the
reference potential approach for constructing inverse potentials of alpha-alpha
scattering. Methods: Two smoothly joined Morse potentials, regular for
short-range nuclear interaction and inverted for long range Coulomb, are used
in tandem as a reference potential in the phase function method to obtain the
scattering phase shifts for the S, D and G states of alpha-alpha scattering.
The model parameters are optimized by choosing to minimize the mean absolute
percentage error between the obtained and experimental scattering phase shift
values. Results: The constructed inverse potentials for S, D and G states have
resulted in mean absolute percentage errors of 0.8, 0.5, and 0.4 respectively.
The obtained resonances for D and G states closely match the experimental ones.
Conclusion: The reference potential approach using a combination of smoothly
joined Morse functions is successful in accurately accounting for the Coulomb
interaction between charged particles in nuclear scattering studies.
