The experimental differential cross-sections of 16 O + 16 O elastic scattering in the energy range 75 MeV E lab 1120 MeV are analysed using families of non-monotonic (NM) shallow nucleus-nucleus potential in the framework of the optical model. The experimental data is reproduced successfully using six families of NM potentials. It is found that all families converge at 350 MeV. The clear indication of the convergence of the potential families at 350 MeV conforms to the Goldberg criterion concerning the removal of discrete ambiguities even for the shallow NM potential. The study further suggests that the energy of convergence heralds the occurrence of the primary rainbow at that incident energy.

The experimental differential cross section of the 12C + 12C elastic scattering over a wide laboratory energy scale 25 ⩽ E lab ⩽ 360 MeV are analyzed within the framework of the optical model (OM) using non-monotonic (NM) nucleus–nucleus potential. The real parts of the NM potentials are derived from the energy density functional (EDF) formalism with the sudden approximation embodying the Pauli exclusion principle and the imaginary parts are taken as phenomenology. The diffractive and the refractive scattering with Airy structures in the whole angular region of the 12C + 12C elastic scattering in the above mentioned energy range are found profoundly successful in OM with the NM nucleus–nucleus potentials in five of different potential families. All the families at lower energies converge at 240 MeV to the unique potential family starting with the EDF potential. This, in conjunction with our recent findings for the 16O + 16O system in Islam et al (2021 J. Phys. G 48 075109), not only verifies the Goldberg criterion for elimination of discrete potential ambiguities for NM potentials, but also establishes that this leads uniquely to the EDF family. The 90° excitation function is also successfully reproduced with extension using NM potentials. The near- and far-side (N/F) decomposition of total elastic scattering amplitude has also been studied using our NM potentials.

Nonmonotonic (NM) nucleus-nucleus potential families rooted in the Pauli-compliant Energy Density Functional (EDF) theory and especially their behavior at higher energies, have been investigated using experimental data for $^{16}$O+$^{16}$O elastic scattering in the range $25 \leq E_{lab} \leq 1120$ MeV. At $E_{lab}= 75$ MeV, the $^{16}$O+$^{16}$O NM potentials, in a simple optical model (OM) are found to support five rotational bands of $^{16}$O+$^{16}$O bound and quasimolecular states in $^{32}$S with cluster global quantum numbers $G = 24$, 26, 28, 30 and 32. The lowest band in the experimental spectrum starting at $E_x = 7.5357$ MeV, and having $I^{\pi}$ = 0$^+$, 2$^+$, 4$^+$, 6$^+$ and 8$^+$, has been located for the first time. In the simple OM, the NM potentials are found to reproduce the experimental $^{16}$O+$^{16}$O fusion cross sections in the energy range 12 - 31 MeV. The present work shows that both the $^{16}$O+$^{16}$O cluster-bands and fusion cross sections in the Coulomb-barrier region can be reproduced using NM potentials.