Background: In earlier work, inversion of $S$ matrix for 330 MeV ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$ resulted in highly undulatory potentials; the $S$ matrix resulted from the inclusion of strong coupling to states of projectile and target nuclei. $L$-independent $S$-matrix equivalent potentials for other explicitly $L$-dependent potentials have been found to be undulatory.

Purpose: To investigate the possible implications of the undulatory dynamic polarization potential for an underlying $L$ dependence of the ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$ optical potential.

Methods: $S$ matrix to potential, $S_L\to V\left(r\right)$, inversion which yields local potentials that reproduce the elastic channel $S$ matrix of coupled channel (CC) calculations, will be applied to the $S$ matrix for 115.9 MeV ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$. Further, $S_L$ for explicitly $L$-dependent potentials are inverted and the resulting $L$-independent potentials are characterized and compared with the undulatory potentials found for ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$.

Results: Some of the undulatory features exhibited by the potentials modified by channel coupling for 115.9 MeV ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$ can be simulated by simple parameterized $L$-dependent potentials.

Conclusions: The elastic scattering of ${}^{16}\mathrm{O}$ by ${}^{12}\mathrm{C}$ is a particularly favorable case for revealing the effective $L$ dependence of the potential modified by channel coupling. Nevertheless, there is no reason to suppose that undularity is not a generic property leading in many cases to the choice: nucleus-nucleus potentials are (i) smooth and $L$-dependent, (ii) $L$-independent and undulatory, or (iii) both.

• Received 27 April 2016
• Revised 2 June 2016

DOI:https://doi.org/10.1103/PhysRevC.94.034602