Background: Double charge exchange (DCE) nuclear reactions have recently attracted much interest as tools to provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-$\mathrm{<ruby><rb>\beta </rb><rt>べーた</rt></ruby>}$ decay. In this framework, a good description of the reaction mechanism and a complete knowledge of the initial and final-state interactions are mandatory. Presently, not enough is known about the details of the optical potentials and nuclear response to isospin operators for many of the projectile-target systems proposed for future DCE studies. Among these, the ${}^{20}\mathrm{Ne}+{}^{76}\mathrm{Ge}$ DCE reaction is particularly relevant due to its connection with ${}^{76}\mathrm{Ge}$ double-$\mathrm{<ruby><rb>\beta </rb><rt>べーた</rt></ruby>}$ decay.

Purpose: We intend to characterize the initial-state interaction for the ${}^{20}\mathrm{Ne}+{}^{76}\mathrm{Ge}$ reactions at 306 MeV bombarding energy and determine the optical potential and the role of the couplings between elastic channel and inelastic transitions to the first low-lying excited states.

Methods: We determine the experimental elastic and inelastic scattering cross-section angular distributions, compare the theoretical predictions by adopting different models of optical potentials with the experimental data, and evaluate the coupling effect through the comparison of the distorted-wave Born approximation calculations with the coupled channels ones.

Results: Optical models fail to describe the elastic angular distribution above the grazing angle ($\approx {9.4}^{\circ }$). A correction in the geometry to effectively account for deformation of the involved nuclear systems improves the agreement up to about ${14}^{\circ }$. Coupled channels effects are crucial to obtain good agreement at large angles in the elastic scattering cross section.

Conclusions: The analysis of elastic and inelastic scattering data turned out to be a powerful tool to explore the initial and final-state interactions in heavy-ion nuclear reactions at high transferred momenta.

• Received 18 July 2019

DOI:https://doi.org/10.1103/PhysRevC.100.034620