Extension of the ratio method to proton-rich nuclei

The ratio method has been developed to improve the study of one-neutron halo nuclei through reactions. By taking the ratio of angular distributions for two processes, viz. breakup and elastic scattering, this new observable is nearly independent of the reaction mechanism and hence much more sensitive to the projectile structure than the cross sections for each single process. We study the extension of the ratio method to proton-rich nuclei and also explore the optimum experimental conditions for measuring this new observable. We compare accurate dynamical calculations of reactions for proton-rich projectiles to the prediction of the ratio method. We use the dynamical eikonal approximation that provides good results for this kind of reaction at intermediate energy. Our tests for ⁸B, an archetypical one-proton halo nucleus, on Pb, Ni, and C targets at 44 MeV/nucleon show that, the ratio works less well than for neutron halos due to the non-negligible Coulomb interaction between the valence proton and the target. Nevertheless, thanks to its strong sensitivity to the single-particle structure of the projectile, the ratio method still provides pertinent information about nuclear structure on the proton-rich side of the valley of stability. To account for the lower quality of the method applied to charged systems, we suggest variations in its application from the original idea. Interestingly the method is not affected if energy ranges - or bins - are considered in the projectile continuum. This makes the ratio easier to measure experimentally by increasing the breakup cross section. We also extend our analysis to ¹⁷F, ²⁵Al, and ²⁷P, whose study is of interest to both nuclear astrophysics and nuclear structure. We show that, albeit less precise than for one-neutron halo nuclei, nuclear-structure information can be inferred from the ratio method applied to exotic proton-rich nuclei. For nuclei in which the valence proton is deeply bound and/or sits in an l ≥2 orbital, the method provides only estimates of nuclear-structure features, like the one-proton separation energy or the orbital angular momentum of the valence proton in the ground state. When the valence proton is loosely bound in an s or p orbital, viz. for proton halo nuclei, more detailed structure information can be obtained through this new reaction observable.