Analysis of proton-Be9,10,11,12 scattering using an energy-, density-, and isospin-dependent microscopic optical potential
The proton elastic scattering of 9,10,11,12Be isotopes at a wide energy range from 3 to 200 MeV/nucleon is analyzed using the optical model with the partial-wave expansion method. The microscopic optical potential (OP) is taken within the single-folded model. The density- and isospin-dependent M3Y-Paris nucleon-nucleon (NN) interaction is used for the real part and the NN-scattering amplitude of the high-energy approximation is used for the imaginary one. The surface contribution to the imaginary part is included. The analysis reveals that the partial-wave expansion with this microscopic OP reproduces well the basic scattering observables at energies up to 100 MeV/nucleon. For higher energies, the eikonal approximation with the same OP gives results better than the partial-wave expansion calculations. The volume integrals of the OP parts have systematic energy dependencies, and they are parameterized in empirical formulas. In addition, the volume integral's parametrizations determine the true energy dependence for the depths of the OP parts. The study of increasing the number of neutrons for a given isotope shows that the imaginary volume integrals and reaction cross sections depend on the matter radii of the scattered nuclei. Further, they are found to have larger values for the halo nucleus scattering (Be11+p) than those for the scattering of their isotopes.