2nd-order optical model of the isotopic dependence of heavy ion absorption cross sections for radiation transport studies

Heavy ion absorption cross sections play an important role in radiation transport codes used in risk assessment and for shielding studies of galactic cosmic ray (GCR) exposures. Due to the GCR primary nuclei composition and nuclear fragmentation leading to secondary nuclei heavy ions of charge number, Z with 3 ≤ Z ≥ 28 and mass numbers, A with 6 ≤ A ≥ 60 representing about 190 isotopes occur in GCR transport calculations. In this report we describe methods for developing a data-base of isotopic dependent heavy ion absorption cross sections for interactions. Calculations of a 2nd-order optical model solution to coupled-channel solutions to the Eikonal form of the nucleus-nucleus scattering amplitude are compared to 1st-order optical model solutions. The 2nd-order model takes into account two-body correlations in the projectile and target ground-states, which are ignored in the 1st-order optical model. Parameter free predictions are described using one-body and two-body ground state form factors for the isotopes considered and the free nucleon-nucleon scattering amplitude. Root mean square (RMS) matter radii for protons and neutrons are taken from electron and muon scattering data and nuclear structure models. We report on extensive comparisons to experimental data for energy-dependent absorption cross sections for over 100 isotopes of elements from Li to Fe interacting with carbon and aluminum targets. Agreement between model and experiments are generally within 10% for the 1st-order optical model and improved to less than 5% in the 2nd-order optical model in the majority of comparisons. Overall the 2nd-order optical model leads to a reduction in absorption compared to the 1st-order optical model for heavy ion interactions, which influences estimates of nuclear matter radii.