Universal odd-even staggering in isotopic fragmentation and spallation cross sections of neutron-rich fragments

An evident odd-even staggering (OES) in fragment cross sections has been experimentally observed in many fragmentation and spallation reactions. However, quantitative comparisons of this OES effect in different reaction systems are still scarce for neutron-rich nuclei near the neutron drip line. By employing a third-order difference formula, the magnitudes of this OES in extensive experimental cross sections are systematically investigated for many neutron-rich nuclei with (N - Z) from 1 to 23 over a broad range of atomic numbers (Z approximate to 3-50). A comparison of these magnitude values extracted from fragment cross sections measured in different fragmentation and spallation reactions with a large variety of projectile-target combinations over a wide energy range reveals that the OES magnitude is almost independent of the projectile-target combinations and the projectile energy. The weighted average of these OES magnitudes derived from cross sections accurately measured in different reaction systems is adopted as the evaluation value of the OES magnitude. These evaluated OES magnitudes are recommended to be used in fragmentation and spallation models to improve their predictions for fragment cross sections.