Systematic studies of odd-even staggering in isotopic cross sections with new difference formulas*

Abstract Although a 3rd-order difference formula has often been employed to investigate the odd-even staggering (OES) in experimental cross sections, other formulas can also be very useful. In this work, three formulas, the 2nd, 4th, and 5th-order difference formulas, are proposed for systematic OES studies. These new difference formulas with different orders are applied to extract the OES magnitudes in extensive accurate cross sections measured in different fragmentation and spallation reaction systems over a broad energy range. According to comparisons of these (2nd, 4th, and 5th-order) OES magnitudes derived from different reaction systems, they almost do not rely on the projectile-target combinations or the projectile energy. A similar universality was observed for the 3rd-order OES magnitudes obtained from various reaction systems in our previous studies of the 3rd-order OES. The weighted average values of the 2nd, 4th, and 5th-order OES magnitudes extracted from different experimental datasets are recommended as the 2nd, 4th, and 5th-order OES evaluations, respectively. Finally, comparisons of these (new) 2nd, 4th, 5th, and previous 3rd-order OES evaluations support that these OES evaluations with different orders are consistent and that all the difference formulas with different orders are applicable to OES studies.