Universal odd-even staggering in isotopic fragmentation and spallation cross sections

Abstract

In a recent work [Phys. Rev. C 97, 044619 (2018)], a universal odd-even staggering (OES) has been observed in isotopic cross sections of neutron-rich nuclei produced by various fragmentation and spallation reactions. However, the universality of this OES is not clear for neutron-deficient nuclei, and thus more quantitative studies of this OES effect are required for these nuclei from different reactions. For neutron-deficient nuclei with ($N\ensuremath{-}Z$) from 0 to $\ensuremath{-}4$, the OES magnitudes are calculated by a third-order difference formula using cross sections measured in various fragmentation and spallation systems and they are applied to derive the evaluation values of the OES magnitudes. The evaluated OES magnitudes for both neutron- and proton-rich nuclei are benchmarked with some additional experimental data from fragmentation as well as spallation reactions. Furthermore, the OES factors predicted by two recent fragmentation and spallation models are checked by comparing with the OES magnitudes evaluated from extensive experimental data. This comparison suggests that the OES factors in these fragmentation and spallation models should be improved to reproduce measured cross sections.