Accurate odd-even staggering relations for fragmentation and spallation cross sections

Abstract

Isotopic cross sections measured in many different fragmentation and spallation reactions display a universal odd-even staggering (OES). On the basis of this universality, four OES relations are proposed for the first time to accurately calculate fragmentation and spallation cross sections. Comparison with extensive experimental data measured in various reaction systems reveals that cross sections calculated by two OES relations agree excellently with 95% measured data within a factor smaller than 1.2, while another two OES relations also show a similar good agreement (within a factor around 1.5). These remarkable agreements, which can hardly be reached by other existing models, strongly support that these simple OES relations open new paths for very accurate and fast calculations of fragmentation as well as spallation cross sections. As an application of these relations, significant discrepancies between some measured cross sections are scrutinized and well resolved by using the OES magnitudes and accurate OES relations first proposed in this work. Finally, based on recent experimental data, small cross sections (down to ${10}^{\ensuremath{-}13}$ mb) of some new isotopes near the drip-lines are accurately extrapolated or interpolated with these OES relations, which will be very useful for exploring undiscovered isotopes.