Methods for a quantitative evaluation of odd-even staggering effects

TL;DR

This paper reviews existing and proposes new methods for quantitatively evaluating odd-even staggering effects in nuclear reaction fragment yields, emphasizing the importance of high-statistics data and reliable analysis techniques.

Contribution

It introduces new methods for quantifying staggering effects and compares their effectiveness using Monte Carlo simulations, identifying the most reliable approaches.

Findings

Non-linear fit with oscillating functions is reliable

Finite difference approaches are effective

High-statistics data is crucial to avoid spurious results

Abstract

Odd-even effects, also known as "staggering" effects, are a common feature observed in the yield distributions of fragments produced in different types of nuclear reactions. We review old methods, and we propose new ones, for a quantitative estimation of these effects as a function of proton or neutron number of the reaction products. All methods are compared on the basis of Monte Carlo simulations. We find that some are not well suited for the task, the most reliable ones being those based either on a non-linear fit with a properly oscillating function or on a third (or fourth) finite difference approach. In any case, high statistic is of paramount importance to avoid that spurious structures appear just because of statistical fluctuations in the data and of strong correlations among the yields of neighboring fragments.