Methods for a quantitative evaluation of odd-even staggering effects

Abstract

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.

Odd-even staggering for production cross sections ofnuclei near the neutron drip-line *

“…In addition, four OES relations proposed in Ref. [29] will be validated further with these experimental data approaching the neutron drip-line. Finally, the OES for some experimental cross sections of neutron-rich isotopes produced by in-flight fission 345 MeV/nucleon U+ Be [14,15] are also investigated in this work, and the OES relations are applied for calculations of projectile fission cross sections.…”

“…Considering that the universality of OES and OES relations proposed in our previous publications [24,25,29] is mostly based on accurate experimental data not far from stability, the present work is focused on validating the universality of the OES and OES relations by using the cross sections for many isotopes near the neutron drip-line, as measured for several fragmentation and inflight fission reactions [1,3,14,15]. Recently, production cross sections of many very neutron-rich nuclei close to the neutron drip-line have been measured for two fragmentation reactions, i.e., 132 MeV/nucleon Ge+ Be [1] and 139 MeV/nucleon Se+ Be [3], by Tarasov et al.…”

“…In particular, accurate calculations of these cross sections are extremely challenging for isotopes approaching the drip-lines. Finally, four OES relations based on the universal OES in various reaction systems have been proposed recently for very fast and accurate calculations of fragmentation and spallation cross sections [29]. These accurate OES relations, as well as other reaction models, should be benchmarked with more experimental data, especially for isotopes approaching the neutron drip-line.…”

“…Our previous studies in Refs. [17,18,24,25,28,29] reveal that it is very suitable to calculate the OES in production cross sections of isotopes along a constant isospin chain. According to these studies, the OES magnitude for experimental cross sections of four neighboring nuclei along a constant isospin chain can be well described using a third-order difference formula…”

“…In the following, cross sections of very neutron-rich isotopes (including dozens of new ones) produced by Ge+ Be [1], Se+ Be [3], and U+ Be [14,15]) measured in the above mentioned experiments are used for validating the calculations by a set of OES relations recently proposed by Mei in Ref. [29]. On the basis of Eq.…”