Systematic investigation of projectile fragmentation using beams of unstable B and C isotopes

Background: Models describing nuclear fragmentation and fragmentation fission deliver important input for planning nuclear physics experiments and future radioactive ion beam facilities. These models are usually benchmarked against data from stable beam experiments. In the future, two-step fragmentation reactions with exotic nuclei as stepping stones are a promising tool for reaching the most neutron-rich nuclei, creating a need for models to describe also these reactions. Purpose: We want to extend the presently available data on fragmentation reactions towards the light exotic region on the nuclear chart. Furthermore, we want to improve the understanding of projectile fragmentation especially for unstable isotopes. Method: We have measured projectile fragments from (10,12-18C) and B10-15 isotopes colliding with a carbon target. These measurements were all performed within one experiment, which gives rise to a very consistent data set. We compare our data to model calculations. Results: One-proton removal cross sections with different final neutron numbers (1 pxn) for relativistic C-10,C-12-18 and B10-15 isotopes impinging on a carbon target. Comparing model calculations to the data, we find that the EPAX code is not able to describe the data satisfactorily. Using ABRABLA07 on the other hand, we find that the average excitation energy per abraded nucleon needs to be decreased from 27 MeV to 8.1 MeV. With that decrease ABRABLA07 describes the data surprisingly well. Conclusions: Extending the available data towards light unstable nuclei with a consistent set of new data has allowed a systematic investigation of the role of the excitation energy induced in projectile fragmentation. Most striking is the apparent mass dependence of the average excitation energy per abraded nucleon. Nevertheless, this parameter, which has been related to final-state interactions, requires further study.

Finding the set of k-additive dominating measures viewed as a flow problem

n this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it.