E-polynomials of the SL(2, C)-character varieties of surface groups

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a once-punctured surface of any genus into SL(2, C), for any possible holonomy around the puncture. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behavior of the E-polynomial under fibrations.

E-polynomial of SL(2,C)-character varieties of complex curves of genus 3.

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve of genus g = 3 into SL(2, C), and also of the moduli space of twisted representations. The case of genus g = 1, 2 has already been done in [12]. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations.

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.