Abstract: In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the pattern of this distribution. We discuss the main features of the latter and explain analytically those that we understand. In particular, we prove that it is a nonperturbative property and we find out a large/small coupling constant duality. We also find and study features that may connect our problem with certain aspects of nonlinear classical dynamics, such as the existence of resonances and sensitive dependence on the state of the system. We show that the latter has, indeed, a similar origin than in classical mechanics: the appearance of small denominators in the perturbative series. Inspired by the proof of the Kolmogorov-Arnold-Moser theorem, we are able to deal with this problem by introducing a cutoff in energies that eliminates these small denominators. We also formulate some conjectures that we are not able to prove at present but can be supported by numerical experiments.

Abstract: The Xi(0)(c) baryon is unstable and usually decays into charmless final states by the c -> sud transition. It can, however, also disintegrate into a pi(-) meson and a Lambda(+)(c) baryon via s quark decay or via cs -> dc weak scattering. The interplay between the latter two processes governs the size of the branching fraction B(Xi(0)(c) -> pi(-) Lambda(+)(c)), first measured here to be (0.55 +/- 0.02 +/- 0.18)%, where the first uncertainty is statistical and second systematic. This result is compatible with the larger of the theoretical predictions that connect models of hyperon decays using partially conserved axial currents and SU(3) symmetry with those involving the heavy-quark expansion and heavy-quark symmetry. In addition, the branching fraction of the normalization channel, B(Xi(+)(c) -> pK(-) pi(+)) = (1.135 +/- 0.002 +/- 0.387)% is measured.

Abstract: We measured the neutron capture-to-fission cross-section ratio (alpha ratio) and the capture cross section of U-235 between 0.2 and 200 eV at the nTOF facility at CERN. The simultaneous measurement of neutron-induced capture and fission rates was performed by means of the nTOF BaF2 Total Absorption Calorimeter (TAC), used for detection of gamma rays, in combination with a set of micromegas detectors used as fission tagging detectors. The energy dependence of the capture cross section was obtained with help of the Li-6(n, t) standard reaction determining the n_TOF neutron fluence; the well-known integral of the U-235(n, f) cross section between 7.8 and 11 eV was then used for its absolute normalization. The alpha ratio, obtained with slightly higher statistical fluctuations, was determined directly, without need for any reference cross section. To perform the analysis of this measurement we developed a new methodology to correct the experimentally observed effect that the probabilities of detecting a fission reaction in the TAC and the micromegas detectors are not independent. The results of this work have been used in a new evaluation of U-235 performed within the scope of the Collaborative International Evaluated Library Organisation (CIELO) Project, and are consistent with the ENDF/B-VIII.0 and JEFF-3.3 capture cross sections below 4 eV and above 100 eV. However, the measured capture cross section is on average 10% larger between 4 and 100 eV.