An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions

We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.Comment: 4 pages; comments added, proof simplifie

Constrained caloric curves and phase transition for hot nuclei

Simulations based on experimental data obtained from multifragmenting quasi-fused nuclei produced in central $^{129}$Xe + $^{nat}$Sn collisions have been used to deduce event by event freeze-out properties in the thermal excitation energy range 4-12 AMeV [Nucl. Phys. A809 (2008) 111]. From these properties and the temperatures deduced from proton transverse momentum fluctuations, constrained caloric curves have been built. At constant average volumes caloric curves exhibit a monotonic behaviour whereas for constrained pressures a backbending is observed. Such results support the existence of a first order phase transition for hot nuclei.Comment: 14 pages, 5 figures, accepted in Physics Letters

Nuclear multifragmentation time-scale and fluctuations of largest fragment size

Distributions of the largest fragment charge, Zmax, in multifragmentation reactions around the Fermi energy can be decomposed into a sum of a Gaussian and a Gumbel distribution, whereas at much higher or lower energies one or the other distribution is asymptotically dominant. We demonstrate the same generic behavior for the largest cluster size in critical aggregation models for small systems, in or out of equilibrium, around the critical point. By analogy with the time-dependent irreversible aggregation model, we infer that Zmax distributions are characteristic of the multifragmentation time-scale, which is largely determined by the onset of radial expansion in this energy range.Comment: Accepted for publication in Physical Review Letters on 8/4/201

Coulomb chronometry to probe the decay mechanism of hot nuclei

In 129 Xe+ nat Sn central collisions from 8 to 25 MeV/A, the three-fragment exit channel occurs with a significant cross section. We show that these fragments arise from two successive binary splittings of a heavy composite system. The sequence of fragment production is determined. Strong Coulomb proximity effects are observed in the three-fragment final state. A comparison with Coulomb trajec-tory calculations shows that the time scale between the consecutive break-ups decreases with increasing bombarding energy, becoming quasi-simultaneous above excitation energy E * = 4.0$\pm$0.5 MeV/A. This transition from sequential to simultaneous break-up was interpreted as the signature of the onset of multifragmentation for the three-fragment exit channel in this system.Comment: 12 pages; 13 Figures; 4 Table; Accepted for publication in Physical Review

Isospin transport in 84Kr + 112,124Sn collisions at Fermi energies

Isotopically resolved fragments with Z<=20 have been studied with high resolution telescopes in a test run for the FAZIA collaboration. The fragments were produced by the collision of a 84Kr beam at 35 MeV/nucleon with a n-rich (124Sn) and a n-poor (112Sn) target. The fragments, detected close to the grazing angle, are mainly emitted from the phase-space region of the projectile. The fragment isotopic content clearly depends on the n-richness of the target and it is a direct evidence of isospin diffusion between projectile and target. The observed enhanced neutron richness of light fragments emitted from the phase-space region close to the center of mass of the system can be interpreted as an effect of isospin drift in the diluted neck region.Comment: 8 pages, 7 figure

N and Z odd-even staggering in Kr + Sn collisions at Fermi energies

The odd-even staggering of the yield of final reaction products has been studied as a function of proton (Z) and neutron (N) numbers for the collisions 84 Kr+112 Sn and 84 Kr+124 Sn at 35 MeV/nucleon, in a wide range of elements (up to Z ~ 20). The experimental data show that staggering effects rapidly decrease with increasing size of the fragments. Moreover the staggering in N is definitely larger than the one in Z. Similar general features are qualitatively reproduced by the GEMINI code. Concerning the comparison of the two systems, the staggering in N is in general rather similar, being slightly larger only for the lightest fragments produced in the n-rich system. In contrast the staggering in Z, although smaller than that in N, is sizably larger for the n-poor system with respect to the n-rich one.Comment: 6 pages, 5 figures, Revtex forma

Energy measurement and fragment identification using digital signals from partially depleted Si detectors

A study of identification properties of a Si-Si DE-E telescope exploiting an underdepleted residual-energy detector has been performed. Five different bias voltages have been used, one corresponding to full depletion, the others associated with a depleted layer ranging from 90% to 60% of the detector thickness. Fragment identification has been performed using either the DE-E technique or Pulse Shape Analysis (PSA). Both detectors are reverse mounted: particles enter from the low field side, to enhance the PSA performance. The achieved charge and mass resolution has been quantitatively expressed using a Figure of Merit (FoM). Charge collection efficiency has been evaluated and the possibility of energy calibration corrections has been considered. We find that the DE-E performance is not affected by incomplete depletion even when only 60% of the wafer is depleted. Isotopic separation capability improves at lower bias voltages with respect to full depletion, though charge identification thresholds are higher than at full depletion. Good isotopic identification via PSA has been obtained from a partially depleted detector whose doping uniformity is not good enough for isotopic identification at full depletion.Comment: 13 pages, 10 figures 5 tables; submitted to European Physical Journal

FAZIA applications

International audienceThe present status and the perspectives of the FAZIA project are presented. The main achievements in terms of identification thresholds and isotopic resolution are discussed, together with the adopted technical solutions. The detector is particularly well suited for the investigation of isospin transport phenomena at intermediate beam energies; perspectives to reduce the identification thresholds to cope with lower energy ISOL beams are briefly introduced. Some experimental results concerning isospin transport effects obtained with a test telescope are presented. The study of isospin transport phenomena can give information on the symmetry energy term of the nuclear equation of state by comparing the experimental results on isospin related observables with the predictions of transport codes

Isospin transport in ^{84}Kr + ^{112,124}Sn reactions at Fermi energies : first physics results from FAZIA

The FAZIA Collaboration studied collisions of a ^{84}Kr beam at 35 AMeV with ^{112}Sn and ^{124}Sn targets by means of a three-layer telescope. A good isotopic resolution up to Z = 20 was reached. The isotopic content of the products was found to depend on the neutron richness of the target, which is an evidence of isospin diffusion. Neutron-rich light fragments emitted from the phase space close to the centre-of-mass were observed, which can be interpreted as an effect of isospin drift in the neck region of low density