Crossover from a fission-evaporation scenario towards multifragmentation in spallation reactions

Mostly for the purpose of applications for the energy and the environment and for the design of sources of neutrons or exotic nuclides, intense research has been dedicated to spallation, induced by protons or light projectiles at incident energies of around 1 GeV. In this energy range, while multifragmentation has still a minor share in the total reaction cross section, it was observed to have, together with fission, a prominent role in the production and the kinematics of intermediate-mass fragments, so as to condition the whole production of light and heavy nuclides. The experimental observables we dispose of attribute rather elusive properties to the intermediate-mass fragments and do not allow to classify them within one exclusive picture which is either multifragmentation or fission. Indeed, these two decay mechanisms, driven by different kinds of instabilities, exhibit behaviours which are closely comparable. High-resolution measurements of the reaction kinematics trace the way for probing finer features of the reaction kinematics.Comment: Conference proceedings: International Meeting "Selected topics on nuclear methods for non-nuclear applications", September 27-30, 2006, Varna (Bulgaria). Invited tal

Inhomogeneity growth in two-component fermionic systems

The dynamics of fermionic many-body systems is investigated in the framework of Boltzmann-Langevin (BL) stochastic one-body approaches. Within the recently introduced BLOB model, we examine the interplay between mean-field effects and two-body correlations, of stochastic nature, for nuclear matter at moderate temperature and in several density conditions, corresponding to stable or mechanically unstable situations. Numerical results are compared to analytic expectations for the fluctuation amplitude of isoscalar and isovector densities, probing the link to the properties of the employed effective interaction, namely symmetry energy (for isovector modes) and incompressibility (for isoscalar modes). For unstable systems, clusterization is observed. The associated features are compared to analytical results for the typical length and time scales characterizing the growth of unstable modes in nuclear matter and for the isotopic variance of the emerging fragments. We show that the BLOB model is generally better suited than simplified approaches previously introduced to solve the BL equation, and it is therefore more advantageous in applications to open systems, like heavy ion collisions.Comment: 19 pages, 13 figure

Frustrated fragmentation and re-aggregation in nuclei: a non-equilibrium description in spallation

Heavy nuclei bombarded with protons and deuterons in the 1 GeV range have a large probability of undergoing a process of evaporation and fission; less frequently, the prompt emission of few intermediate-mass fragments can also be observed. We employ a recently developed microscopic approach, based on the Boltzmann-Langevin transport equation, to investigate the role of mean-field dynamics and phase-space fluctuations in these reactions. We find that the formation of few IMF's can be confused with asymmetric fission when relying on yield observables, but it can not be assimilated to the statistical decay of a compound nucleus when analysing the dynamics and kinematic observables: it can be described as a fragmentation process initiated by phase-space fluctuations, and successively frustrated by the mean-field resilience. As an extreme situation, which corresponds to non-negligible probability, the number of fragments in the exit channel reduces to two, so that fission-like events are obtained by re-aggregation processes. This interpretation, inspired by nuclear-spallation experiments, can be generalised to heavy-ion collisions from Fermi to relativistic energies, for situations when the system is closely approaching the fragmentation threshold

Bifurcations in Boltzmann-Langevin One Body dynamics for fermionic systems

We investigate the occurrence of bifurcations in the dynamical trajectories depicting central nuclear collisions at Fermi energies. The quantitative description of the reaction dynamics is obtained within a new transport model, based on the solution of the Boltzmann-Langevin equation in three dimensions, with a broad applicability for dissipative fermionic dynamics. Dilute systems formed in central collisions are shown to fluctuate between two energetically favourable mechanisms: reverting to a compact shape or rather disintegrating into several fragments. The latter result can be connected to the recent observation of bimodal distributions for quantities characterising fragmentation processes and may suggest new investigations

Mean-field instabilities and cluster formation in nuclear reactions

We review recent results on intermediate mass cluster production in heavy ion collisions at Fermi energy and in spallation reactions. Our studies are based on modern transport theories, employing effective interactions for the nuclear mean-field and incorporating two-body correlations and fluctuations. Namely we will consider the Stochastic Mean Field (SMF) approach and the recently developed Boltzmann-Langevin One Body (BLOB) model. We focus on cluster production emerging from the possible occurrence of low-density mean-field instabilities in heavy ion reactions. Within such a framework, the respective role of one and two-body effects, in the two models considered, will be carefully analysed. We will discuss, in particular, fragment production in central and semi-peripheral heavy ion collisions, which is the object of many recent experimental investigations. Moreover, in the context of spallation reactions, we will show how thermal expansion may trigger the development of mean-field instabilities, leading to a cluster formation process which competes with important re-aggregation effects

Bifurcations in dissipative fermionic dynamics

The Boltzmann-Langevin One-Body model (BLOB), is a novel one-body transport approach, based on the solution of the Boltzmann-Langevin equation in three dimensions; it is used to handle large-amplitude phase-space fluctuations and has a broad applicability for dissipative fermionic dynamics. We study the occurrence of bifurcations in the dynamical trajectories describing heavy-ion collisions at Fermi energies. The model, applied to dilute systems formed in such collisions, reveals to be closer to the observation than previous attempts to include a Langevin term in Boltzmann theories. The onset of bifurcations and bimodal behaviour in dynamical trajectories, determines the fragment-formation mechanism. In particular, in the proximity of a threshold, fluctuations between two energetically favourable mechanisms stand out, so that when evolving from the same entrance channel, a variety of exit channels is accessible. This description gives quantitative indications about two threshold situations which characterise heavy-ion collisions at Fermi energies. First, the fusion-to-multifragmentation threshold in central collisions, where the system either reverts to a compact shape, or splits into several pieces of similar sizes. Second, the transition from binary mechanisms to neck fragmentation (in general, ternary channels), in peripheral collisions.Comment: Conf. proc. ECHIC November 6-8, 2013 Messina (Italy

Spinodal instability growth in new stochastic approaches

Are spinodal instabilities the leading mechanism in the fragmentation of a fermionic system? Numerous experimental indications suggest such a scenario and stimulated much effort in giving a suitable description, without being finalised in a dedicated transport model. On the one hand, the bulk character of spinodal behaviour requires an accurate treatment of the one-body dynamics, in presence of mechanical instabilities. On the other hand, pure mean-field implementations do not apply to situations where instabilities, bifurcations and chaos are present. The evolution of instabilities should be treated in a large-amplitude framework requiring fluctuations of Langevin type. We present new stochastic approaches constructed by requiring a thorough description of the mean-field response in presence of instabilities. Their particular relevance is an improved description of the spinodal fragmentation mechanism at the threshold, where the instability growth is frustrated by the mean-field resilience.Comment: Conf. proc. IWM2014-EC, Catania, 6-9 May 201

From multifragmentation to supernovae and neutron stars

The thermodynamics properties of globally neutral dense stellar matter are analyzed both in terms of mean field instabilities and structures beyond the mean field. The mean field response to finite wavelenght fluctuations is calculated with the realistic Sly230a effective interaction. A Monte Carlo simulation of a schematic lattice Hamiltonian shows the importance of calculations beyond the mean field to calculate the phase diagram of stellar matter. The analogies and differences respect to the thermodynamics of nuclear matter and finite nuclei are stressed.Comment: To be published in Acta Phys. Hung.

Reading the Lost Folia of the Archimedean Palimpsest: The Last Proposition of the "Method"

The Method is the work in which Archimedes sets out his way of finding the areas and volumes of various figures. It can be divided into three parts. The first part is the preface addressed to Eratosthenes, in which Archimedes explains his motivation for writing the work. We find that he was sending demonstrations of results that he had communicated before—the volume of two novel solids, which we call hoof and vault in this article. As Archimedes thought that it was a good occasion to reveal his way of finding results that he had previously published with rigorous demonstration, he decided to include an exposition of this “way” (tropos in Greek, not method, as is usually assumed in modern accounts.) Thus, the first eleven propositions show how the results in his previous works (Quadrature of the Parabola, Sphere and Cylinder and Conoids and Spheroids) were found. We call this group of propositions the second part of the work. The third and last part, beginning with Prop. 12, treats the two novel solids and gives a demonstration of their volumes. Unfortunately, the end of the Method is lost. As is well known, the Method is known only through the palimpsest found in 1906, and some pages had already been lost. The text of the Method breaks off definitively near the end of the demonstration of the volume of the hoof, the first of the two novel solids announced in the preface. We have no testimony concerning how Archimedes demonstrated the volume of the vault, the second novel solid. In this article, we try to reconstruct this lost demonstration, based on recent studies

Il progetto Maurolico

Viene raccontata la storia del "progetto Maurolico", con particolare riferimento ai risultati ottenuti nello studio dei testi archimedei prodotti da Francesco Maurolico (1494-1575