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

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

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

An improved method for estimating the neutron background in measurements of neutron capture reactions

The relation between the neutron background in neutron capture measurements and the neutron sensitivity related to the experimental setup is examined. It is pointed out that a proper estimate of the neutron background may only be obtained by means of dedicated simulations taking into account the full framework of the neutron-induced reactions and their complete temporal evolution. No other presently available method seems to provide reliable results, in particular under the capture resonances. An improved neutron background estimation technique is proposed, the main improvement regarding the treatment of the neutron sensitivity, taking into account the temporal evolution of the neutron-induced reactions. The technique is complemented by an advanced data analysis procedure based on relativistic kinematics of neutron scattering. The analysis procedure allows for the calculation of the neutron background in capture measurements, without requiring the time-consuming simulations to be adapted to each particular sample. A suggestion is made on how to improve the neutron background estimates if neutron background simulations are not available.Comment: 11 pages, 9 figure

Compensation effect between deaths from Covid-19 and crashes: The Italian case

Emergencies such as the Covid-19 pandemic pose several decision-making issues, while clear evidence of successful strategies are still unavailable, different policies may be identified. However, in such emergencies, the preservation of public health, by firstly reducing human loss of life may be prioritized and then restrictive measures are implemented. The trade-off between damage due to the threat and the decrease in damage due to the lockdown is largely unexplored. Here we show that there is a degree of compensation between damage from epidemic deaths and from traffic deaths, especially in the case of immediate restrictive measures imposed by governments. Based on the Italian case, we found that damage from loss of human Capital and health care costs could have been fully compensated if the lockdown had been imposed ten days earlier. Considering only one Italian region (Puglia), where the epidemic was delayed and then restrictions were timely, damage due to loss of human Capital was largely compensated in the real scenario. However, damage due to loss of welfare could not have been fully compensated for, since Covid-19 deaths largely outnumber traffic deaths in the simulated epidemic period and loss of welfare damage is scarcely dependent on the age-at-death. From a broader perspective, societies seem to react to external threats as a whole organism, thus tending to restore the original equilibrium. Governmental decisions could accelerate this process. However, in the case of similar threats, some wounds cannot be compensated for, such as the incalculable damage due to loss of welfare

Analysis of Boltzmann-Langevin Dynamics in Nuclear Matter

The Boltzmann-Langevin dynamics of harmonic modes in nuclear matter is analyzed within linear-response theory, both with an elementary treatment and by using the frequency-dependent response function. It is shown how the source terms agitating the modes can be obtained from the basic BL correlation kernel by a simple projection onto the associated dual basis states, which are proportional to the RPA amplitudes and can be expressed explicitly. The source terms for the correlated agitation of any two such modes can then be extracted directly, without consideration of the other modes. This facilitates the analysis of collective modes in unstable matter and makes it possible to asses the accuracy of an approximate projection technique employed previously.Comment: 13 latex pages, 4 PS figure

Time development of a density perturbation in the unstable nuclear matter

We present the solution of the time development of an unstable initial density perturbation in the linearized Vlasov equation, completing the previous analysis in the literature. The additional contributions found are usually damped and can be neglected at large times in the unstable region. The work clarifies also the problem of the normalization of the solution with respect to the initial perturbation of the density.Comment: revision of the discussion, different initial perturbation, 9 pages, 4 figures included, uses epsfi