A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach

Lacroix, Denis; Tanimura, Yusuke; Ayık, S.; Yilmaz, B.

doi:10.1140/epja/i2016-16094-1

Cited by 16 publications

(20 citation statements)

References 25 publications

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“…In a series of works, it was shown that it surprisingly well accounts for correlations beyond mean-field [37][38][39] while treating properly the dynamic close to a spontaneous symmetry breaking [38]. It is also able to include approximately many-body correlation to all orders by connecting the evolution to the BBGKY hierarchy [40]. Some formal and practical aspects are reviewed in Ref.…”

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confidence: 99%

Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

2017

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We show that the total kinetic energy (TKE) of nuclei after the spontaneous fission of 258 Fm can be well reproduced using simple assumptions on the quantum collective phase-space explored by the nucleus after passing the fission barrier. Assuming energy conservation and phase-space exploration according to the stochastic mean-field approach, a set of initial densities is generated. Each density is then evolved in time using the nuclear time-dependent density-functional theory with pairing. This approach goes beyond mean-field by allowing spontaneous symmetry breaking as well as a wider dynamical phase-space exploration leading to larger fluctuations in collective space. The total kinetic energy and mass distributions are calculated. New information on the fission process: fluctuations in scission time, strong correlation between TKE and collective deformation as well as pre-scission particle emission, are obtained. We conclude that fluctuations of TKE and mass are triggered by quantum fluctuations.PACS numbers: 21.60. Jz, 24.75.+i, 25.85.Ca, 27.90.+b The dynamical modeling of a nuclear Fermi quantum droplet that spontaneously breaks into two pieces represents one of the most exciting challenges of nuclear physics today. Beside its description, a deeper microscopic understanding of spontaneous fission (SF) is of great importance to form the heaviest elements at the frontier of the nuclear chart [1][2][3] or to further improve our knowledge about the competition between the r-process and fission during the primordial nucleosynthesis [4]. Motivated also by its importance in nuclear energy production, intensive experimental efforts have been made to accumulate precise measurements [5][6][7][8][9]. In recent years, an increasing effort was made to remove empirical ingredients that are employed in macroscopic modeling of fission and use microscopic theories [10,11]. The nuclear Density Functional Theory (DFT) is a suitable starting point to describe some aspects related to the large amplitude collective motion (LACM). A minimal information obtained from DFT is the adiabatic collective energy landscape [11]. One challenge to describe spontaneous fission (SF) is the necessity to explicitly treat the evolution as a quantum dynamic in collective space. Progresses have been made with the Time-Dependent Generator Coordinate Method (TDGCM) [12][13][14]. This theory by treating quantally collective degrees of freedom (DOF) is promising. However, the adiabatic assumption often made becomes critical especially close to scission [15]. Dissipation of the collective motion into internal excitations also plays a key role to understand the excitation energy and kinetic energy sharing during fragments separation [16]. Understanding this dissipation requires to include many-body states beyond the adiabatic limit [17]. It is yet unclear how the pre-scission neutron and proton emissions can be incorporated in the TDGCM.The nuclear time-dependent DFT (TDDFT) overcomes some of these limitations. With recently developed symmetry unrest...

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confidence: 99%

Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

2017

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“…New stochastic extensions have been recently proposed for time-dependent quantum approaches [54,55]. A possibility is to inject quantum and/or thermal fluctuations just in the initial conditions of TDHF calculations, leading to a spread of dynamical trajectories and corresponding variances of physical observables.…”

Section: Theoretical Description Of Collision Dynamicsmentioning

confidence: 99%

“…As anticipated above, if a suited stochastic approach is adopted, simplified higher-order contributions to the dynamics are taken into account even though not explicitly implemented. Already within a firstorder-truncation scheme, it was found that a stochastic approach, including fluctuations only in the initial conditions, can be used to restore all the BBGKY missing orders approximately [54], and generate large-amplitude fluctuations; in this case, a coherent ensemble of mean-field states is propagated along different trajectories from an initial stochastic distribution. Such scheme, which appears appropriate in low-energy framework, is however insufficient to address highly dissipative regimes.…”

Section: Semi-classical Stochastic Modelsmentioning

confidence: 99%

“…A qualitative illustration of the mechanism is given in Fig.14. In addition to volume instabilities, surface effects (and related instabilities) are particularly important for the description of the configuration paths encountered in low-and Fermi-energy heavy ion collisions. As far as the description of low-energy nuclear processes is concerned, it is worth mentioning that stochastic extensions of time-dependent quantum approaches have been recently proposed [54,127,55]. Within this scheme, quantum and/or thermal fluctuations are injected in the initial conditions, leading to a spread of dynamical trajectories and corresponding variances of physical observables.…”

Section: Reaction Dynamics At Medium Energy: Semi-peripheral Collisionsmentioning

confidence: 99%

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Collision dynamics at medium and relativistic energies

Colonna

2020

Progress in Particle and Nuclear Physics

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Recent results connected to nuclear collision dynamics, from low up to relativistic energies, are reviewed. Heavy ion reactions offer the unique opportunity to probe the complex nuclear manybody dynamics and to explore, in laboratory experiments, transient states of nuclear matter under several conditions of density, temperature and charge asymmetry. From the theoretical point of view, transport models are an essential tool to undertake these investigations and make a connection betwen the nuclear effective interaction and sensitive observables of experimental interest. In this article, we mainly focus on the description of results of transport models for a selection of reaction mechanisms, also considering comparisons of predictions of different approaches. This analysis can help understanding the impact of the interplay between mean-field and correlation effects, as well as of in-medium effects, on reaction observables, which is an essential point also for extracting information on the nuclear Equation of State. A special emphasis will be given to the review of recent studies aimed at constraining the density behavior of the nuclear symmetry energy. For reactions at medium (Fermi) energies, we will describe light particle and fragment emission mechanisms, together with isospin transport effects. Collective effects characterizing nuclear collision dynamics, such as transverse and elliptic flows, will be discussed for relativistic heavy ion reactions, together with meson production and isotopic ratios.

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“…[23]). In particular, correlations beyond the kinetic-equation level (or, equivalently, the upper orders beyond two-body correlations in a BBGKY hierarchy [24]) are introduced in full phase-space continuously in time. Such correlations are introduced by letting collide phase-space portions of extended size, large enough that the occupancy variance in h 3 cells corresponds to the scattering of two nucleons, and by simultaneously imposing that the Pauli blocking of initial and final states is nowhere violated over the full phase-space extension.…”

Section: -Modelling Volume and Surface Fluctuations: From Nuclear Mat...mentioning

confidence: 99%

How nuclear jets form and disintegrate into clusters in heavy-ion collisions

Napolitani,

Colonna

2019

Preprint

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The most extreme deformations that can be explored in heavy-ion collisions at Fermi-energies are collimated flows of nuclear matter which recall jet dynamics. From microphysics to the cosmological scale, jets are rather common topologies. In nuclear physics, pioneering works focused on the breakup of these structures, resulting into early nuclear-fission models in analogy to the droplet formation in viscous liquids; such view became emblematic to explain surface-energy effects and surface instability by analogy with the Rayleigh instability. Through a dynamical approach based on the Boltzmann-Langevin equation, well adapted to out-of-equilibrium conditions, we explored the possibility that nuclear jets could arise in heavy-ion collisions from different conditions than those leading to fission or neck fragmentation, and that they can breakup from mechanisms that are almost unrelated to cohesive properties.

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A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach

Cited by 16 publications

References 25 publications

Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

Collision dynamics at medium and relativistic energies

How nuclear jets form and disintegrate into clusters in heavy-ion collisions

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