Stochastic semi-classical description of fusion at near-barrier energies

Ayık, S.; Yilmaz, B.; Lacroix, Denis

doi:10.1103/physrevc.81.034605

Cited by 41 publications

(34 citation statements)

References 39 publications

(43 reference statements)

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“…[41]. Although the stochastic mean-field technique was applied to simple models [37][38][39]42] or to obtain expressions of transport coefficients [40,[43][44][45][46], we present here the first application to a realistic physical phenomena where the phasespace sampling is explicitly made.…”

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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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Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

2017

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“…Here, we employ a stochastic approach, which is much simpler than the generator coordinate method, and is based on the fact that initial state fluctuations (quantal and thermal) dominate the fluctuation dynamics at low energies [8,9]. This idea has been proposed nearly 30 years ago by Esbensen et al in a macroscopic model of nuclear reactions [10,11], and more recently tested in heavy-ion fusion reactions [12]. Following a similar idea, recently, a stochastic mean-field approach (SMF) has been proposed [13] to treat fluctuations beyond mean-field description.…”

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Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

2012

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Dynamics of spontaneous symmetry breaking and fluctuations in the Lipkin-Meshkov-Glick model are investigated in a stochastic mean-field approach. Different from the standard mean-field, in the stochastic approach, initial state fluctuations, are incorporated. In weak coupling, the approach perfectly reproduces the exact quantal dynamics. On the other hand, for increasing coupling strength, above the symmetry breaking threshold, the approach provides description of gross properties (i.e. time averaged behavior) of the exact quantal evolution.

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“…In the extension including pairing, additional fluctuations originating from particle-particle and holehole channels appears from Eqs. (6)(7). This is an important new aspect which allows to explore initial conditions with non-zero anomalous densities.…”

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“…By considering an ensemble of mean-field trajectories with a specific choice of the fluctuations (quantal zero-point and thermal) in the initial state, it is possible to overcome some of these shortcomings. Several applications, especially in the nuclear physics context [5][6][7][8], have shown that this approach can improve the mean-field description by including important dissipative aspects in transport properties of heavy-ion collisions. More recently, we illustrated that such an approach, in addition to fluctuations, can accurately tackle the problem of symmetry breaking close to bifurcation point in collective energy landscape [9].…”

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Quantal corrections to mean-field dynamics including pairing

2013

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Extending the stochastic mean-field model by including pairing, an approach is proposed for describing evolutions of complex many-body systems in terms of an ensemble of Time-Dependent Hartree-Fock Bogoliubov trajectories which is determined by incorporating fluctuations in the initial state. Non-linear evolution of the initial fluctuations provides an approximate description of quantal correlations and fluctuations of collective observables. Since the initial-state fluctuations break the particle-number symmetry, the dynamical description in which pairing correlations play a crucial role is greatly improved as compare to the mean-field evolution. The approach is illustrated for a system of particles governed by a pairing Hamiltonian. Under certain conditions, it is possible to provide an approximate description for quantal evolution of a system in terms of an ensemble of classical trajectories with proper choice of initial conditions. This aspect appears naturally in the path integral formulation of quantum dynamics and has been recognized in refs. [1,2]. In recent years, this idea has been pushed forward to improved the mean-field description of many-body interacting systems [3,4]. Mean-field description cannot describe essential quantal effects associated to collective motion and severely underestimates fluctuations of collective observables. By considering an ensemble of mean-field trajectories with a specific choice of the fluctuations (quantal zero-point and thermal) in the initial state, it is possible to overcome some of these shortcomings. Several applications, especially in the nuclear physics context [5][6][7][8], have shown that this approach can improve the mean-field description by including important dissipative aspects in transport properties of heavy-ion collisions. More recently, we illustrated that such an approach, in addition to fluctuations, can accurately tackle the problem of symmetry breaking close to bifurcation point in collective energy landscape [9]. Up to now, the stochastic mean-field (SMF) approach with initial fluctuations has been developed starting from a Time-Dependent HartreeFock (TDHF) version of the mean-field. Nowadays, there are increasing interests in the treatment of pairing to describe evolution of strongly interacting Fermi liquids [10][11][12][13][14] employing the Time-Dependent Hartree-Fock Bogoliubov (TDHFB) approach or its simplified BCS limit. While the TDHFB theory provides an important improvement beyond TDHF, it still suffers from the above quoted limitations: i.e. underestimation of quantum collective fluctuations and impossibility to spontaneously break symmetries. Due to the successful description of * Electronic address: lacroix@ganil.fr the SMF approach in geometric symmetry breaking, it is rather tempting to introduce quantum fluctuations through initial sampling to treat pairing where the U (1) symmetry breaking plays an important role.In this work, we present an extension of the SMF approach by incorporating pairing into the description. In the standa...

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Stochastic semi-classical description of fusion at near-barrier energies

Cited by 41 publications

References 39 publications

Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

Quantal corrections to mean-field dynamics including pairing

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