Importance of realistic phase-space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions

Yilmaz, B.; Lacroix, Denis; Curebal, Resul

doi:10.1103/physrevc.90.054617

Cited by 17 publications

(29 citation statements)

References 39 publications

(69 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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“…The initial state fluctuations, which can be specified in a suitable manner, are incorporated into the dynamics by generating an ensemble of single-particle density matrix according to the fluctuations in the initial state. In a number of applications, it was illustrated that the SMF approach provides very good approximation for exact quantal evolution of the many-body systems at low energies, where collisional dissipation mechanism does not play an important role [11][12][13]. For a description of the approach and its various applications we refer to [14,15].…”

Section: Introductionmentioning

confidence: 99%

Quantal description of nucleon exchange in a stochastic mean-field approach

et al. 2015

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“…[15], a proper account for the initial quantum phase-space might require to go beyond the Gaussian assumption of the initial sampling. In simple models, it is possible to directly get the initial phasespace with some semi-classical techniques as in [15]. In more complex systems, this seems more complicated and the sampling beyond the Gaussian approximation might not be possible.…”

Section: Discussionmentioning

confidence: 99%

“…In addition, we have shown recently that an improved treatment of the initial phase-space [15] without the Gaussian approximation can further ameliorate the many-body dynamics beyond the mean-field and allows to describe initially correlated many-body states.…”

Section: The Smf Approach and Itsmentioning

confidence: 99%

“…For this purpose, we took as an example the Lipkin-MeshkovGlick (LMG) Model [20][21][22][23] that has already been used to benchmark the SMF theory using phase-space initial sampling both in the Gaussian [11] and non-Gaussian [15] assumptions. In the two previous applications, a set of mean-field trajectories have been explicitly followed in time using the equations of motion:…”

Section: Applicationmentioning

confidence: 99%

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

et al. 2016

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The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here, that this approach is equivalent to a simplified version of the Bogolyubov-BornGreen-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-, ..., N-body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for short time evolution. In that case, it gives information on the evolution time-scale close to a saddle point associated to a quantum phase-transition. For long time evolution and strong coupling, we observed that the simplified BBGKY hierarchy cannot be truncated and only the full SMF with initial sampling leads to reasonable results.

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Importance of realistic phase-space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions

Cited by 17 publications

References 39 publications

Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

Quantal description of nucleon exchange in a stochastic mean-field approach

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

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