Fusion window problem in time-dependent Hartree-Fock theory revisited

Tohyama, Mitsuru; Umar, A. S.

doi:10.1103/physrevc.65.037601

Cited by 33 publications

(79 citation statements)

References 14 publications

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“…By comparing with the standard TDHF calculations, an increase of the fluctuations has been found and the agreement with experimental data has been much improved. The two-body dissipation arising from nucleon-nucleon collisions has been taken into account in a quantum mechanical way with the extended TDHF [25,26] or time-dependent density matrix (TDDM) approaches [27][28][29]. So far only a few studies on the dynamical fluctuation and two-body dissipation have been implemented because beyond TDHF calculations require a lot of numerical efforts and computational time.…”

Section: Introductionmentioning

confidence: 99%

Dissipation dynamics and spin-orbit force in time-dependent Hartree-Fock theory

et al. 2014

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We investigate the one-body dissipation dynamics in heavy-ion collisions of 16 O+ 16 O using a fully three-dimensional time-dependent Hartree-Fock (TDHF) theory with the modern Skyrme energy functional and without any symmetry restrictions. The energy dissipation is revealed to decrease in deep-inelastic collisions of the light systems as the bombarding energy increases owing to the competition between collective motion and single-particle degrees of freedom. The role of spin-orbit force is given particular emphasis in deep-inelastic collisions. The spin-orbit force causes a significant enhancement of the dissipation. The time-even coupling of spin-orbit force plays a dominant role at low energies, while the influence of time-odd terms is notable at high energies. About 40-65% of the total dissipation depending on the different parameter sets is predicted to arise from the spin-orbit force. The theoretical fusion cross section has a reasonably good agreement with the experimental data, considering that no free parameters are adjusted to reaction dynamics in the TDHF approach.

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Section: Introductionmentioning

confidence: 99%

Dissipation dynamics and spin-orbit force in time-dependent Hartree-Fock theory

et al. 2014

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“…This is done for instance in the Time-Dependent Density Matrix theory (TDDM) where both the one-body density matrix and the two-body correlation operator are followed in time [28]. These theories are however rarely applied due to the large number of degrees of freedom to consider [29].…”

Section: A Generalities On Perturbation Theory and Stochastic Mechanicsmentioning

confidence: 99%

Stochastic mean-field dynamics for fermions in the weak-coupling limit

Lacroix

2006

Phys. Rev. C

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Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond mean-field is first presented. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states D = |Φa Φ b | / Φ b | Φa where |Φa and |Φ b are antisymmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical 40 Ca nucleus under the influence of a statistical ensemble of two-body contact interaction. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. Restricting to two particles-two holes residual interaction, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as D = |Φ Φ| where |Φ is a normalized Slater determinant. The associated stochastic Schroedinger equation for single-particle wave-functions is given.

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“…Realistic calculations for those approaches are limited so far to light systems and low energies [16][17][18].…”

Section: Dynamic Modelsmentioning

confidence: 99%

Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions

2017

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Background: The distribution of protons and neutrons in the matter created in heavy-ion collisions is one of the main points of interest for the collision physics, especially at supranormal densities. We report results of the first systematic simulation of proton and neutron density distributions in central heavy-ion collisions within the beam energy range of E beam ≤ 800 MeV/nucl. Method: The Boltzmann-Uhlenbeck-Uehling (pBUU) transport model with four empirical models for the density dependence of the symmetry energy was employed. Results of simulations using pure Vlasov dynamics were added for completeness. In addition, the Time Dependent Hartree Fock (TDHF) model, with the SV-bas Skyrme interaction, was used to model the heavy-ion collisions at E beam ≤ 40 MeV/nucl. Maximum proton and neutron densities ρ max p and ρ max n , reached in the course of a collision, were determined from the time evolution of ρ p and ρ n .Results: The highest total densities predicted at E beam = 800 MeV/nucl were of the order of ∼ 2.5 ρ 0 (ρ 0 = 0.16 fm −3 ) for both Sn and Ca systems. They were found to be only weakly dependent on the initial conditions, beam energy, system size and a model of the symmetry energy.The proton-neutron asymmetry δ = (ρ max n −ρ max p )/(ρ max n +ρ max p ) at maximum density does depend, though, on these parameters. The highest value of δ found in all systems and at all investigated beam energies was ∼ 0.17. Summary:We report the first systematic simulation of proton and neutron densities in matter produced in heavy-ion collisions of Ca and Sn systems at beam energies below 800 MeV/nucl using pBUU and TDHF models. We find limits on the maximum proton and neutron densities and the related proton-neutron asymmetry δ as a function of the initial state, beam energy, system size and a symmetry energy model. While the maximum densities are almost independent of these parameters, our simulation reveals, for the first time, their subtle impact on the protonneutron asymmetry. Most importantly, we find that variations in the proton-neutron asymmetry at maximum densities are related at most at 50% level to the details in the symmetry energy at supranormal density. The reminder is due to the details in the symmetry energy at subnormal densities and its impact on proton and neutron distributions in the initial state. This result puts to forefront the need of a proper initialization of the nuclei in the simulation, but also brings up the question of microscopy, such as shell effects, that affect initial proton and neutron densities, 2 but cannot be consistently incorporated into semiclassical transport models.

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Fusion window problem in time-dependent Hartree-Fock theory revisited

Cited by 33 publications

References 14 publications

Dissipation dynamics and spin-orbit force in time-dependent Hartree-Fock theory

Dissipation dynamics and spin-orbit force in time-dependent Hartree-Fock theory

Stochastic mean-field dynamics for fermions in the weak-coupling limit

Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions

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