Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1008.3033 · Physical Review Letters

Particle Transfer Reactions with the Time-Dependent Hartree-Fock Theory Using a Particle Number Projection Technique

C. Simenel

Published Nov 4, 2010• 201 citations
arXivHTMLPDF

Abstract

A particle-number projection technique is used to calculate transfer probabilities in the 16O+208Pb reaction below the fusion barrier. The time evolution of the many-body wave function is obtained with the time-dependent Hartree-Fock (TDHF) mean-field theory. The agreement with experimental data for the sum of the proton-transfer channels is good, considering that TDHF has no parameter adjusted on the reaction mechanism. Some perspectives for extensions beyond TDHF to include cluster transfers are discussed.

DOI
10.1103/physrevlett.105.192701

Related papers

Particle-Number Fluctuations and Correlations in Transfer Reactions Obtained Using the Balian-Vénéroni Variational Principle

C. Simenel

The Balian-Vénéroni (BV) variational principle, which optimizes the evolution of the state according to the relevant observable, is used at the mean-field level to determine the particle-number fluctuations in fragments of many-body systems. For fermions, the numerical evaluation of such fluctuations requires the use of a time-dependent Hartree-Fock (TDHF) code. Proton, neutron, and total nucleon number fluctuations in fragments produced in collisions of two (40)Ca are computed well above the fusion barrier. For deep-inelastic collisions, the fluctuations calculated from the BV variational principle are much larger than standard TDHF results, and closer to experimental fluctuations. Correlations between proton and neutron numbers are determined. These correlations are shown to be larger with exotic systems where charge equilibration occurs.

arXiv:1011.2293•Physical Review Letters•Mar 16, 2011•118 citations

Time-dependent generator coordinate method for many-particle tunneling

N. Hasegawa, K. Hagino, Yusuke Tanimura

It has been known that the time-dependent Hartree-Fock (TDHF) method, or the time-dependent density functional theory (TDDFT), fails to describe many-body quantum tunneling. We overcome this problem by superposing a few time-dependent Slater determinants with the time-dependent generator coordinate method (TDGCM). We apply this method to scattering of two α particles in one dimension, and demonstrate that the TDGCM method yields a finite tunneling probability even at energies below the Coulomb barrier, at which the tunneling probability is exactly zero in the TDHF. This is the first case in which a many-particle tunneling is simulated with a microscopic real-time approach.

arXiv:2006.06944•Physics Letters B•Aug 12, 2020•10 citations

Numerical Calculations of TDHF

P. D. Stevenson

We discuss some aspects of implementing the time-dependent Hartree-Fock method in the case of nuclear physics. Topics discussed include implementation of the time-stepping algorithm, considerations involving the effective interaction, and the use (or not) of particular optional terms in the energy density functional, and boundary conditions. Examples of application of the technique to giant resonances and reactions are given, concentrating on issues to do with numerical and conceptual interpretation.

Frontiers in nuclear and particle physics•Jun 27, 2019•3 citations

Microscopic description of pair transfer between two superfluid Fermi systems. II. Quantum mixing of time-dependent Hartree-Fock-Bogolyubov trajectories

David Regnier, Denis Lacroix A

While superfluidity is accurately grasped with a state that explicitly breaks the particle number symmetry, a precise description of phenomena such as the particle transfer during heavy-ion reactions can only be achieved by considering systems with good particle numbers. We investigate the possibility to restore particle number in many-body dynamical problems by mixing up several time-dependent Hartree-Fock-Bogolyubov (TDHFB) trajectories. In our approach, each trajectory is independent from the others and the quantum mixing between trajectories is deduced from a variational principle. The associated theory can be seen as a simplified version of the multiconfiguration TDHFB (MC-TDHFB) theory. Its accuracy to tackle the problem of symmetry restoration in dynamical problems is illustrated for the case of two superfluid systems that exchange particles during a short time. In Phys. Rev. C 97, 034627 (2018), using a schematic model where two systems initially described by a pairing Hamiltonians are coupled during a short contact time, it was demonstrated that statistical mixing of TDHFB trajectories can only qualitatively describe the transfer process and that a fully quantum treatment is mandatory. We show here that the present MC-TDHFB approach gives an excellent agreement with the exact solution when the two superfluids are the same (symmetric case) or different (asymmetric case) and from weak to strong interaction strength. Finally, we discuss the benefits and bottleneck of this method in view of its application to realistic systems.

arXiv:1902.06491•Physical Review C•Jun 21, 2019•22 citations

Accuracy of the time-dependent Hartree-Fock approximation

Claude Bardos, François Golse, Alex D. Gottlieb +1 more

This article examines the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find the TDHF approximation to be accurate when there are sufficiently many particles and the initial many-particle state is a Slater determinant, or any Gibbs equilibrium state for noninteracting fermions. Assuming a bounded two-particle interaction, we obtain a bound on the error of the TDHF approximation, valid for short times. We further show that the error of the the TDHF approximation vanishes at all times in the mean field limit.

arXiv:math-ph/0303070•Mar 30, 2003•0 citations

Large amplitude motion with a stochastic mean-field approach

Denis Lacroix A, Sakir Ayik B, Bulent Yilmaz +1 more

In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.

arXiv:1210.2519•EPJ Web of Conferences•Jan 1, 2012•0 citations
A particle-number projection technique is used to calculate transfer probabilities in the 16O+208Pb reaction below the fusion barrier. The time evolution of the many-body wave function is obtained with the time-dependent Hartree-Fock (TDHF) mean-field theory. The agreement with experimental data for the sum of the proton-transfer channels is good, considering that TDHF has no parameter adjusted on the reaction mechanism. Some perspectives for extensions beyond TDHF to include cluster transfers are discussed.
The Balian-Vénéroni (BV) variational principle, which optimizes the evolution of the state according to the relevant observable, is used at the mean-field level to determine the particle-number fluctuations in fragments of many-body systems. For fermions, the numerical evaluation of such fluctuations requires the use of a time-dependent Hartree-Fock (TDHF) code. Proton, neutron, and total nucleon number fluctuations in fragments produced in collisions of two (40)Ca are computed well above the fusion barrier. For deep-inelastic collisions, the fluctuations calculated from the BV variational principle are much larger than standard TDHF results, and closer to experimental fluctuations. Correlations between proton and neutron numbers are determined. These correlations are shown to be larger with exotic systems where charge equilibration occurs.
It has been known that the time-dependent Hartree-Fock (TDHF) method, or the time-dependent density functional theory (TDDFT), fails to describe many-body quantum tunneling. We overcome this problem by superposing a few time-dependent Slater determinants with the time-dependent generator coordinate method (TDGCM). We apply this method to scattering of two α particles in one dimension, and demonstrate that the TDGCM method yields a finite tunneling probability even at energies below the Coulomb barrier, at which the tunneling probability is exactly zero in the TDHF. This is the first case in which a many-particle tunneling is simulated with a microscopic real-time approach.
We discuss some aspects of implementing the time-dependent Hartree-Fock method in the case of nuclear physics. Topics discussed include implementation of the time-stepping algorithm, considerations involving the effective interaction, and the use (or not) of particular optional terms in the energy density functional, and boundary conditions. Examples of application of the technique to giant resonances and reactions are given, concentrating on issues to do with numerical and conceptual interpretation.
While superfluidity is accurately grasped with a state that explicitly breaks the particle number symmetry, a precise description of phenomena such as the particle transfer during heavy-ion reactions can only be achieved by considering systems with good particle numbers. We investigate the possibility to restore particle number in many-body dynamical problems by mixing up several time-dependent Hartree-Fock-Bogolyubov (TDHFB) trajectories. In our approach, each trajectory is independent from the others and the quantum mixing between trajectories is deduced from a variational principle. The associated theory can be seen as a simplified version of the multiconfiguration TDHFB (MC-TDHFB) theory. Its accuracy to tackle the problem of symmetry restoration in dynamical problems is illustrated for the case of two superfluid systems that exchange particles during a short time. In Phys. Rev. C 97, 034627 (2018), using a schematic model where two systems initially described by a pairing Hamiltonians are coupled during a short contact time, it was demonstrated that statistical mixing of TDHFB trajectories can only qualitatively describe the transfer process and that a fully quantum treatment is mandatory. We show here that the present MC-TDHFB approach gives an excellent agreement with the exact solution when the two superfluids are the same (symmetric case) or different (asymmetric case) and from weak to strong interaction strength. Finally, we discuss the benefits and bottleneck of this method in view of its application to realistic systems.
This article examines the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find the TDHF approximation to be accurate when there are sufficiently many particles and the initial many-particle state is a Slater determinant, or any Gibbs equilibrium state for noninteracting fermions. Assuming a bounded two-particle interaction, we obtain a bound on the error of the TDHF approximation, valid for short times. We further show that the error of the the TDHF approximation vanishes at all times in the mean field limit.
In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.