Time-dependent Hartree-Fock Simulations Research Articles

Shell effects in fission and quasi-fission

Quantum shell effects are responsible for asymmetric fission. They are also expected to affect the formation of fission fragments in quasi-fission reactions occurring in heavy-ion collisions. Shell effects in fission are studied with the single-particle energy level density near the Fermi level. In particular, shell effects in the pre-fragments and their role in fixing the final mass asymmetry of the fission fragments are discussed. Systematic time-dependent Hartree-Fock simulations of heavy-ion collisions show that quasi-fission fragment properties share strong similarities with fragments formed in fission of the compound nuclei. This is an indication that similar shell effects are responsible for the final asymmtery in both mechanisms.

Shell effects in fission and quasi-fission reactions

Quantum shell effects are responsible for asymmetric fission. They are also expected to affect the formation of fission fragments in quasi-fission reactions occurring in heavy-ion collisions. Systematic time-dependent Hartree-Fock simulations of 40–56Ca+176Yb collisions show that quasi-fission fragment properties share strong similarities with fragments formed in fission of the compound nuclei. This is an indication that similar shell effects are responsible for the final asymmtery in both mechanisms.

Microscopic study of fusion reactions with a weakly bound nucleus: Effects of deformed halo

We present a microscopic study on the fusion reactions C14,15+Th232 by emphasizing the effect of deformed halo structure on reaction dynamics within the framework of time-dependent density functional theory. The internuclear potentials are obtained by using the density-constraint frozen Hartree-Fock approach and then are adopted to calculate the fusion cross sections of C14,15+Th232, taking all the orientations of deformed reactants into account. Our microscopic calculations not only reproduce the enhancement of fusion cross sections at sub-barrier energies without any adjustable parameters, but also reveal the underlying mechanism of this enhancement, which is driven by the deformed halo structure of C15. More interestingly, by performing particle number projection based on the wave functions from time-dependent Hartree-Fock simulation, we find that the one-neutron transfer probabilities are more sensitive to the orientations of C15 than Th232, indicating the notable effects of halo structure on the reaction dynamics.Received 30 August 2022Accepted 17 November 2022DOI:https://doi.org/10.1103/PhysRevC.107.L011601©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear density functional theoryNuclear reactionsUnstable nuclei induced nuclear reactionsNuclear Physics

Comparison of fission and quasi-fission modes

Quantum shell effects are known to affect the formation of fragments in nuclear fission. Shell effects also affect quasi-fission reactions occurring in heavy-ion collisions. Systematic time-dependent Hartree-Fock simulations of 50Ca+176Yb collisions show that the mass equilibration between the fragments in quasi-fission is stopped when they reach similar properties to those in the asymmetric fission mode of the 226Th compound nucleus. Similar shell effects are then expected to determine the final repartition of nucleons between the nascent fragments in both mechanisms. Future experimental studies that could test these observations are discussed.

Fusion hindrance in heavy systems with time-dependent Hartree-Fock

We analyze fusion hindrance in heavy systems, where the fusion probability around the Coulomb barrier is hindered compared with that in light and medium-mass systems. We perform simulations of central collisions around the Coulomb barrier in heavy systems with time-dependent Hartree‒Fock (TDHF) and find that the fusion hindrance is realized in TDHF simulations. We extract nucleus‒nucleus potential and energy dissipation in heavy systems by a method combining a microscopic TDHF evolution to a macroscopic collective equation of motion. We find that the extracted potentials exhibit a dynamical increase at small relative distances, while the extracted friction coefficients show rather a behavior similar to that in light and medium-mass systems. We find from our analysis that the dynamical increase in potential is a main contribution to this fusion hindrance.

Fission dynamics within time-dependent Hartree-Fock. II. Boost-induced fission

Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe induced fission processes, using quadrupole boosts in the nuclide $^{240}$Pu as an example. Methods: Quadrupole constrained Hartree-Fock calculations are used to create a potential energy surface. An isomeric state and a state beyond the second barrier peak are excited by means of instantaneous as well as temporally extended gauge boosts with quadrupole shapes. The subsequent deexcitation is studied in a time-dependent Hartree-Fock simulation, with emphasis on fissioned final states. The corresponding fission fragment mass numbers are studied. Results: In general, the energy deposited by the quadrupole boost is quickly absorbed by the nucleus. In instantaneous boosts, this leads to fast shape rearrangements and violent dynamics that can ultimately lead to fission. This is a qualitatively different process than the deformation-induced fission. Boosts induced within a finite time window excite the system in a relatively gentler way, and do induce fission but with a smaller energy deposition. Conclusions: The fission products obtained using boost-induced fission in time-dependent Hartree-Fock are more asymmetric than the fragments obtained in deformation-induced fission, or the corresponding adiabatic approaches.

Quantum breathing mode of interacting particles in a one-dimensional harmonic trap

Extending our previous work, we explore the breathing mode---the [uniform] radial expansion and contraction of a spatially confined system. We study the breathing mode across the transition from the ideal quantum to the classical regime and confirm that it is not independent of the pair interaction strength (coupling parameter). We present the results of time-dependent Hartree-Fock simulations for 2 to 20 fermions with Coulomb interaction and show how the quantum breathing mode depends on the particle number. We validate the accuracy of our results, comparing them to exact Configuration Interaction results for up to 8 particles.

Time-dependent Hartree-Fock studies of the dynamical fusion threshold

A microscopic description of dynamical fusion threshold in heavy ion collisions is performed in the framework of time-dependent Hartree-Fock (TDHF) theory using Skyrme energy density functional (EDF). TDHF fusion threshold is in a better agreement with experimental fusion barrier. We find that the onset of extra push lies at the effective fissility 33, which is consistent with the prediction of Swiatecki’s macroscopic model. The extra push energy in our TDHF simulation is systematically smaller than the prediction in macroscopic model. The important dynamical effects and the way to fit the parameter might be responsible for the different results.

Quantum breathing mode of interacting particles in harmonic traps

The breathing mode – the uniform radial expansion and contraction of a system of interacting particles – is analyzed. Extending our previous work [Bauch et al 2009 Phys. Rev. B. 80 054515] we present a systematic analysis of the breathing mode for fermions with an inverse power law interaction potential w(r) ~ r−dwith d = 1,2,3 in the whole range of coupling parameters. The results thus cover the range from the ideal "gas" to the Wigner crystal-like state. In addition to exact results for two particles obtained from a solution of the time-dependent Schrödinger equation we present results for N = 4,6 from multiconfiguration time-dependent Hartree-Fock simulations.

Numerical Bound State Electron Dynamics of Carbon Dioxide in the Strong-Field Regime

Time-dependent Hartree-Fock simulations for a linear triatomic molecule (CO(2)) interacting with a short IR (1.63 eV) three-cycle pulse reveal that the carrier-envelope shape and phase are the essential field parameters determining the bound state electron dynamics during and after the laser-molecule interaction. Analysis of the induced dipole oscillation reveals that the envelope shape (Gaussian or trapezoidal) controls the excited state population distribution. Varying the carrier envelope phase for each of the two pulse envelope shapes considerably changes the excited state populations. Increasing the electric field amplitude alters the relative populations of the excited states, generally exciting higher states. A windowed Fourier transform analysis of the dipole evolution during the laser pulse reveals the dynamics of state excitation and in particular state coupling as the laser intensity increases.

Electronic optical response of molecules in intense fields: Comparison of TD-HF, TD-CIS, and TD-CIS(D) approaches

Time-dependent Hartree-Fock (TD-HF) and time-dependent configuration interaction (TD-CI) methods with Gaussian basis sets have been compared in modeling the response of hydrogen molecule, butadiene, and hexatriene exposed to very short, intense laser pulses (760 nm, 3 cycles). After the electric field of the pulse returns to zero, the molecular dipole continues to oscillate due to the coherent superposition of excited states resulting from the nonadiabatic excitation caused by the pulse. The Fourier transform of this residual dipole gives a measure of the nonadiabatic excitation. For low fields, only the lowest excited states are populated, and TD-CI simulations using singly excited states with and without perturbative corrections for double excitations [TD-CIS(D) and TD-CIS, respectively] are generally in good agreement with the TD-HF simulations. At higher field strengths, higher states are populated and the methods begin to differ significantly if the coefficients of the excited states become larger than approximately 0.1. The response of individual excited states does not grow linearly with intensity because of excited state to excited state transitions. Beyond a threshold in the field strength, there is a rapid increase in the population of many higher excited states, possibly signaling an approach to ionization. However, without continuum functions, the present TD-HF and TD-CI calculations cannot model ionization directly. The TD-HF and TD-CIS simulations are in good accord because the excitation energies obtained by linear response TD-HF [also known as random phase approximation (RPA)] agree very well with those obtained from singly excited configuration interaction (CIS) calculations. Because CIS excitation energies with the perturbative doubles corrections [CIS(D)] are on average lower than the CIS excitation energies, the TD-CIS(D) response is generally stronger than TD-CIS.

Polarization effects on the hyper-Raman spectra of carbon tetrachloride: a joint experimental-theoretical study.

Hyper-Raman spectra of pure carbon tetrachloride in the liquid phase are recorded for different combinations of the polarizations of the incident and scattered lights and are compared to ab initio time-dependent Hartree-Fock simulations. Both the calculated intensities of the Raman and hyper-Raman spectra give indeed a quite satisfactory agreement with polarized experimental spectra.

Many-body effects in molecular photoionization in intense laser fields; time-dependent Hartree-Fock simulations.

The time evolution of the reduced single electron density matrix for eight electrons in a one-dimensional finite box potential driven by an intense laser field is calculated by numerically integrating the time-dependent Hartree-Fock equations. We study the effects of the Coulomb interaction, field intensity, and frequency on the time profile of the ionization process. Our computed saturation ionization intensity (Isat) is in good agreement with experimental results for decatetraene [Ivanov et al. J. Chem. Phys. 117, 1575 (2002)].

Hartree-Fock dynamical electron-correlation effects in C60 after laser excitation.

In the static Hartree-Fock limit, the on-site electron-electron interaction has no effect on the electronic properties of C60. But upon the laser excitation, the dynamical correlation effect appears. The time-dependent Hartree-Fock simulation through the Hubbard model shows that such an effect originates from the charge fluctuation, but an increase in the on-site electron-electron interaction suppresses the charge fluctuation and reduces the absorbed energy and the bond structure distortion.

Charge and bonding redistribution in octatetraene driven by a strong laser field: Time-dependent Hartree–Fock simulation

The time evolution of the reduced single electron density matrix for the π electrons in conjugated molecules in an intense laser field is calculated by numerically integrating the time-dependent Hartree–Fock equations for the Pariser–Parr–Pople model Hamiltonian. We study the field frequency and intensity dependence of the π-electron response, the charge fluctuations with respect to the ground state, and the molecular polarization in unsubstituted and acceptor–donor substituted octatetraene, where we also examine the interaction between a permanent electric dipole moment and the laser field. Our results demonstrate the origin of large nonperturbative changes in the π-electronic charges and bond orders (diagonal and off-diagonal density matrix elements, respectively) induced by a strong laser field.

Beating of monopole modes in nuclear dynamics

Time-dependent Hartree-Fock simulations of the evolution of excited gold fragments have been performed. The observed dynamics appears more complex than the collective expansion picture. The minimum density is often not reached during the first density oscillation because of the beating of several collective compression modes.

Time-dependent Hartree-Fock simulation of the expansion of abraded nuclei

A recent interpretation of the caloric curve based on the expansion of the abraded spectator nucleus is reanalyzed in the framework of the time-dependent Hartree-Fock (TDHF) evolution. It is shown that the TDHF dynamics is more complex than a single monopolar collective motion at moderate energy. The inclusion of other important collective degrees of freedom may lead to the dynamical creation of hollow structure. Then, low density regions could be locally reached after a long time by the creation of these exotic density profiles. In particular the systematic of the minimum density reached during the expansion (the so-called turning points) appears to be different.