Time-dependent Hartree-Fock Approach Research Articles

Theoretical uncertainty quantification for heavy-ion fusion

Many aspects of physics that spans from the origin of the elements to nuclear technologies rely on a robust description of nuclear reactions. One therefore needs predictive modelling of nuclear quantum many-body dynamics in which the uncertainties are well-understood. The authors use the time-dependent Hartree-Fock approach, and apply uncertainty quantification to the nuclear dynamics, considering a collection of low-energy heavy-ion fusion reactions. They find that the uncertainty in the theoretical results mainly arises from structure properties, such as the skin of neutron-rich nuclei, which are particularly ill-constrained. This work highlights the importance of including reaction data in the construction and constraint of new theoretical models that can treat dynamics and structure on the same footing.

Microscopic study of the fusion reactions Ca40,48+Ni78 and the effect of the tensor force

We provide a microscopic description of the fusion reactions between $^{40,48}\mathrm{Ca}$ and $^{78}\mathrm{Ni}$. The internuclear potentials are obtained using the density-constrained (DC) time-dependent Hartree-Fock (TDHF) approach and fusion cross sections are calculated via the incoming wave boundary condition method. By performing DC-TDHF calculations at several selected incident energies, the internuclear potentials for both systems are obtained and the energy-dependence of fusion barrier are revealed. The influence of tensor force on internuclear potentials of $^{48}\mathrm{Ca}+^{78}\mathrm{Ni}$ is more obvious than those of $^{40}\mathrm{Ca}+^{78}\mathrm{Ni}$. By comparing the calculated fusion cross sections between $^{40}\mathrm{Ca}+^{78}\mathrm{Ni}$ and $^{48}\mathrm{Ca}+^{78}\mathrm{Ni}$, an interesting enhancement of subbarrier fusion cross sections for the former system is found, which can be explained by the narrow width of internuclear potential for $^{40}\mathrm{Ca}+^{78}\mathrm{Ni}$ while the barrier heights and positions are very close to each other. The tensor force suppresses the subbarrier fusion cross sections of both two systems.

Evolution of static and dynamical density correlations of one-dimensional soft-core bosons from the Tonks-Girardeau limit to a clustering fluid

Repulsive soft-core atomic systems may undergo clustering if their density is high enough that core overlap is unavoidable. In one-dimensional bosonic quantum systems, it has been shown that this instability triggers a transition from a Luttinger liquid to various cluster Luttinger liquids. Here, we focus on the Luttinger liquid regime and theoretically study the evolution of key observables related to density fluctuations, which manifest a striking dependence on density. We tune the interaction so that the low-density regime corresponds to a Tonks-Girardeau gas and show that as the density is increased the system departs more and more from Tonks-Girardeau behavior, displaying a much larger compressibility as well as rotonic excitations that finally drive the clustering transition. We compare various theoretical approaches, which are accurate in different regimes. Using quantum Monte Carlo methods and analytic continuation as a benchmark, we investigate the regime of validity of the mean-field Bogoliubov and the real-time multiconfiguration time-dependent Hartree-Fock approaches. Part of the behavior that we describe should be observable in ultracold Rydberg-dressed gases, provided that system losses are prevented.

Multiorbital impact on strong-field ionization of HCl molecules

We have put forward the time-dependent Hartree-Fock approach to investigate ionization dynamics of HCl molecules subjected to strong few-cycle laser pulses, which is based on the finite-element discrete-variable representation in prolate spheroidal coordinates and the Crank-Nicolson method. It is demonstrated that the electron is favored to be freed by the peak electric field pointing towards the H atom for the HCl molecule possessing the bonding length $R=2.5$ a.u., while the ionization prefers to occur for the maximum electric field pointing from the H nucleus to Cl nucleus with increasing internuclear separations. Analysis indicates that the ionization yield of $5\ensuremath{\sigma}$ electrons becomes significant with respect to that of $2\ensuremath{\pi}$ electrons with stretching bonding lengths, and the relative contributions of the ionization from $5\ensuremath{\sigma}$ and $2\ensuremath{\pi}$ electrons change as a function of internuclear separations, which gives rise to the above distinct oriented ionization of HCl molecules.

Ionization of the CO molecule in intense short two-color laser pulses

We present numerical results for the CO single ionization in the intense short two-color laser pulses consisting of a fundamental laser field and its second harmonic. Using a time-dependent Hartree–Fock approach, the ionization probabilities have been computed for different choices of the fundamental field intensity, intensity ratio and relative phase difference between the two colors. When the fundamental field intensity runs from 1×1013 to 2×1014 W/cm2, the dominant contribution of the highest occupied molecular orbital to the CO two-color ionization is emphasized. The contribution of the inner valence orbitals can be manipulated by varying the relative phase and the intensity ratio. Present numerical results reveal a higher CO ionization probability when laser electric field points from the C nucleus towards the O nucleus.

Static-field ionization model of He-like ions for diagnostics of light-field intensity

We study static-field ionization of He-like ions with nuclear charge number in the range of $2\le Z \le 36$. Both the tunneling and over-the-barrier regimes are considered. We calculate the ionization rates by three approximate methods: a fitting formula based on the Perelemov-Popov-Terent'ev (PPT) formula, a perturbative expansion in powers of $1/Z$, and a single-active electron approximation, and compare them with reference ionization rates computed by the multiconfiguration time-dependent Hartree-Fock (MCTDHF) approach. The relative deviation of the rates computed by the PPT-based fitting formula and the third-order perturbation theory from the rates computed by the MCTDHF approach is found to be around 10\%. We discuss quantitatively the contribution from the exchange interaction during the ionization by comparing the single-active electron rates and the reference rates in which multielectron effects are included. We find that a single-active electron approximation, where the exchange interaction is neglected, results in the overestimation of the ionization rates by 30\% for He and 2\% for He-like Kr, showing that the magnitude of the effect of the exchange interaction scales approximately as $1/Z$.

Plasmon-enhanced high order harmonic generation of open-ended finite-sized carbon nanotubes: The effects of incident field's intensity and frequency and the interference between the incident and scattered fields.

The nonlinear optical properties of hybrid systems composed of a silver nanosphere and an open-ended finite-sized armchair single-walled carbon nanotube (SWCNT) are systematically investigated by the hybrid time-dependent Hartree-Fock (TDHF)/finite difference time domain (FDTD) approach, which combines the real-time TDHF approach for the molecular electronic dynamics with the classical computational electrodynamics approach, the FDTD, for solving Maxwell's equations. The high order harmonic generation (HHG) spectra of SWCNTs are studied as a function of the intensity (I0) and frequency (ω0) of the incident field, and SWCNTs length as well. It is found that the near field generated by a Ag nanoparticle has an overall enhancement to the molecular HHG in all the energy range, and it extends the HHG spectra to high energy. The inhomogeneity of the near field results in the appearance of even-order harmonics, and their corresponding spectral intensities are sensitive to ω0, therefore the near field's gradient. When ω0 is far away from the frequency of plasmon resonance of the silver nanosphere (ωc), the interference between the incident and scattering light beams extends the spectral range and makes the HHG spectra more sensitive to I0, while at ω0 = ωc, the impact of the interference on the spectra is negligible.

Collective oscillations of a two-component Fermi gas on the repulsive branch

We calculate frequencies of collective oscillations of two-component Fermi gas that is kept on the repulsive branch of its energy spectrum. Not only is a paramagnetic phase explored, but also a ferromagnetically separated one. Both in-, and out-of-phase perturbations are investigated, showing contributions from various gas excitations. Additionally, we compare results coming from both time-dependent Hartree-Fock and density-functional approaches.

Predictions of New Neutron-Rich Isotopes at N = 126 in the Multinucleon Transfer Reaction 136Xe + 194Ir

Aiming to produce new neutron-rich nuclei around $N=126$, the multi-nucleon transfer reaction $^{136}$Xe+$^{194}$Ir is investigated by using the GRAZING model and the three-dimensional time-dependent Hartree-Fock (TDHF) approach. De-excitation processes of the primary fragments are taken into account in both models. The results of GRAZING indicate that this system is a promising candidate for producing new neutron-rich isotones with $N=126$. In contrast, no such nuclei are observed in TDHF. Nucleon transfer process in TDHF collisions is studied and the relation to final isotopic production cross sections is discussed.

Low-symmetry A3B type pentachlorocyclotriphosphazene substituted phthalocyanine with improved nonlinear optical properties: Synthesis, spectroscopic and ab initio/(TD)DFT study

In the present work, we performed structural modification of 2-hydroxy-9(10),16(17),23(24)-tri-tert-butyl-29H,31H-phthalocyanine (1) using phosphonitrilic chloride trimer (hexachlorocyclotriphosphazene). Despite the wide availability of phosphazenes and their derivatives, including polymeric materials based on them, this is one of the few examples of the introduction of an active phosphazene cycle into the structure of a macroheterocyclic compound. Target free-base ligand 2 was characterized by the MALDI-TOF/TOF mass spectrometry, as well as the 1H, 31P NMR and FT-IR spectroscopy. Also, a tendency towards H-aggregation in polar media was demonstrated. Theoretical calculations based on time-dependent Hartree-Fock approach for nonlinear optical properties have allowed revealing a self-defocusing effect in the case of phthalocyanine 2, which makes it an interesting candidate for all-optical switching, two-photon imaging, and optical power limiting applications.

Impact of initial fluctuations on the dissipative dynamics of interacting Fermi systems: A model case study

Standard methods used for computing the dynamics of a quantum many-body system are the mean-field (MF) approximations such as the time-dependent Hartree-Fock (TDHF) approach. Even though MF approaches are quite successful, they suffer some well-known shortcomings, one of which is insufficient dissipation of collective motion. The stochastic mean-field approach (SMF), where a set of MF trajectories with random initial conditions are considered, is a good candidate to include dissipative effects beyond mean field. In this approach, the one-body density matrix elements are treated initially as a set of stochastic Gaussian c numbers that are adjusted to reproduce first and second moments of collective one-body observables. It is shown that the predictive power of the SMF approach can be further improved by relaxing the Gaussian assumption for the initial probabilities. More precisely, using Gaussian or uniform distributions for the matrix elements generally leads to overdamping for long times, whereas distributions with smaller kurtosis lead to much better reproduction of the long time evolution.

Deformed shell effects in Ca48+Bk249 quasifission fragments

Background: Quasifission is the main reaction channel hindering the formation of superheavy nuclei (SHN). Its understanding will help to optimize entrance channels for SHN studies. Quasifission also provides a probe to understand the influence of shell effects in the formation of the fragments.Purpose: Investigate the role of shell effects in quasifission and their interplay with the orientation of the deformed target in the entrance channel.Methods: $^{48}\mathrm{Ca}+^{249}\mathrm{Bk}$ collisions are studied with the time-dependent Hartree-Fock approach for a range of angular momenta and orientations.Results: Unlike similar reactions with a $^{238}\mathrm{U}$ target, no significant shell effects which could be attributed to the $^{208}\mathrm{Pb}$ ``doubly magic'' nucleus are found. However, the octupole deformed shell gap at $N=56$ seems to strongly influence quasifission in the most-central collisions.Conclusions: Shell effects similar to those observed in fission affect the formation of quasifission fragments. Mass-angle correlations could be used to experimentally isolate the fragments influenced by $N=56$ octupole shell gaps.

Microscopic studies of production cross sections in multinucleon transfer reaction Ni58+Sn124

Background: Multinucleon transfer reactions at low-energy collisions are considered to be promising for the production of new exotic nuclei, which are difficult to produce by other methods. Theoretical studies are required to provide reliable predictions for the experiments and to help understand the microscopic mechanism in multinucleon transfer reactions.Purpose: We provide a predictive approach for production cross sections and show how and to what extent the microscopic approach works well in multinucleon transfer reactions.Methods: We employ the $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ approach, which combines the microscopic time-dependent Hartree-Fock (TDHF) model with the state-of-art statistical model $\text{GEMINI}\phantom{\rule{0.16em}{0ex}}++$, to take into account both the multinucleon transfer dynamics and the secondary de-excitation process. The properties of primary products in multinucleon transfer process, such as transfer probabilities and primary cross sections, are extracted from TDHF dynamics using the particle-number projection method. Production cross sections for secondary products are evaluated using the statistical model $\text{GEMINI}\phantom{\rule{0.16em}{0ex}}++$.Results: We investigate the influence of colliding energies and deformation orientations of target and projectile nuclei on multinucleon transfer dynamics in the reaction $^{58}\mathrm{Ni}+^{124}\mathrm{Sn}$. More nucleons are observed to transfer in the tip collision than in the side collision. The production cross sections for secondary fragments with $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ calculations well reproduce the experimental measurements at energies close to the Coulomb barrier. At sub-barrier energy, the theoretical results gradually deviate from the experimental data with the increase of the number of transferred neutrons, showing the limitations of a single mean-field approximation in the TDHF approach. Possible origins for this discrepancy are discussed. The total cross sections integrated over all the neutron transfer channels are in good agreement with the experimental data for all the energies. We compare the production cross sections of $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ calculations with those from GRAZING model and find that our approach gives a description as quantitatively good as the semiclassical model, although there is no adjustable parameters for the reaction dynamics in the microscopic TDHF method.Conclusions: The microscopic $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ approach reasonably reproduces the experimental data at energies close to the Coulomb barrier and well accounts for the multinucleon transfer mechanism. The present studies clearly reveal the applicability of $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ method in multinucleon transfer reactions, which thus is a promising tool for predicting the properties of new reactions.

Time-dependent Hartree-Fock plus Langevin approach for hot fusion reactions to synthesize the Z=120 superheavy element

We develop a novel approach to fusion reactions for syntheses of superheavy elements, which combines the time-dependent Hartree-Fock (TDHF) method with a dynamical diffusion model based on the Langevin equation. In this approach, the distance of the closest approach for the capture process is estimated within the TDHF approach, which is then plugged into the dynamical diffusion model as an initial condition. We apply this approach to hot fusion reactions leading to formation of the element $Z=120$, that is, the $^{48}$Ca+$^{254,257}$Fm, $^{51}$V+$^{249}$Bk, and $^{54}$Cr+$^{248}$Cm reactions. Our calculations indicate that the distances of the closest approach for these systems are similar to each other and thus the difference in the probabilities of evaporation residue formation among those reaction systems originates mainly from the evaporation process, which is sensitive to the fission barrier height and the excitation energy of a compound nucleus.

Production mechanism of neutron-rich nuclei around N = 126 in the multi-nucleon transfer reaction 132Sn + 208Pb**Supported by National Natural Science Foundation of China (11705118, 11475115, 11647026) and Natural Science Foundation of SZU (2016017)

The time-dependent Hartree-Fock approach in three dimensions is employed to study the multi-nucleon transfer reaction 132Sn + 208Pb at various incident energies above the Coulomb barrier. Probabilities for different transfer channels are calculated by using the particle-number projection method. The results indicate that neutron stripping (transfer from the projectile to the target) and proton pick-up (transfer from the target to the projectile) are favored. De-excitation of the primary fragments is treated by using the state-of-art statistical code GEMINI++. Primary and final production cross sections of the target-like fragments (with Z=77 to Z=87) are investigated. The results reveal that fission decay of heavy nuclei plays an important role in the de-excitation process of nuclei with Z > 82. It is also found that the final production cross sections of neutron-rich nuclei depend only slightly on the incident energy, while those of neutron-deficient nuclei depend strongly on the incident energy.

Exploring Zeptosecond Quantum Equilibration Dynamics: From Deep-Inelastic to Fusion-Fission Outcomes in ^{58}Ni+^{60}Ni Reactions.

Energy dissipative processes play a key role in how quantum many-body systems dynamically evolve toward equilibrium. In closed quantum systems, such processes are attributed to the transfer of energy from collective motion to single-particle degrees of freedom; however, the quantum many-body dynamics of this evolutionary process is poorly understood. To explore energy dissipative phenomena and equilibration dynamics in one such system, an experimental investigation of deep-inelastic and fusion-fission outcomes in the ^{58}Ni+^{60}Ni reaction has been carried out. Experimental outcomes have been compared to theoretical predictions using time dependent Hartree-Fock and time dependent random phase approximation approaches, which, respectively, incorporate one-body energy dissipation and fluctuations. Excellent quantitative agreement has been found between experiment and calculations, indicating that microscopic models incorporating one-body dissipation and fluctuations provide a potential tool for exploring dissipation in low-energy heavy ion collisions.

On the multi-layer multi-configurational time-dependent Hartree approach for bosons and fermions.

A multi-layer multi-configurational time-dependent Hartree (MCTDH) approach using a second quantization representation (SQR) based on optimized time-dependent orbitals is introduced. The approach combines elements of the multi-layer MCTDH-SQR approach of Wang and Thoss, which employs a preselected time-independent orbital basis, and the MCTDH for bosons and multi-configuration time-dependent Hartree-Fock approaches, which do not use multi-layering but employ time-dependent orbital bases. In contrast to existing MCTDH-type approaches, the results of the present approach for a given number of configurations are not invariant with respect to unitary transformations of the time-dependent orbital basis. Thus a natural orbital representation is chosen to achieve fast convergence with respect to the number of configurations employed. Equations of motion for the present ansatz, called (multi-layer) MCTDH in optimized second quantization representation, are derived. Furthermore, a scheme for the calculation of optimized unoccupied single-particle functions is given which can be used to avoid singularities in the equations of motion.

Theoretical and experimental investigations on linear and nonlinear optical response of metal complexes doped PMMA films

Metal organic complexes, diaceto bis benzimidazole cobalt(II) and diaceto bis benzimidazole copper(II), are synthesized by a simple chemical route. The synthesized powders are doped in PMMA with 1, 3, 5 wt% and deposited as free standing films of thickness ∼1 μm. For theoretical simulation, metal organic complex (MOC) embedded into the PMMA matrix is subjected to polarizability and hyperpolarizability calculations using the PM6 algorithm in MOPAC2012 package. It is found that the minimum interaction distance between PMMA and MOC is about 34 nm and does not vary with respect to the dopant. The copper complex shows higher interaction energy with the polymer matrix than the cobalt complex. Time dependent Hartree Fock approach is used to calculate the α, β and γ values for static, 0.25 and 0.5 eV energies; the cobalt complex shows higher polarizability and hyperpolarizability than the copper complex. Experimentally, the optical absorption, thermo-optic coefficient, nonlinear absorption coefficient and nonlinear refractive index of the samples are determined. The thermo-optic coefficients of the samples are seen to increase with increasing dopant concentration. From open aperture Z-scan studies the films are found to exhibit reverse saturable absorption behaviour, and from the closed aperture Z-scan all samples are found to exhibit self-focusing effects. The calculated third order susceptibility is in the order of 10−5 esu. The optical limiting properties are studied at 650 nm using a 20 mW laser and all the samples are found to exhibit good optical limiting in the operating wavelength.

Sensitivity of the fusion cross section to the density dependence of the symmetry energy

It is the aim of this paper to discuss the impact of nuclear fusion on the EOS. This is a timely subject given the expected availability of increasingly exotic beams at rare isotope facilities\,\cite{balantekin2014}. In practice, we focus on $^{48}$Ca+$^{48}$Ca fusion. We employ three different approaches to calculate fusion cross-sections for a set of energy density functionals with systematically varying nuclear matter properties. Fusion calculations are performed using frozen densities, using a dynamic microscopic method based on density-constrained time-dependent Hartree-Fock (DC-TDHF) approach, as well as direct TDHF study of above barrier cross-sections. For these studies, we employ a family of Skyrme parametrizations with systematically varied nuclear matter properties. We find a slight preference for forces which deliver a slope of symmetry energy of $L\approx 50$\,MeV that corresponds to a neutron-skin thickness of $^{48}$Ca of $R_\mathrm{skin}\!=\!(0.180\!-\!0.210)$\,fm.

Superfluid fission dynamics with microscopic approaches

Recent progresses in the description of the latter stage of nuclear fission are reported. Dynamical effects during the descent of the potential towards scission and in the formation of the fission fragments are studied with the time-dependent Hartree-Fock approach with dynamical pairing correlations at the BCS level. In particular, this approach is used to compute the final kinetic energy of the fission fragments. Comparison with experimental data on the fission of 258Fm are made.