Time-dependent Hartree-Fock Research Articles

Enhanced nucleon transfer in tip collisions of U238+Sn124

Multinucleon transfer processes in low-energy heavy ion reactions have attracted increasing interest in recent years aiming at production of new neutron-rich isotopes. Clearly, it is an imperative task to further develop understanding of underlying reaction mechanisms to lead experiments to success. In this paper, from systematic time-dependent Hartree-Fock calculations for the $^{238}$U+$^{124}$Sn reaction, it is demonstrated that transfer dynamics depend strongly on the orientations of $^{238}$U, quantum shells, and collision energies. Two important conclusions are obtained: (i) Experimentally observed many-proton transfer from $^{238}$U to $^{124}$Sn can be explained by a multinucleon transfer mechanism governed by enhanced neck evolution in tip collisions; (ii) Novel reaction dynamics are observed in tip collisions at energies substantially above the Coulomb barrier, where a number of nucleons are transferred from $^{124}$Sn to $^{238}$U, producing transuranium nuclei as primary reaction products, that could be a means to synthesize superheavy nuclei. Both results indicate the importance of the neck (shape) evolution dynamics, which are sensitive to the orientations, shell effects and collision energies, for exploring possible pathways to produce new unstable nuclei.

Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model

Due to integrability, baryon-baryon scattering in the massless Gross-Neveu model at large N features only forward elastic scattering. A bare mass term breaks integrability and is therefore expected to induce backward elastic scattering as well as inelastic reactions. We confirm these expectations by a study of baryon-baryon scattering in the massive Gross-Neveu model near the non-relativistic limit. This restriction enables us to solve the time-dependent Hartree-Fock equations with controlled approximations, using a combination of analytical methods from an effective field theory and the numerical solution of partial differential equations.

Collective excitations of a dilute Bose gas at finite temperature: time dependent Hartree–Fock–Bogoliubov theory

Using the time-dependent Hartree–Fock–Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings computed by quantum Monte Carlo simulations. We present also a systematic investigation of the collective modes of a Bose condensate confined in an external trap. Our predictions are in qualitative agreement with previous experimental and theoretical results. We show in particular that our theory is capable of explaining the so-called anomalous behavior of the mode.

Transport properties of isospin asymmetric nuclear matter using the time-dependent Hartree-Fock method

Background: The study of deep-inelastic reactions of nuclei provide a vehicle to investigate nuclear transport phenomena for a full range of equilibration dynamics. These inquires provide us the ingredients to model such phenomena and help answer important questions about the nuclear Equation of State (EOS) and its evolution as a function of neutron-to-proton $(N/Z)$ ratio. Purpose: The motivation is to examine the real-time dynamics of nuclear transport phenomena and its dependence on $(N/Z)$ asymmetry from a microscopic point of view to avoid any pre-conceived assumptions about the involved processes. Method: Time-dependent Hartree-Fock (TDHF) method in full 3D is employed to calculate deep-inelastic reactions of $^{78}$Kr+$^{208}$Pb and $^{92}$Kr+$^{208}$Pb systems at 8.5~MeV$/A$. The impact parameter and energy-loss dependence of relevant observables are calculated. In addition, density constrained TDHF method is used to compute excitation energies of the primary fragments. The statistical deexcitation code GEMINI is utilized to examine the final reaction products. Results: The kinetic energy loss and sticking times as a function of impact parameter are calculated. Final properties of the fragments (charge, mass, scattering angle, kinetic energy) are computed. Conclusions: We find a smooth dependence of the energy loss, $E_\mathrm{loss}$, on the impact parameter for both systems. On the other hand the transfer properties for low $E_\mathrm{loss}$ values are very different for the two systems but become similar in the higher $E_\mathrm{loss}$ regime. The mean life time of the charge equilibration process, obtained from the final $(N-Z)/A$ value of the fragments, is shown to be $\sim 0.5$~zs. This value is slightly larger (but of the same order) than the value obtained from reactions at Fermi energies.

Effect of disorder on exciton dissociation in conjugated polymers**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474218 and 11575116).

By using a multi-configurational time-dependent Hartree–Fock (MCTDHF) method for the time-dependent Schrödinger equation and a Newtonian equation of motion for lattice, we investigate the disorder effects on the dissociation process of excitons in conjugated polymer chains. The simulations are performed within the framework of an extended version of the Su–Schrieffer–Heeger model modified to include on-site disorder, off-diagonal, electron–electron interaction, and an external electric field. Our results show that Coulomb correlation effects play an important role in determining the exciton dissociation process. The electric field required to dissociate an exciton can practically impossibly occur in a pure polymer chain, especially in the case of triplet exciton. However, when the on-site disorder effects are taken into account, this leads to a reduction in mean dissociation electric fields. As the disorder strength increases, the dissociation field decreases effectively. On the contrary, the effects of off-diagonal disorder are negative in most cases. Moreover, the dependence of exciton dissociation on the conjugated length is also discussed.

Microscopic description of production cross sections including deexcitation effects

Background: At the forefront of the nuclear science, production of new neutron-rich isotopes is continuously pursued at accelerator laboratories all over the world. To explore the currently-unknown territories in the nuclear chart far away from the stability, reliable theoretical predictions are inevitable. Purpose: To provide a reliable prediction of production cross sections taking into account secondary deexcitation processes, both particle evaporation and fission, a new method called TDHF+GEMINI is proposed, which combines the microscopic time-dependent Hartree-Fock (TDHF) theory with a sophisticated statistical compound-nucleus deexcitation model, GEMINI++. Results: The method is applied for multinucleon transfer processes in low-energy heavy ion reactions. It is shown that the inclusion of secondary deexcitation processes, which are dominated by neutron evaporation in the present systems, substantially improves agreement with the experimental data. The magnitude of the evaporation effects is very similar to the one observed in GRAZING calculations. TDHF+GEMINI provides better description of the absolute value of the cross sections for channels involving transfer of more than one protons, compared with the GRAZING results. However, there remain discrepancies between the measurements and the calculated cross sections, indicating a limit of the theoretical framework that works with a single mean-field potential. Possible causes of the discrepancies are discussed. Conclusions: In order to perfectly reproduce experimental cross sections for multinucleon transfer processes, one should go beyond the standard self-consistent mean-field description. Nevertheless, the proposed method will provide valuable information to optimize production mechanisms of new neutron-rich nuclei through its microscopic, non-empirical predictions. (Shortened due to the word limit)

Experimental and computational studies on second-and third-order nonlinear optical properties of a novel D-π-A type chalcone derivative: 3-(4-methoxyphenyl)-1-(4-nitrophenyl) prop-2-en-1-one

The present study reports the theoretical and experimental investigations of linear and nonlinear optical (static and dynamic) properties of 3-(4-methoxyphenyl)-1-(4-nitrophenyl)prop-2-en-1-one (MNC). The crystal structure was confirmed from powder X-ray diffraction (PXRD) analysis and evaluated the crystalline quality using high-resolution X-ray diffraction (HRXRD). Linear absorption and fluorescence spectra were recorded and the optical band gap was determined by Tauc’s relation. Third-order nonlinear optical (NLO) characteristics along with optical limiting behavior were explored using the femtosecond (fs) Z-scan technique at 800 and 900nm wavelengths (Ti: sapphire laser, 150fs, 80MHz). The experimental results are supported by theoretical calculations obtained from the density functional theory (DFT). The optimized geometry, linear optical absorption, HOMO-LUMO energy gap, molecular electrostatic potential (MEP), dipole moments and global chemical reactivity descriptors (GCRD) were computed by employing B3LYP/6-311+G(d) level of theory. The static and dynamic linear polarizability (α), first hyperpolarizability (β) and second hyperpolarizability (γ) components were calculated using time-dependent Hartree–Fock (TDHF) method. The computed first hyperpolarizability β(−2ω;ω,ω) at 1064nm wavelength was found to be 55 times greater than that of urea standard. The experimental and calculated dynamic molecular second hyperpolarizabilities γ(−3ω;ω,ω,ω) are in good accordance at 800 and 900nm wavelengths.

Einstein-Podolsky-Rosen-entangled Bose-Einstein condensates in state-dependent potentials: A dynamical study

We study generation of non-local correlations by atomic interactions in a pair of bi-modal Bose-Einstein Condensates in state-dependent potentials including spatial dynamics. The wave-functions of the four components are described by combining a Fock state expansion with a time-dependent Hartree-Fock Ansatz, so that both the spatial dynamics and the local and non-local quantum correlations are accounted for. We find that despite the spatial dynamics, our protocole generates enough non-local entanglement to perform an EPR steering experiment with two spatially separated con-densates of a few thousands of atoms.

Angular momentum dependence of quasifission dynamics in the reaction 48Ca+244Pu

The quasifission dynamics in the reaction $^{48}$Ca+$^{244}$Pu is investigated in the framework of time-dependent Hartree-Fock (TDHF) theory.The calculations are performed in three-dimensional Cartesian coordinate without any symmetry restrictions.The full Skyrme energy functional is incorporated in our TDHF implementation.The quasifission dynamics is quite sensitive to the angular momentum of colliding system.The contact time of quasifission decreases as a function of angular momentum and then forms a plateauwith small oscillations. The quasifission process is accompanied by an important multi-nucleon transfer.The quantum shell effect plays a crucial role in the mass and charge of quasifission fragments.The mass-angle distribution of the fragments is calculated, which can be compared directly with future experiments.

Optimized pulses for Raman excitation through the continuum: Verification using the multiconfigurational time-dependent Hartree-Fock method

We have verified a mechanism for Raman excitation of atoms through continuum levels previously obtained by quantum optimal control using the multiconfigurational time-dependent Hartree-Fock (MCTDHF) method. For the optimal control, which requires running multiple propagations to determine the optimal pulse sequence, we used the computationally inexpensive time-dependent configuration interaction singles (TDCIS) method. TDCIS captures all of the necessary correlation of the desired processes but assumes that ionization pathways reached via double excitations are not present. MCTDHF includes these pathways and all multiparticle correlations in a set of time-dependent orbitals. The mechanism that was determined to be optimal in the Raman excitation of the Ne $1{s}^{2}2{s}^{2}2{p}^{5}3{p}^{1}$ valence state via the metastable $1{s}^{2}2{s}^{1}2{p}^{6}3{p}^{1}$ resonance state involves a sequential resonance-valence excitation. First, a long pump pulse excites the core-hole state, and then a shorter Stokes pulse transfers the population to the valence state. This process represents the first step in a multidimensional x-ray spectroscopy scheme that will provide a local probe of valence electronic correlations. Although at the optimal pulse intensities at the TDCIS level of theory the MCTDHF method predicts multiple ionization or excitation ionization of the atom, at slightly lower intensities (reduced by a factor of about 4) the TDCIS mechanism is shown to hold qualitatively. Quantitatively, the MCTDHF populations are reduced from the TDCIS calculations by a factor of 4.

Single-photon double ionization: renormalized-natural-orbital theory versus multi-configurational Hartree–Fock

The N-particle wavefunction has too many dimensions for a direct time propagation of a many-body system according to the time-dependent Schrödinger equation (TDSE). On the other hand, time-dependent density functional theory (TDDFT) tells us that the single-particle density is, in principle, sufficient. However, a practicable equation of motion for the accurate time evolution of the single-particle density is unknown. It is thus an obvious idea to propagate a quantity which is not as reduced as the single-particle density but less dimensional than the N-body wavefunction. Recently, we have introduced time-dependent renormalized-natural-orbital theory (TDRNOT). TDRNOT is based on the propagation of the eigenfunctions of the one-body reduced density matrix, the so-called natural orbitals. In this paper we demonstrate how TDRNOT is related to the multi-configurational time-dependent Hartree–Fock (MCTDHF) approach. We also compare the performance of MCTDHF and TDRNOT versus the TDSE for single-photon double ionization (SPDI) of a 1D helium model atom. SPDI is one of the effects where TDDFT does not work in practice, especially if one is interested in correlated photoelectron spectra, for which no explicit density functional is known.

Electron correlation in beryllium: Effects in the ground state, short-pulse photoionization, and time-delay studies

We apply a three-dimensional (3D) implementation of the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) method to investigate effects of electron correlation in the ground state of Be as well as in its photoionization dynamics by short XUV pulses, including time-delay in photoionization. First, we obtain the ground state by propagation in imaginary time. We show that the flexibility of the TD-RASSCF on the choice of the active orbital space makes it possible to consider only relevant active space orbitals, facilitating the convergence to the ground state compared to the multiconfigurational time-dependent Hartree-Fock method, used as a benchmark to show the accuracy and efficiency of TD-RASSCF. Second, we solve the equations of motion to compute photoelectron spectra of Be after interacting with a short linearly polarized XUV laser pulse. We compare the spectra for different RAS schemes, and in this way we identify the orbital spaces that are relevant for an accurate description of the photoelectron spectra. Finally, we investigate the effects of electron correlation on the magnitude of the relative time-delay in the photoionization process into two different ionic channels. One channel, the ground state channel in the ion, is accessible without electron correlation. The other channel is only accessible when including electron correlation. The time-delay is highly sensitivity to the choice of the active space, and hence to the account of electron-electron correlation.

Probing autoionizing states of molecular oxygen with XUV transient absorption: Electronic-symmetry-dependent line shapes and laser-induced modifications

The dynamics of autoionizing Rydberg states of oxygen are studied using attosecond transient absorption technique, where extreme ultraviolet (XUV) initiates molecular polarization and near infrared (NIR) pulse perturbs its evolution. Transient absorption spectra show positive optical density (OD) change in the case of $ns\sigma_g$ and $nd\pi_g$ autoionizing states of oxygen and negative OD change for $nd\sigma_g$ states. Multiconfiguration time-dependent Hartree-Fock (MCTDHF) calculation are used to simulate the transient absorption spectra and their results agree with experimental observations. The time evolution of superexcited states is probed in electronically and vibrationally resolved fashion and we observe the dependence of decay lifetimes on effective quantum number of the Rydberg series. We model the effect of near-infrared (NIR) perturbation on molecular polarization and find that the laser induced phase shift model agrees with the experimental and MCTDHF results, while the laser induced attenuation model does not. We relate the electron state symmetry dependent sign of the OD change to the Fano parameters of the static absorption lineshapes.

Helium Atom Excitations by the GW and Bethe-Salpeter Many-Body Formalism

The helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger equation is known for helium ground and excited states, and it represents a benchmark for any many-body methodology. Here, we check the abinitio many-body GW approximation and the Bethe-Salpeter equation (BSE) against the exact solution for helium. Starting from the Hartree-Fock method, we show that the GW and the BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving the time-dependent Hartree-Fock method. These findings suggest that the accuracy of the BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.

High-harmonic spectra from time-dependent two-particle reduced-density-matrix theory

The accurate description of the non-linear response of many-electron systems to strong-laser fields remains a major challenge. Methods that bypass the unfavorable exponential scaling with particle number are required to address larger systems. In this paper we present a fully three-dimensional implementation of the time-dependent two-particle reduced density matrix (TD-2RDM) method for many-electron atoms. We benchmark this approach by a comparison with multi-configurational time-dependent Hartree-Fock (MCTDHF) results for the harmonic spectra of beryllium and neon. We show that the TD-2RDM is very well-suited to describe the non-linear atomic response and to reveal the influence of electron-correlation effects.

A local framework for calculating coupled cluster singles and doubles excitation energies (LoFEx-CCSD)

ABSTRACTThe recently developed Local Framework for calculating Excitation energies (LoFEx) is extended to the coupled cluster singles and doubles (CCSD) model. In the new scheme, a standard CCSD excitation energy calculation is carried out within a reduced excitation orbital space (XOS), which is composed of localised molecular orbitals and natural transition orbitals determined from time-dependent Hartree–Fock theory. The presented algorithm uses a series of reduced second-order approximate coupled cluster singles and doubles (CC2) calculations to optimise the XOS in a black-box manner. This ensures that the requested CCSD excitation energies have been determined to a predefined accuracy compared to a conventional CCSD calculation. We present numerical LoFEx-CCSD results for a set of medium-sized organic molecules, which illustrate the black-box nature of the approach and the computational savings obtained for transitions that are local compared to the size of the molecule. In fact, for such local transitions, the LoFEx-CCSD scheme can be applied to molecular systems where a conventional CCSD implementation is intractable.

Time-dependent restricted-active-space self-consistent-field theory with space partition

Aiming at efficient numerical analysis of time-dependent (TD) many-electron dynamics of atoms involving multielectron continua, the TD restricted-active-space self-consistent-field theory with space partition (TD-RASSCF-SP) is presented. The TD-RASSCF-SP wave function is expanded in terms of TD configuration-interaction coefficients with Slater determinants composed of two kinds of TD orbitals: $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ orbitals are defined to be nonvanishing in the inner region ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{V}$), a small volume around the atomic nucleus, and $\stackrel{\ifmmode \check{}\else \v{}\fi{}}{M}$ orbitals are nonvanishing in the large outer region ($\stackrel{\ifmmode \check{}\else \v{}\fi{}}{V}$). For detailed discussion of the SP strategy, the equations of motion are derived by two different formalisms for comparison. To ensure continuous differentiability of the wave function across the two regions, one of the formalisms makes use of the property of the finite-element discrete-variable-representation (FEDVR) functions and introduces additional time-independent orbitals. The other formalism is more general and is based on the Bloch operator as in the $R$-matrix theory, but turns out to be less practical for numerical applications. Hence, using the FEDVR-based formalism, the numerical performance is tested by computing double-ionization dynamics of atomic beryllium in intense light fields. To achieve high accuracy, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ should be set large to take into account the strong many-electron correlation around the nucleus. On the other hand, $\stackrel{\ifmmode \check{}\else \v{}\fi{}}{M}$ can be set much smaller than $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ for capturing the weaker correlation between the two outgoing photoelectrons. As a result, compared with more accurate multiconfigurational TD Hartree-Fock (MCTDHF) method, the TD-RASSCF-SP method may achieve comparable accuracy in the description of the double-ionization dynamics. There are, however, difficulties related to the stiffness of the equations of motion of the TD-RASSCF-SP method, which makes the required time step for this method smaller than the one needed for the MCTDHF approach.

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.

Natural excitation orbitals from linear response theories: Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory.

Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In contrast, in a basis of natural orbitals (NOs) or Hartree-Fock orbitals, excitations often employ many orbitals and are accordingly hard to characterize. We demonstrate that it is possible in these cases to transform to natural excitation orbitals (NEOs) which resemble very closely the KS orbitals and afford the same simple description of excitations. The desired transformation has been obtained by diagonalization of a submatrix in the equations of linear response time-dependent 1-particle reduced density matrix functional theory (LR-TDDMFT) for the NO transformation, and that of a submatrix in the linear response time-dependent Hartree-Fock (LR-TDHF) equations for the transformation of HF orbitals. The corresponding submatrix is already diagonal in the KS basis in the LR-TDDFT equations. While the orbital shapes of the NEOs afford the characterization of the excitations as (mostly) simple orbital-to-orbital transitions, the orbital energies provide a fair estimate of excitation energies.

Dependence of fusion on isospin dynamics

We introduce a new microscopic approach to calculate the dependence of fusion barriers and cross-sections on isospin dynamics. The method is based on the time-dependent Hartree-Fock theory and the isoscalar and isovector properties of the energy density functional (EDF). The contribution to the fusion barriers originating from the isoscalar and isovector parts of the EDF is calculated. It is shown that for non-symmetric systems the isovector dynamics influence the sub-barrier fusion cross-sections. For most systems this results in an enhancement of the sub-barrier cross-sections, while for others we observe differing degrees of hindrance. We use this approach to provide an explanation of recently measured fusion cross sections which show a surprising enhancement at low $E_\mathrm{c.m.}$ energies for the system $^{40}$Ca+$^{132}$Sn as compared to the more neutron-rich system $^{48}$Ca+$^{132}$Sn, and discuss the dependence of sub-barrier fusion cross-sections on transfer.