Hartree-Fock Approach Research Articles

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.

A hybrid model of Skyrme- and Brueckner-type interactions for neutron star matter

Abstract We suggest a hybrid model for neutron star matter to discuss the hyperon puzzle inherent in the 2.0 M$_{\odot}$ of the neutron star. For the nucleon–nucleon ($NN$) interaction, we employ the Skyrme–Hartree–Fock approach based on various Skyrme interaction parameter sets, and take the Brueckner–Hartree–Fock approach for the interactions related to hyperons. For the many-body interactions including hyperons, we make use of the multi-pomeron-exchange model, whose parameters have been adjusted to the data deduced from various hypernuclei properties. For clear understanding of the physics in the hybrid model, we discuss fractional functions of related particles, symmetry energies, and chemical potentials in dense matter. Finally, we investigate the equations of state and mass–radius relation of neutron stars, and show that the hybrid model can properly describe the 2.0 M$_{\odot}$ neutron star mass data with the many-body interaction employed in the hybrid model. Recent tidal deformability data from the gravitational wave observation are also compared to our calculations, especially in terms of the neutron skin of $^{208}$Pb and nuclear incompressibility.

Modulated phases of graphene quantum Hall polariton fluids

This work is placed in the context of solid-state systems in the regime of ultra-strong light-matter coupling. To date, the highest light-matter coupling strengths have been measured in experiments with polaritons in semiconductor systems under the conditions of the Integer Quantum Hall effect. Polaritons are excitations resulting from strong coupling of light with a dipole-carrying matter excitation. In Pellegrino et al. (2016), we studied the impact of electron-electron interaction on polaritons in cavities in the case of graphene under the conditions of the Integer Quantum Hall effect. By using a mean-field (Hartree-Fock) approach we have shown the possibility of formation of spatially modulated light-matter phases characterized by a wavelength that is dependent on the value of the applied static magnetic field and the concentration of carriers, which is tunable by varying the gate voltage.

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.

Deformed K− nuclei in the Skyrme–Hartree–Fock approach

Abstract The properties of kaonic nuclei are studied using a two-dimensional Skyrme–Hartree–Fock model with a $KN$ Skyrme force. We focus in particular on the instability of the solutions for a too strong $KN$ interaction, which determines a maximum value of the kaon binding in this approach. We then analyze the change of the deformation properties of several core-deformed nuclei caused by the added kaon, and find a shrinking of the core and in some cases a complete loss of deformation.

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.

Pseudospin symmetry restoration and the in-medium balance between nuclear attractive and repulsive interactions

The mechanism that restores the pseudo-spin symmetry (PSS) are investigated under the relativistic Hartree-Fock (RHF) approach, by focusing on the in-medium balance between nuclear attractive and repulsive interactions. It is illustrated that the modelings of both the equilibrium of nuclear dynamics and the in-medium effects can be essentially changed by the $\rho$-tensor coupling that play the role almost fully via the Fock terms, from which the model discrepancy on the PSS restoration is verified. Specifically, the largely different density-dependent behaviors of the isoscalar coupling strengths $g_\sigma$ and $g_\omega$, deduced from the parametrization of the RHF Lagrangian PKA1, play an essential role in restoring the PSS of the high-$l'$ pseudo-spin doublets around the Fermi levels. Qualitatively, a guidance is provided for the modelings of both the equilibrium of nuclear dynamics and the in-medium effects via the PSS restoration.

Excitation functions of the Zn(p,xn)Ga reactions

The excitation functions for 64,66,67,68,70Zn(p,n)64,66,67,68,70Ga and 64,66,67,68,70Zn(p,2n)63,65,66,67,69Ga have been calculated for incident proton energies from threshold values to 30 MeV using the statistical model code TALYS-1.6. The (p,n) and (p,2n) cross sections have been calculated using both phenomenological Koning and Delaroche (KD) and semimicroscopic Jeukenne-Lejeune-Mahaux-Bruyeres (JLMB) optical model potentials. The phenomenological back-shifted Fermi gas model (BFM) and microscopic Hartree-Fock (HF) approaches for calculation of level densities have been compared in the present work. The pre-equilibrium process has been treated using exciton model. The sensitivity of cross section data to different models of optical model potential and level density have been investigated. It is found that the (p,n) and (p,2n) cross section calculations with semimicroscopic JLMB optical model potential and microscopic HF level density show agreement with the data. The (p,n) and (p,2n) cross section calculations have been compared with corresponding cross sections from nuclear data library, TENDL-2019. The (p,xn) cross sections obtained will be useful in several applications, particularly, for optimization of production routes for Ga isotopes.

A nuclear matter calculation with the tensor-optimized Fermi sphere method with central interaction

Abstract The tensor-optimized Fermi sphere (TOFS) theory is applied first for the study of the property of nuclear matter using the Argonne V4$^\prime$$NN$ potential. In the TOFS theory, the correlated nuclear matter wave function is taken to be a power-series type of the correlation function $F$, where $F$ can induce central, spin–isospin, tensor, etc. correlations. This expression has been ensured by a linked cluster expansion theorem established in the TOFS theory. We take into account the contributions from all the many-body terms arising from the product of the nuclear matter Hamiltonian $\mathcal{H}$ and $F$. The correlation function is optimally determined in the variation of the total energy of nuclear matter. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced up to the nuclear matter density $\rho \simeq 0.20$ fm$^{-3}$ in the present numerical calculation, in comparison with other methods such as the Brueckner–Hartree–Fock approach.

Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D regime

We study the anisotropic quantum Heisenberg antiferromagnet for spin-1/2 that interpolates smoothly between the one-dimensional (1D) and the two-dimensional (2D) limits. Using the spin Hartree-Fock approach we construct a quantitative theory of heat capacity in the quasi-1D regime with a finite coupling between spin chains. This theory reproduces closely the exact result of Bethe Ansatz in the 1D limit and does not produces any spurious phase transitions for any anisotropy in the quasi-1D regime at finite temperatures in agreement with the Mermin-Wagner theorem. We study the static spin-spin correlation function in order to analyse the interplay of lattice geometry and anisotropy in these systems. We compare the square and triangular lattice. For the latter we find that there is a quantum transition point at an intermediate anisotropy of $\sim0.6$. This quantum phase transition establishes that the quasi-1D regime extends upto a particular point in this geometry. For the square lattice the change from the 1D to 2D occurs smoothly as a function of anisotropy, i.e. it is of the crossover type. Comparing the newly developed theory to the available experimental data on the heat capacity of $\rm{Cs}_2\rm{CuBr}_4$ and $\rm{Cs}_2\rm{CuCl}_4$ we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields.

Effect of shell structure on the fission of sub-lead nuclei

Fission of atomic nuclei often produces mass asymmetric fragments. However, the origin of this asymmetry was believed to be different in actinides and in the sub-lead region [A. Andreyev {\it et al.}, Phys. Rev. Lett. {\bf 105}, 252502 (2010)]. It has recently been argued that quantum shell effects stabilising pear shapes of the fission fragments could explain the observed asymmetries in fission of actinides[G. Scamps and C. Simenel, Nature {\bf 564}, 382 (2018)]. This interpretation is tested in the sub-lead region using microscopic mean-field calculations of fission based on the Hartree-Fock approach with BCS pairing correlations. The evolution of the number of protons and neutrons in asymmetric fragments of mercury isotope fissions is interpreted in terms of deformed shell gaps in the fragments. A new method is proposed to investigate the dominant shell effects in the pre-fragments at scission. We conclude that the mechanisms responsible for asymmetric fissions in the sub-lead region are the same as in the actinide region, which is a strong indication of their universality.

Low-Cost Molecular Excited States from a State-Averaged Resonating Hartree-Fock Approach.

Quantum chemistry methods that describe excited states on the same footing as the ground state are generally scarce. In previous work, ( Gill J. Phys. Chem. A , 112 , 2008 , 13164 and later Sundstrom ; ; Head-Gordon J. Chem. Phys. , 140 , 2014 , 114103 ) considered excited states resulting from a nonorthogonal configuration interaction (NOCI) on stationary solutions of the Hartree-Fock equations. We build upon those contributions and present the state-averaged resonating Hartree-Fock (sa-ResHF) method, which differs from NOCI in that spin-projection and orbital relaxation effects are incorporated from the onset. Our results in a set of small molecules (alanine, formaldehyde, acetaldehyde, acetone, formamide, and ethylene) suggest that sa-ResHF excitation energies are a notable improvement over configuration interaction singles, at a mean-field computational cost. The orbital relaxation in sa-ResHF, carried out in the presence of a spin-projection operator, generally results in excitation energies that are closer to the EOM-CCSD and experimental values than the corresponding NOCI ones.

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.

Energy of a finite three-dimensional electron gas of spinless electrons

We study a finite three-dimensional electron gas system consisting of an arbitrary number of electrons embedded in a finite cubic domain. The electrons are treated as spinless particles implying that the system under consideration represents a fully spin-polarized Fermi quantum phase of electrons. The cubic region is uniformly filled with a positive background that ensures overall charge neutrality. We apply a Hartree-Fock approach that starts with a Slater determinant wave function of normalized plane wave orbitals. The treatment enables us to obtain the energy per particle of the finite system at any given number of electrons. The potential (exchange) energy is conveniently obtained by simplifying the calculation of the ensuing two-particle integrals over the finite cubic domain in terms of expressions that involve compact analytic auxiliary functions. Results are provided for both the kinetic and potential energy per particle for various numbers of electrons. It is shown that the kinetic and the potential energy per particle converge towards their bulk thermodynamic limit values in a non-monotonic way as a function of the number of particles. The results derived may apply to finite systems of delocalized electrons in alkali metal nanoclusters in which the positive ionic core is approximated as a cubic jellium region.

Global α - nucleus optical model based on an Dirac Brueckner Hartree Fock approach

The global α-nucleus optical model is studied based on the nucleon self-energies in an Dirac-Brueckner-Hartree-Fock (DBHF) approach. The newly developed nucleon-nucleus optical model CTOM derived from DBHF, is used as the basis to consistently generate the real and imaginary potentials of the α-nucleus optical potential by double-folding model. The same range correction a of the improved local density approximation (ILDA) in CTOM is adopted, which is also suitable to modify the nucleon interaction range in α-nucleus systems. To get better description of experimental data, the re-normalization factors (NR,NI) are introduced in α-nucleus scattering calculations, and the individual optimized (NR,NI) for all nuclei and energies are searched out under the guidance of χ2 criterion. We systematically explore the energy dependence of NR and NI by considering the α elastic scattering from 12C to 208Pb at incident energies below 120MeV/nucleon and a simple exponential function is extracted. With this global α-nucleus optical potential, a reasonable description of all available experimental data for α scattering from nuclei is achieved.

Tensor optimized Fermi sphere method for nuclear matter—Power series correlated wave function and a cluster expansion

A new formalism, called “tensor optimized Fermi sphere (TOFS) method”, is developed to treat the nuclear matter using a bare interaction among nucleons. In this method, the correlated nuclear matter wave function is taken to be a power series type, ΨN=[∑n=0N(1∕n!)Fn]Φ0 and an exponential type, Ψex=exp(F)Φ0, with the uncorrelated Fermi-gas wave function Φ0, where the correlation operator F can induce central, spin–isospin, tensor, etc. correlations, and Ψex corresponds to a limiting case of ΨN (N→∞). In the TOFS formalism based on Hermitian form, it is shown that the energy per particle in nuclear matter with Ψex can be expressed in terms of a linked-cluster expansion. On the basis of these results, we present the formula of the energy per particle in nuclear matter with ΨN. We call the Nth-order TOFS calculation for evaluating the energy with ΨN, where the correlation functions are optimally determined in the variation of the energy. The TOFS theory is applied for the study of symmetric nuclear matter using a central NN potential with short-range repulsion. The calculated results are fairly consistent to those of other theories such as the Brueckner–Hartree–Fock approach etc.

Self-consistent Hartree-Fock approach to many-body localization

In this work, we develop a self-consistent Hartree-Fock approach to theoretically study the far-from-equilibrium quantum dynamics of interacting fermions, and apply this approach to explore the onset of many-body localization (MBL) in these systems. We investigate the dynamics of a state with a nonequilibrium density profile; we find that at weak disorder the density profile equilibrates rapidly, whereas for strong disorder it remains frozen on the accessible timescales. We analyze this behavior in terms of the Hartree-Fock self-energy. At weak disorder the self-energy fluctuates strongly and can be interpreted as a self-consistent noise process. By contrast, at strong disorder the self-energy evolves with a few coherent oscillations which cannot delocalize the system. Accordingly, the non-equilibrium site-resolved spectral function shows a broad spectrum at weak disorder and sharp spikes at strong disorder. Our Hartree-Fock theory incorporates spatial fluctuations and rare-region effects. As a consequence, we find subdiffusive relaxation in random systems; but, when the system is subjected to weak quasi-periodic potentials, the subdiffusive response ceases to exist, as rare region effects are absent in this case. This self-consistent Hartree-Fock approach can be regarded as a relatively simple theory that captures much of the MBL phenomenology.

Relation between fermionic and qubit mean fields in the electronic structure problem.

For quantum computing applications, the electronic Hamiltonian for the electronic structure problem needs to be unitarily transformed into a qubit form. We found that mean-field procedures on the original electronic Hamiltonian and on its transformed qubit counterpart can give different results. We establish conditions of when fermionic and qubit mean fields provide the same or different energies. In cases when the fermionic mean-field (Hartree-Fock) approach provides an accurate description (electronic correlation effects are small), the choice of molecular orbitals for the electron Hamiltonian representation becomes the determining factor in whether the qubit mean-field energy will be equal to or higher than that of the fermionic counterpart. In strongly correlated cases, the qubit mean-field approach has a higher chance to undergo symmetry breaking and lower its energy below the fermionic counterpart.

Energy levels and transition rates for Al-like Cu XVII

Energy levels and transition rates for electric-dipole, electric-quadrupole, magnetic-dipole, and magnetic-quadrupole transitions among the levels arising from the n≤5 configurations in Al-like Cu XVII are calculated respectively by two state-of-the-art methods, namely, the Multi-Configuration Dirac–Hartree–Fock approach and the second-order many-body perturbation theory. Our results are compared with available experimental and other theoretical values. In addition, effective collision strengths of direct excitation between these levels are provided using the distorted wave approximation. Several line pairs are pointed out that might be useful for density diagnostics.