arXiv subjects

D. Van Neck

Publications and source records attributed to D. Van Neck.

At least 19 recordsLinked to original sources

arXiv2020

Richardson-Gaudin mean-field for strong correlation in quantum chemistry

Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly-interacting pairs of electrons. While other geminal wavefunctions may only be employed in a projected Schrödinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of Coulomb Hamiltionans and we present results for atoms and dissociation curves which are in agreement with doubly-occupied configuration interaction (DOCI) data. The present approach will serve as the starting point for a many-body theory of pairs, much as Hartree-Fock is the starting point for weakly-correlated electrons.

physics.chem-ph↗

arXiv2010

A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix

The quantum many-body problem can be rephrased as a variational determination of the two-body reduced density matrix, subject to a set of N-representability constraints. The mathematical problem has the form of a semidefinite program. We adapt a standard primal-dual interior point algorithm in order to exploit the specific structure of the physical problem. In particular the matrix-vector product can be calculated very efficiently. We have applied the proposed algorithm to a pairing-type Hamiltonian and studied the computational aspects of the method. The standard N-representability conditions perform very well for this problem.

cond-mat.str-el↗

arXiv2010

Nonlocal extension of the dispersive-optical-model to describe data below the Fermi energy

Present applications of the dispersive-optical-model analysis are restricted by the use of a local but energy-dependent version of the generalized Hartree-Fock potential. This restriction is lifted by the introduction of a corresponding nonlocal potential without explicit energy dependence. Such a strategy allows for a complete determination of the nucleon propagator below the Fermi energy with access to the expectation value of one-body operators (like the charge density), the one-body density matrix with associated natural orbits, and complete spectral functions for removal strength. The present formulation of the dispersive optical model (DOM) therefore allows the use of elastic electron-scattering data in determining its parameters. Application to ${}^{40}$Ca demonstrates that a fit to the charge radius leads to too much charge near the origin using the conventional assumptions of the functional form of the DOM. A corresponding incomplete description of high-momentum components is identified, suggesting that the DOM formulation must be extended in the future to accommodate such correlations properly. Unlike the local version, the present nonlocal DOM limits the location of the deeply-bound hole states to energies that are consistent with (\textit{e,e}$^{\prime}$\textit{p}) and (\textit{p,2p}) data.

nucl-th↗

arXiv2010

Accuracy of the Faddeev Random Phase Approximation for Light Atoms

The accuracy of the Faddeev random phase approximation (FRPA) method is tested by calculating the total and ionization energies of a set of light atoms up to Ar. Comparisons are made with the results of coupled-cluster singles and doubles (CCSD), third-order algebraic diagrammatic construction [ADC(3)], and with the experiment. It is seen that even for two-electron systems, He and Be-2+, the inclusion of RPA effects leads to satisfactory results and therefore it does not over-correlate the ground state. The FRPA becomes progressively better for larger atomic numbers where it gives about 5 mH more correlation energy and it shifts ionization potentials by 2-10 mH, with respect to its sister method ADC(3). The corrections for ionization potentials consistently reduce the discrepancies with the experiment.

physics.chem-ph↗

arXiv2009

Ab-initio Green's Functions Calculations of Atoms

The Faddeev random phase approximation (FRPA) method is applied to calculate the ground state and ionization energies of simple atoms. First ionization energies agree with the experiment at the level of ~10 mH or less. Calculations with similar accuracy are expected to provide information required for developing the proposed quasiparticle-DFT method.

physics.chem-ph↗

arXiv2007

Quasiparticles in Neon using the Faddeev Random Phase Approximation

The spectral function of the closed-shell Neon atom is computed by expanding the electron self-energy through a set of Faddeev equations. This method describes the coupling of single-particle degrees of freedom with correlated two-electron, two-hole, and electron-hole pairs. The excitation spectra are obtained using the Random Phase Approximation, rather than the Tamm-Dancoff framework employed in the third-order algebraic diagrammatic contruction [ADC(3)] method. The difference between these two approaches is studied, as well as the interplay between ladder and ring diagrams in the self-energy. Satisfactory results are obtained for the ionization energies as well as the energy of the ground state with the Faddeev-RPA scheme that is also appropriate for the high-density electron gas.

physics.chem-ph↗

arXiv2006

Quasiparticle properties in a density functional framework

We propose a framework to construct the ground-state energy and density matrix of an N-electron system by solving selfconsistently a set of single-particle equations. The method can be viewed as a non-trivial extension of the Kohn-Sham scheme (which is embedded as a special case). It is based on separating the Green's function into a quasi-particle part and a background part, and expressing only the background part as a functional of the density matrix. The calculated single-particle energies and wave functions have a clear physical interpretation as quasiparticle energies and orbitals.

physics.chem-ph↗

arXiv2003

On the nuclear symmetry energy and the neutron skin in neutron-rich nuclei

The symmetry energy for nuclear matter and its relation to the neutron skin in finite nuclei is discussed. The symmetry energy as a function of density obtained in a self-consistent Green function approach is presented and compared to the results of other recent theoretical approaches. A partial explanation of the linear relation between the symmetry energy and the neutron skin is proposed. The potential of several experimental methods to extract the neutron skin is examined.

nucl-th↗

arXiv2003

Nuclear Equation of State and Neutron Star Structure

The hadronic equation of state for a neutron star is discussed with a particular emphasis on the symmetry energy. The results of several microscopic approaches are compared and also a new calculation in terms of the self-consistent Green function method is presented. In addition possible constraints on the symmetry energy coming from empirical information from the neutron skin of finite nuclei are considered.

nucl-th↗

arXiv2003

Saturation of nuclear matter and short-range correlations

A fully self-consistent treatment of short-range correlations in nuclear matter is presented. Different implementations of the determination of the nucleon spectral functions for different interactions are shown to be consistent with each other. The resulting saturation densities are closer to the empirical result when compared with (continuous-choice) Brueckner-Hartree-Fock values. Arguments for the dominance of short-range correlations in determining the nuclear-matter saturation density are presented. A further survey of the role of long-range correlations suggests that the inclusion of pionic contributions to ring diagrams in nuclear matter leads to higher saturation densities than empirically observed. A possible resolution of the nuclear-matter saturation problem is suggested.

nucl-th↗

arXiv2003

Electromagnetic interaction in chiral quantum hadrodynamics and decay of vector and axial-vector mesons

The chiral invariant QHD-III model of Serot and Walecka is applied in the calculation of some meson properties. The electromagnetic interaction is included by extending the symmetry of the model to the local U(1) \times SU(2)_{R} \times SU(2)_{L} group. The minimal and nonminimal contributions to the electromagnetic Lagrangian are obtained in a new representation of QHD-III. Strong decays of the axial-vector meson, a_{1} \to πρ, a_{1} \to πσ, and the electromagnetic decays ρ\to ππγ, a_{1} \to πγand ρ\to πγare calculated. The low-energy parameters for the π-πscattering are calculated in the tree-level approximation. The effect of the auxiliary Higgs bosons, introduced in QHD-III in order to generate masses of the vector and axial-vector mesons via the Higgs mechanism, is studied as well. This is done on the tree level for π-πscattering and on the level of one-loop diagrams for the a_{1} \to πγdecay. It is demonstrated that the model successfully describes some features of meson phenomenology in the non-strange sector.

nucl-th↗

arXiv2001

Coherent Compton scattering on light nuclei in the delta resonance region

Coherent Compton scattering on light nuclei in the delta resonance region is studied in the impulse approximation and is shown to be a sensitive probe of the in-medium properties of the delta resonance. The elementary amplitude on a single nucleon is calculated from the unitary K-matrix approach developed previously. Modifications of the properties of the delta resonance due to the nuclear medium are accounted for through the self-energy operator of the delta, calculated from the one-pion loop. The dominant medium effects such as the Pauli blocking, mean-field modification of the nucleon and delta masses, and particle-hole excitations in the pion propagator are consistently included in nuclear matter.

nucl-th↗

arXiv2001

Short-range correlations in nuclear matter using Green's functions within a discrete pole approximation

We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon-nucleon potential, within the framework of a self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle-particle and hole-hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.

nucl-th↗

arXiv2001

Improved lower bounds for the ground-state energy of many-body systems

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They are constructed by considering not only the energy in the two-particle system, but also the structure of the pair wave function. We apply the formal results to various numerical examples, and show that in some cases dramatic improvement over the existing bounds is reached.

nucl-th↗

arXiv1999

Correlation effects in single-particle overlap functions and one-nucleon removal reactions

Single-particle overlap functions and spectroscopic factors are calculated on the basis of the one-body density matrices (ODM) obtained for the nucleus $^{16}O$ employing different approaches to account for the effects of correlations. The calculations use the relationship between the overlap functions related to bound states of the (A-1)-particle system and the ODM for the ground state of the A-particle system. The resulting bound-state overlap functions are compared and tested in the description of the experimental data from (p,d) reactions for which the shape of the overlap function is important.

nucl-th↗

arXiv1998

Production of e+e- pairs in proton-deuteron capture to 3He

The process p+d \leftrightarrow 3He + γ* at intermediate energies is described using a covariant and gauge-invariant model, and a realistic pd3He vertex. Both photodisintegration of 3He and proton-deuteron capture with production of e+e- pairs are studied, and results for cross sections and response functions are presented. The effect of time-like formfactors on the dilepton cross sections is investigated as well.

nucl-th↗

arXiv1998

Relationships between two--particle overlap functions and the two--body density matrix for many-fermion systems

Relationships are obtained connecting the two-nucleon overlap function of the eigenstates in the (A-2) particle system with the asymptotic behavior of the two-body density matrix for the ground state of the A-particle system.This makes it possible to calculate the two-body overlap functions, spectroscopic factors and separation energies on the basis of a realistic two-body density matrix. The procedure can be used in describing the (e,e'NN) and (γ, NN) reactions where the two--body overlap functions are a key ingredient in the analysis.

nucl-th↗

arXiv1998

Center-of-mass effects on the quasi-hole spectroscopic factors in the 16O(e,e'p) reaction

The spectroscopic factors for the low-lying quasi-hole states observed in the 16O(e,e'p)15N reaction are reinvestigated with a variational Monte Carlo calculation for the structure of the initial and final nucleus. A computational error in a previous report is rectified. It is shown that a proper treatment of center-of-mass motion does not lead to a reduction of the spectroscopic factor for $p$-shell quasi-hole states, but rather to a 7% enhancement. This is in agreement with analytical results obtained in the harmonic oscillator model. The center-of-mass effect worsens the discrepancy between present theoretical models and the experimentally observed single-particle strength. We discuss the present status of this problem, including some other mechanisms that may be relevant in this respect.

nucl-th↗