Search results for "Hartree–Fock method"
showing 10 items of 51 documents
Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation
2005
As a contribution to the study of Hartree-Fock theory we prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential mu) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, {S}_z = sum_x n_{x,\uparrow} - n_{x,\downarrow}, and we find that the ch…
Experimental and theoretical study of thenf-level lifetimes of potassium
2008
The theoretical and experimental values of the 5f ,6 f ,7 f, and 8f radiative lifetimes of neutral potassium are reported. The reduced matrix elements for all allowed electric-dipole nf5/2-nd5/2, nf5/2-nd3/2, and nf7/2-nd5/2 transitions with n =5–8 in K arecalculated using the relativistic linearized coupled-cluster method with single and double excitations of Dirac-Fock wave functions included to all orders in many-body perturbation theory. The resulting electric-dipole matrix elements are used to evaluate the lifetimes of the 5f ,6 f ,7 f, and 8f states in neutral K and their uncertainties. The contributions from the nf5/2-ng7/2, nf7/2-ng7/2, and nf7/2-ng9/2 transitions to the lifetimes o…
Direct perturbation theory in terms of energy derivatives: Fourth-order relativistic corrections at the Hartree–Fock level
2011
In this work, the quantum-chemical treatment of relativistic effects by means of direct perturbation theory is extended from its lowest order, DPT2, to the next higher order, DPT4. The required theory is given in terms of energy derivatives with the DPT4 energy correction defined as the corresponding second derivative with respect to the relativistic perturbation parameter λ(rel) = c(2) and c as the speed of light. To facilitate the implementation in standard quantum-chemical program packages, a general formulation of DPT starting from a nonrelativistic Lagrangian is developed, thereby expanding both wave function and operators in terms of λ(rel). The corresponding expressions, which incorp…
Empirical determination of Einstein A-coefficient ratios of bright [Fe II] lines
2014
The Einstein spontaneous rates (A-coefficients) of Fe+ lines have been computed by several authors with results that differ from each other by up to 40%. Consequently, models for line emissivities suffer from uncertainties that in turn affect the determination of the physical conditions at the base of line excitation. We provide an empirical determination of the A-coefficient ratios of bright [Fe II] lines that would represent both a valid benchmark for theoretical computations and a reference for the physical interpretation of the observed lines. With the ESO-Very Large Telescope X-shooter instrument between 3000 Å and 24700 Å, we obtained a spectrum of the bright Herbig-Haro object HH 1. …
Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry
2017
International audience; We present the development of the extended Skyrme N2LO pseudopotential in the case of spherical even-even nuclei calculations. The energy density functional is first presented. Then we derive the mean-field equations and discuss the numerical method used to solve the resulting fourth-order differential equation together with the behavior of the solutions at the origin. Finally, a fitting procedure for such an N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.
Angular momentum projection of cranked Hartree-Fock states: Application to terminating bands inA~44nuclei
2007
We present the first systematic calculations based on the angular-momentum projection of cranked Slater determinants. We propose the Iy --> I scheme, by which one projects the angular momentum I from the 1D cranked state constrained to the average spin projection of =I. Calculations performed for the rotational band in 46Ti show that the AMP Iy --> I scheme offers a natural mechanism for correcting the cranking moment of inertia at low-spins and shifting the terminating state up by ~2 MeV, in accordance with data. We also apply this scheme to high-spin states near the band termination in A~44 nuclei, and compare results thereof with experimental data, shell-model calculations, and res…
A model study of Hartree-Fock and Linear Response in coordinate space
1979
A fast procedure for spherical Hartree-Fock is obtained by coordinate space representation and a modification of gradient iteration. Along similar lines, the corresponding Linear Response equations are derived and solved, in order to achieve a fully consistent treatment. The Linear Response equations are applied to a change in particle numbers, i.e. to the description of isotopic differences. In a model study we look for their physical and numerical properties, i.e. linearity of the response, numerical stability and consistency requirements for the Hartree-Fock basis.
Self-consistent symmetries in the proton-neutron Hartree-Fock-Bogoliubov approach
2009
Symmetry properties of densities and mean fields appearing in the nuclear Density Functional Theory with pairing are studied. We consider energy functionals that depend only on local densities and their derivatives. The most important self-consistent symmetries are discussed: spherical, axial, space-inversion, and mirror symmetries. In each case, the consequences of breaking or conserving the time-reversal and/or proton-neutron symmetries are discussed and summarized in a tabulated form, useful in practical applications.
Shell-model and Hartree-Fock calculations for even-mass O, Ne, and Mg nuclei
1999
Shell-model and deformed Hartree-Fock plus BCS calculations are reported for even-even nuclei [sup 18[minus]30]O, [sup 18[minus]36]Ne, and [sup 20[minus]42]Mg; shell-model calculations additionally included [sup 38,40]Ne and [sup 44,46,48]Mg. Ground-state binding energies and 2[sub 1][sup +] quadrupole moments are calculated by both models. Shell-model calculations, aided by a new truncation method, include 2[sub 1][sup +] excitation energies and magnetic moments. Hartree-Fock calculations with SkI6, RATP, Z[sub [sigma]][sup [asterisk]], and SkX Skyrme forces include ground-state deformations and rms radii; SkI6 gives the best overall agreement with experiment. The two models are compared w…
The Axial Charge Renormalization in a Relativistic Description of Finite Nuclei
1994
Starting from a realistic One-Boson-Exchange model of the nucleon nucleon interaction the relativistic mean field for nucleons is determined within the Dirac Brueckner Hartree Fock approach for finite nuclei. The matrix elements of the axial charge operator evaluated for the solutions of the Dirac equation with this selfenergy are investigated. These matrix elements are enhanced with respect to the equivalent non relativistic ones obtained from the solutions of the Schr\"odinger equation with the non relativistic equivalent potential. The present results confirm at a qualitative level the results for the axial charge renormalization obtained with perturbative approaches. However, the result…