Atomic ground states in strong magnetic fields: Electron configurations and energy levels

Schimeczek, C.; Boblest, Sebastian; Meyer, Dirk

doi:10.1103/physreva.88.012509

Cited by 15 publications

(36 citation statements)

References 41 publications

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“…Comparison data are for various QMC methods denoted as in Refs. [28] Tables I-IV for "RPDQMC" through "VQMC" and [29] Published results for correlated wave-function methods (WFMs) are only for 0 B 100 a.u. for He and Li, and for the Be atom, 0 B 10 a.u.…”

Section: B Results Of Nb-dft Approximationsmentioning

confidence: 99%

“…with extremely rich, aspherical basis sets and several xc functionals, including one combination which apparently has gone unexplored heretofore. We take advantage of the availability of several Hartree-Fock (HF) [10][11][12][13][14][15][16][17][18] and correlated wave-function studies of at least a few light atoms in an external B field [19][20][21][22][23][24][25][26][27] and of quantum Monte Carlo (QMC) studies [28,29] for comparisons. In particular, comparison of our HF calculations with prior ones provides calibration of the accuracy of our techniques, while comparison with the QMC results gives a measure of absolute accuracy and trends in accuracy for the various DFT approximations.…”

Section: Introductionmentioning

confidence: 99%

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Comparative studies of density-functional approximations for light atoms in strong magnetic fields

2014

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For a wide range of magnetic fields, 0 B 2000 a.u., we present a systematic comparative study of the performance of different types of density-functional approximations in light atoms (2 Z 6). Local, generalized-gradient approximation (GGA; semilocal), and meta-GGA ground-state exchange-correlation (xc) functionals are compared on an equal footing with exact-exchange, Hartree-Fock (HF), and current-densityfunctional-theory (CDFT) approximations. Comparison also is made with published quantum Monte Carlo data. Though all approximations give qualitatively reasonable results, the exchange energies from local and GGA functionals are too negative for large B. Results from the Perdew-Burke-Ernzerhof ground-state GGA and Tao-Perdew-Staroverov-Scuseria (TPSS) ground-state meta-GGA functionals are very close. Because of confinement, self-interaction error in such functionals is more severe at large B than at B = 0, hence selfinteraction correction is crucial. Exact exchange combined with the TPSS correlation functional results in a self-interaction-free (xc) functional, from which we obtain atomic energies of comparable accuracy to those from correlated wave-function methods. Specifically for the B and C atoms, we provide beyond-HF energies in a wide range of B fields. Fully self-consistent CDFT calculations were done with the Vignale-Rasolt-Geldart (VRG) functional in conjunction with the PW92 xc functional. Current effects turn out to be small, and the vorticity variable in the VRG functional diverges in some low-density regions. This part of the study suggests that nonlocal, self-interaction-free functionals may be better than local approximations as a starting point for CDFT functional construction and that some basic variable other than the vorticity could be helpful in making CDFT calculations practical.

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Section: B Results Of Nb-dft Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparative studies of density-functional approximations for light atoms in strong magnetic fields

2014

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“…The wealth of the resulting wavelength information is the basis for the analysis of the spectra presented in this paper. Details of the computational method can be found in Ref., 111 and results from 0 to 800 MG are shown in Fig. 6.…”

Section: 110mentioning

confidence: 99%

White Dwarf Stars

Romero

Pelisoli

Ourique

2017

Int. J. Mod. Phys. Conf. Ser.

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White dwarf stars are the final stage of most stars, born single or in multiple systems. We discuss the identification, magnetic fields, and mass distribution for white dwarfs detected from spectra obtained by the Sloan Digital Sky Survey up to Data Release 13 in 2016, which lead to the increase in the number of spectroscopically identified white dwarf stars from 5 000 to 39 000. This number includes only white dwarf stars with log g ≥ 6.5, i.e., excluding the Extremely Low Mass white dwarfs, which are necessarily the byproduct of stellar interaction.

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“…Mori et al [26,27] have studied mid-Z atoms in strong to intense magnetic fields using perturbation theory as well, obtaining results consistent with previous findings. In recent years Engel and Wunner and co-workers [70][71][72][73][74] have computed accurate results for several atoms in magnetic fields relevant to neutron stars with a variety of techniques involving finite-element methods with B-splines both in the adiabatic approximation and beyond the adiabatic approximation with more than one Landau level. These highly accurate formulations employ a fast parallel Hartree-Fock-Roothan code, in which the electronic wave functions are solved for along the z−direction, with Landau orbitals (and combinations of more than one level in the latter studies) describing the remaining parts of the wave functions.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional pseudospectral Hartree-Fock method for low-Zatoms in intense magnetic fields

Thirumalai

2014

Phys. Rev. A

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The energy levels of the first few low-lying states of helium and lithium atoms in intense magnetic fields up to ≈ 10 8 − 10 9 T are calculated in this study. A pseudospectral method is employed for the computational procedure. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these two-and three-electron systems in a self-consistent manner. The method exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. It is seen that the results obtained here for a few of the most tightly bound states of each of the atoms, helium and lithium, are in good agreement with findings elsewhere. In this regard, we report new data for two new states of lithium that have not been studied thus far in the literature. It is also seen that the pseudospectral method employed here is considerably more economical, from a computational point of view, than previously employed methods such as a finite-element based approach. The key enabling advantage of the method described here is the short computational times which are on the order of seconds for obtaining accurate results for heliumlike systems.

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Atomic ground states in strong magnetic fields: Electron configurations and energy levels

Cited by 15 publications

References 41 publications

Comparative studies of density-functional approximations for light atoms in strong magnetic fields

Comparative studies of density-functional approximations for light atoms in strong magnetic fields

White Dwarf Stars

Two-dimensional pseudospectral Hartree-Fock method for low-Zatoms in intense magnetic fields

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