Matter in a magnetic field in the Thomas-Fermi and related theories

Fushiki, Ikko; Gudmundsson, E. H.; Pethick, C. J.; Yngvason, Jakob

doi:10.1016/0003-4916(52)90041-9

Cited by 60 publications

(49 citation statements)

References 41 publications

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“…In an equally important 1974 paper, Banerjee, Constantinescu, and Rehak 11 ͑hereafter BCR͒ also calculated this exchange energy and obtained a result that looks very similar to that of DG. The calculations of DG and BCR provided the background for a large body of later work on the exchange and correlation energies of the electron gas in high magnetic fields 1,[12][13][14][15][16][17][18] and are also frequently quoted as input for the local-density approximation to current-densityfunctional theory in strong magnetic fields. [18][19][20][21][22] A major limitation of these early calculations is their restriction to complete spin polarization and the lowest Landau level, which in three dimensions requires either magnetic fields that are beyond what is currently achievable in the laboratory or restriction to low-density low-effective-mass systems.…”

Section: Introductionmentioning

confidence: 99%

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

Morbec

Capelle

2008

Phys. Rev. B

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We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit ͑L =0͒ by explicitly including the effect of the second, L = 1, Landau level and arbitrary spin polarization. The inclusion of the L = 1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L = 0 and complete spin polarization. We identify and explain two distinct regimes separated by a critical density n c . Below n c , the per particle exchange energy is lowered by the contribution of L = 1, whereas above n c it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

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Section: Introductionmentioning

confidence: 99%

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

Morbec

Capelle

2008

Phys. Rev. B

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“…Thus the error in the Hartree-Fock approach is expected to be less than the 1% accuracy characteristic of zero-field Hartree-Fock calculations [28,33]. Other calculations of heavy atoms in strong magnetic fields include Thomas-Fermi type statistical models [34,35,36] and density functional theory [37,38,39,40]. The Thomas-Fermi type models are useful in establishing asymptotic scaling relations, but are not adequate for obtaining accurate binding and excitation energies.…”

Section: A Previous Workmentioning

confidence: 99%

Density-functional-theory calculations of matter in strong magnetic fields. I. Atoms and molecules

2006

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We present calculations of the electronic structure of various atoms and molecules in strong magnetic fields ranging from B = 10 12 G to 2×10 15 G, appropriate for radio pulsars and magnetars. For these field strengths, the magnetic forces on the electrons dominate over the Coulomb forces, and to a good approximation the electrons are confined to the ground Landau level. Our calculations are based on the density functional theory, and use a local magnetic exchange-correlation function which is tested to be reliable in the strong field regime. Numerical results of the ground-state energies are given for HN (up to N = 10), HeN (up to N = 8), CN (up to N = 5), and FeN (up to N = 3), as well as for various ionized atoms. Fitting formulae for the B-dependence of the energies are also given. In general, as N increases, the binding energy per atom in a molecule, |EN |/N , increases and approaches a constant value. For all the field strengths considered in this paper, hydrogen, helium, and carbon molecules are found to be bound relative to individual atoms (although for B less than a few ×10 12 G, carbon molecules are very weakly bound relative to individual atoms). Iron molecules are not bound at B < ∼ 10 13 G, but become energetically more favorable than individual atoms at larger field strengths.

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“…The projector IIo on the lowest Landau band with v = 0 is given by the kernel (see, e.g., [25], Appendix) where xl = (xl,x2) is the component of x E R3 perpendicular to the field and P' is the projector in the vectors in C2 with spin component s = -: .…”

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confidence: 99%

Asymptotics of heavy atoms in high magnetic fields: I. Lowest landau band regions

Lieb

Solovej

Yngvason

1994

Comm Pure Appl Math

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The ground state energy of an atom of nuclear charge Ze in a magnetic field B is evaluated exactly to leading order as Z -co. In this and a companion work (see [28]) we show that there are five regions as Z -co: B << Z4/3, B -Z4/3, Z4I3 << B << Z 3 , B -Z3, B >> Z3. Regions 1, 2, 3, and 4 (and conceivably 5) are relevant for neutron stars. Different regions have different physics and different asymptotic theories. Regions I , 2, and 3 are described by a simple density functional theory of the semiclassical Thomas-Fermi form. Here we concentrate mainly on regions 4 and 5 which cannot be so described, although 3,4, and 5 have the common feature (as shown here) that essentially all electrons are in the lowest Landau hand. Region 5 does have, however, a simple non-classical density functional theory (which can be solved exactly). Region 4 does not, but, surprisingly, it can be described by a novel density matrix functional theory! 0

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Matter in a magnetic field in the Thomas-Fermi and related theories

Cited by 60 publications

References 41 publications

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

Density-functional-theory calculations of matter in strong magnetic fields. I. Atoms and molecules

Asymptotics of heavy atoms in high magnetic fields: I. Lowest landau band regions

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