Correction to: A Core-Envelope Massive Distribution with a Parabolic Density Distribution in the Core

The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.

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Relativistic Hirshfeld atom refinement of an organo-gold(I) compound

IUCrJ ◽

10.1107/s2052252521004541 ◽

2021 ◽

Vol 8 (4) ◽

Author(s):

Sylwia Pawlędzio ◽

Maura Malinska ◽

Magdalena Woińska ◽

Jakub Wojciechowski ◽

Lorraine Andrade Malaspina ◽

...

Keyword(s):

Density Distribution ◽

Electron Density ◽

Electron Correlation ◽

Electron Density Distribution ◽

Gold Atom ◽

Relativistic Effects ◽

Model Parameters ◽

Statistical Parameters ◽

Mercury Compounds ◽

The Core

The main goal of this study is the validation of relativistic Hirshfeld atom refinement (HAR) as implemented in Tonto for high-resolution X-ray diffraction datasets of an organo-gold(I) compound. The influence of the relativistic effects on statistical parameters, geometries and electron density properties was analyzed and compared with the influence of electron correlation and anharmonic atomic motions. Recent work in this field has indicated the importance of relativistic effects in the static electron density distribution of organo-mercury compounds. This study confirms that differences in electron density due to relativistic effects are also of significant magnitude for organo-gold compounds. Relativistic effects dominate not only the core region of the gold atom, but also influence the electron density in the valence and bonding region, which has measurable consequences for the HAR refinement model parameters. To study the effects of anharmonic motion on the electron density distribution, dynamic electron density difference maps were constructed. Unlike relativistic and electron correlation effects, the effects of anharmonic nuclear motion are mostly observed in the core area of the gold atom.

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Simultaneous formation of Jupiter and Saturn

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311020655 ◽

2010 ◽

Vol 6 (S276) ◽

pp. 428-429

Author(s):

Octavio M. Guilera ◽

Adrián Brunini ◽

Omar G. Benvenuto

Keyword(s):

Density Distribution ◽

Solar Nebula ◽

Classical Model ◽

Protoplanetary Disk ◽

Instability Mechanism ◽

Simultaneous Formation ◽

The Core ◽

Growth Regime ◽

Significant Change

AbstractWe calculate the simultaneous in situ formation of Jupiter and Saturn by the core instability mechanism considering the oligarchic growth regime for the accretion of planetesimals. We consider a density distribution for the size of planetesimals and planetesimals migration. The planets are immersed in a realistic protoplanetary disk that evolves with time. We find that, within the classical model of solar nebula, the isolated formation of Jupiter and Saturn undergoes significant change when it occurs simultaneously.

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Constraining planetary interiors with the Love number k2

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311020898 ◽

2010 ◽

Vol 6 (S276) ◽

pp. 482-484

Author(s):

Ulrike Kramm ◽

Nadine Nettelmann ◽

Ronald Redmer

Keyword(s):

Density Distribution ◽

Extrasolar Planets ◽

Giant Planets ◽

Love Number ◽

Core Mass ◽

Planetary Interiors ◽

Orbital Parameters ◽

First Order ◽

The Core ◽

Observable Parameter

AbstractFor the solar sytem giant planets the measurement of the gravitational moments J2 and J4 provided valuable information about the interior structure. However, for extrasolar planets the gravitational moments are not accessible. Nevertheless, an additional constraint for extrasolar planets can be obtained from the tidal Love number k2, which, to first order, is equivalent to J2. k2 quantifies the quadrupolic gravity field deformation at the surface of the planet in response to an external perturbing body and depends solely on the planet's internal density distribution. On the other hand, the inverse deduction of the density distribution of the planet from k2 is non-unique. The Love number k2 is a potentially observable parameter that can be obtained from tidally induced apsidal precession of close-in planets (Ragozzine & Wolf 2009) or from the orbital parameters of specific two-planet systems in apsidal alignment (Mardling 2007). We find that for a given k2, a precise value for the core mass cannot be derived. However, a maximum core mass can be inferred which equals the core mass predicted by homogeneous zero metallicity envelope models. Using the example of the extrasolar transiting planet HAT-P-13b we show to what extend planetary models can be constrained by taking into account the tidal Love number k2.

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New Model of Density Distribution for Fermionic Dark Matter Halos

Ukrainian Journal of Physics ◽

10.15407/ujpe63.9.769 ◽

2018 ◽

Vol 63 (9) ◽

pp. 769 ◽

Cited By ~ 1

Author(s):

A. V. Rudakovskyi ◽

D. O. Savchenko

Keyword(s):

Dark Matter ◽

Density Distribution ◽

Density Profile ◽

Initial Phase ◽

Matter Density ◽

Dark Matter Halos ◽

New Model ◽

Dwarf Spheroidal Galaxies ◽

The Core ◽

Dirac Distribution

We formulate a new model of density distribution for halos made of warm dark matter (WDM) particles. The model is described by a single microphysical parameter – the mass (or, equivalently, the maximal value of the initial phase-space density distribution) of dark matter particles. Given the WDM particle mass and the parameters of a dark matter density profile at the halo periphery, this model predicts the inner density profile. In the case of initial Fermi–Dirac distribution, we successfully reproduce cored dark matter profiles from N-body simulations. We calculate also the core radii of warm dark matter halos of dwarf spheroidal galaxies for particle masses mFD = 100, 200, 300, and 400 eV.

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The Influence of the Core-mantle Boundary Irregularities on the Mass Density Distribution Inside the Earth

Geophysical Data Inversion Methods and Applications ◽

10.1007/978-3-322-89416-8_15 ◽

1990 ◽

pp. 233-256 ◽

Cited By ~ 2

Author(s):

Z. Martinec ◽

K. Pěč

Keyword(s):

Density Distribution ◽

Mass Density ◽

Mantle Boundary ◽

Core Mantle Boundary ◽

The Core ◽

The Earth

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Fusion of halo nucleus 6He on 238U : Evidence for tennis-ball (bubble) structure of the core of the halo (even the giant-halo) nucleus

Modern Physics Letters A ◽

10.1142/s0217732319502213 ◽

2019 ◽

Vol 34 (27) ◽

pp. 1950221

Author(s):

Syed Afsar Abbas

Keyword(s):

Density Distribution ◽

Target Nucleus ◽

Halo Nucleus ◽

Halo Nuclei ◽

Tennis Ball ◽

Clear Cut ◽

The Core ◽

Incoming Beam ◽

New Interpretation ◽

The One

In a decade-and-a-half old experiment, Raabe et al. [Nature 431, 823 (2004)], had studied fusion of an incoming beam of halo nucleus 6He with the target nucleus [Formula: see text]. We extract a new interpretation of the experiment, different from the one that has been inferred so far. We show that their experiment is actually able to discriminate between the structures of the target nucleus (behaving as standard nucleus with density distribution described with canonical RMS radius [Formula: see text] with [Formula: see text] fm), and the “core” of the halo nucleus, which surprisingly, does not follow the standard density distribution with the above RMS radius. In fact, the core has the structure of a tennis-ball (bubble)-like nucleus, with a “hole” at the center of the density distribution. This novel interpretation of the fusion experiment provides an unambiguous support to an almost two decades old model [A. Abbas, Mod. Phys. Lett. A 16, 755 (2001)], of the halo nuclei. This Quantum Chromodynamics based model succeeds in identifying all known halo nuclei and makes clear-cut and unique predictions for new and heavier halo nuclei. This model supports the existence of tennis-ball (bubble)-like core, of even the giant-neutron halo nuclei. This should prove beneficial to the experimentalists, to go forward more confidently, in their study of exotic nuclei.

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Isoelectronic Changes in the Core Radius of Fe3+ and Ru3+ Like Ions

Zeitschrift für Naturforschung A ◽

10.1515/zna-1979-1021 ◽

1979 ◽

Vol 34 (10) ◽

pp. 1253-1254

Author(s):

C. V. R. Rao ◽

K. D. Sen

Keyword(s):

Distribution Function ◽

Density Distribution ◽

Charge Density ◽

Empirical Relationship ◽

Wave Functions ◽

Core Radius ◽

Density Distribution Function ◽

Charge Density Distribution ◽

Hartree Fock ◽

The Core

Abstract Isoelectronic changes in the core radius rm , defined as the last minimum in the total radial charge density distribution function 4 π r2 ϱ(r), have been computed for Fe 3+ and Ru 3+ like ions using Hartree-Fock-Slater wave functions. It is found that a linear relationship rm-1 = A' Z + B' holds good within each series. An attempt is made to justify this empirical relationship.

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