Weak-field Scheme Research Articles

Four-hair relations for differentially rotating neutron stars in the weak-field limit

The opportunity to study physics at supra-nuclear densities through X-ray observations of neutron stars has led to in-depth investigations of certain approximately universal relations that can remove degeneracies in pulse profile models. One such set of relations determines all of the multipole moments of a neutron star just from the first three (the mass monopole, the current dipole and the mass quadrupole moment) approximately independently of the equation of state. These three-hair relations were found to hold in neutron stars that rotate rigidly, as is the case in old pulsars, but neutron stars can also rotate differentially, as is the case for proto-neutron stars and hypermassive transient remnants of binary mergers. We here extend the three-hair relations to differentially rotating stars for the first time with a generic rotation law using two approximations: a weak-field scheme (an expansion in powers of the neutron star compactness) and a perturbative differential rotation scheme (an expansion about rigid rotation). These approximations allow us to analytically derive approximately universal relations that allow us to determine all of the multipole moments of a (perturbative) differentially rotating star in terms of only the first four moments. These new four-hair relations for differentially rotating neutron stars are found to be approximately independent of the equation of state to a higher degree than the three-hair relations for uniformly rotating stars. Our results can be instrumental in the development of four-hair relations for rapidly differentially rotating stars in full General Relativity using numerical simulations.

Studies of the g factors and the superhyperfine parameters for Ni3+ in the fluoroperovskites

The g factors and the ligand superhyperfine parameters A' and B' for Ni(3+) in KMgF(3), CsCaF(3) and RbCaF(3) are theoretically studied from the formulas of these parameters for a 3d(7) ion under octahedral environments in the weak field scheme. The unpaired spin densities for the fluorine 2s, 2p, and 2p, orbitals are quantitatively determined from the molecular orbital and configuration interaction coefficients based on the cluster approach. The calculated results show good agreement with the experimental data, based on only one adjustable parameter (i.e., the proportionality factor p related to the ligand s- and p-orbitals). The superhyperfine parameters for the axial and planar ligands in RbCaF(3):Ni(3+) are satisfactorily interpreted from the different impurity-ligand distances due to the elongation of the ligand octahedron during cubic-to-tetragonal phase transition.

Theoretical investigations of the hyperfine interactions for Co 2+ in the fluoroperovskites

The hyperfine structure constant A of central ion and the superhyperfine parameters A′ and B′ of ligands for Co 2+ in LiBaF 3, KMgF 3, KZnF 3 and CsCdF 3 are theoretically studied from a cluster approach based on the weak field scheme. The unpaired spin densities for the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively calculated from the molecular orbital and mixing interaction coefficients based on the cluster approach. The experimental A, A′ and B′ as well as the g factor for Co 2+ in these fluoroperovskites are satisfactorily explained in a uniform way. The results are discussed.

Crystal-field theory ofCo2+in doped ZnO

We present a crystal field theory of transition metal impurities in semiconductors in a trigonally distorted tetrahedral coordination. We develop a perturbative scheme to treat covalency effects within the weak ligand field case (Coulomb interaction dominates over one-particle splitting) and apply it to ZnO:Co$^{2+}$ (3d$^7$). Using the large value of the charge transfer energy $\Delta_{pd}$ compared to the $p$-$d$ hoppings, we perform a canonical transformation which eliminates the coupling with ligands to first order. As a result, we obtain an effective single-ion Hamiltonian, where the influence of the ligands is reduced to the one-particle 'crystal field' acting on $d$-like-functions. This derivation allows to elucidate the microscopic origin of various 'crystal field' parameters and covalency reduction factors which are usually used empirically for the interpretation of optical and ESR experiments. The connection of these parameters with the geometry of the local environment becomes transparent. The experimentally known $g$-values and the zero-field splitting 2D are very well reproduced by the exact diagonalization of the effective single-ion Hamiltonian with only one adjustable parameter $\Delta _{pd}$. Alternatively to the numerical diagonalization we use perturbation theory in the weak field scheme (Coulomb interaction $\gg$ cubic splitting $\gg$ trigonal splitting and spin-orbit coupling) to derive compact analytical expressions for the spin-Hamiltonian parameters that reproduce the result of exact diagonalization within 20% of accuracy.

Spectrum structure and g factor of electron paramagnetic resonance of LiCoO2 crystal doped with Ni

In the weak field scheme, the complete diagonalizing Hamiltonian matrices and th e constants of crystal structure and g factor of electron paramagnetic resonanc e are derived for 3d4/3d6 ions configuration in the trigon al symmetry in terms of Racahs irreducible tensor operator method. The ground- state energy levels and the constants of crystal structure and g factor of elec tron paramagnetic resonance of the Co3+ in LiCoO2 and LiCo O2:Ni crystals are studied. The spin singlets and triplet of the grou nd-state energy levels of the Co3+ in LiCoO2 and LiCoO2:Ni crystals are taken into consideration in the calculation and applica tion of the crystal-field energy of 3d4/3d6. The changes o f the constants of local structure, which are the causes of the changes of the g round-state energy levels of the Co3+, and the values of g factor of electron paramagnetic resonance of Co3+ in LiCoO2 and LiCo O2:Ni crystals are also studied. The theoretical results are in good agreement with the experimental observations.

Magnetic anisotropy of BaM ferrites

Using the point charge model with weak field scheme, a calculation of the single ion anisotropy of Fe 3+ ionsn at all crystal sites in BaFe 12O 19 was made by perturbation theory. The results show that in addition to the 2b site, all other sites have non-negligible contributions.

ChemInform Abstract: JAHN‐TELLER STABILIZATION ENERGIES FOR FX SYSTEMS: ANGULAR‐OVERLAP CALCULATIONS FOR OCTAHEDRAL SYSTEMS IN THE WEAK‐FIELD SCHEME

Chemischer InformationsdienstVolume 13, Issue 49 Physical Inorganic Chemistry ChemInform Abstract: JAHN-TELLER STABILIZATION ENERGIES FOR FX SYSTEMS: ANGULAR-OVERLAP CALCULATIONS FOR OCTAHEDRAL SYSTEMS IN THE WEAK-FIELD SCHEME K. D. WARREN, K. D. WARRENSearch for more papers by this author K. D. WARREN, K. D. WARRENSearch for more papers by this author First published: December 7, 1982 https://doi.org/10.1002/chin.198249002Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume13, Issue49December 7, 1982 RelatedInformation

Jahn-Teller stabilization energies for fx systems: angular-overlap calculations for octahedral systems in the weak-field scheme

Jahn-Teller stabilization energies for fx systems: angular-overlap calculations for octahedral systems in the weak-field scheme

Optical Interactions in Solids

Elements of Quantum Mechanics Elements of Group Theory Connection of Quantum Mechanics with Group Theory The Hydrogen Atom The Complex Atom - Multiplet Theory The Magnetic Ion in a Crystal - The Role of Symmetry The Weak Field Scheme The Medium Field Scheme The Strong Field Scheme Covalent Bonding and Its Effect on Magnetic Ions in Crystals The Quantum Theory of the Radiation Field Molecular Vibrations Lattice Vibrations The Ion-Photon Interaction - Absorption and Emission of Radiation The Ion-Vibration Interaction - Radiationless Processes - Thermal Shift and Broadening of Sharp Lines Vibrational-Electronic Interaction and Spectra Absorption Spectra of Magnetic Ions in Crystals Fluorescence Spectra of Magnetic Ions in Crystals Elements of Laser Theory