Parameterization of the spectra of configurations 3<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">f</Emphasis> and 3<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">f</Emphasis> of a phosphorus ion P II. Gyromagnetic ratios

In the one-configuration approximation, in the formalism of irreducible tensor operators, and in the intermediate (real) coupling scheme, numerical values of the fine-structure parameters are determined for the 3p4f and 3p5f highly excited configurations of the P II phosphorus ion with the energy-operator matrix in the LK-coupling approximation. With these values of the fine-structure parameters, the energy-operator matrix is numerically diagonalized in the LS-coupling approximation. The gyromagnetic ratios calculated in both basis sets in the absence of a field are compared with one another, as well as with their vector counterparts and the experimental g-factors available for the 3p4f configuration. The experimental and theoretical g-factors calculated with the LS basis set are in good agreement with the sole exception of the ³ F ₂ level. Note that the calculation of g-factors from the Zeeman splitting in the linear region totally confirmed their agreement with the values calculated in the LS basis set (g _LS ) in the absence of a field. The gyromagnetic ratios are the main objectives of this and previous papers, especially for configurations for which experimental data are absent. Apart from the g-factors, the specific features of Zeeman splitting (the crossings and anticrossings of magnetic components) in the 3p5f configurations were determined. These data are to be compared with results of future experiments. Comparison of gyromagnetic ratios calculated in the intermediate coupling scheme with their vector counterparts showed that most levels of the configurations studied are closer than in the LK-coupling scheme.     

Coexistence of superconducting and spiral spin orders: Models of ruthenate

The effect of a spiral spin structure on superconducting (SC) pairing in a three-band Hubbard model related to Sr₂RuO₄ is analyzed in the mean-field approximation. Such a structure with incommensurate vector Q=2π (1/3, 1/3) is the simplest one that removes the nesting instability of α and β bands. It is assumed that there is an intralayer pairing interaction between two types of neighbor sites, those with attraction in a singlet channel and with attraction in both two-singlet and triplet channels. In both cases, a mixed singlet-triplet SC order is observed in the γ band: a d-wave singlet order is accompanied by the formation of p-wave triplet pairs (k,-k-Q)? and (k,?k+Q)? with large total momenta ?Q and the spin projections ±1 onto an axis perpendicular to the spin rotation plane of the spiral spin structure. Both the SC and normal states are states with broken time-reversal symmetry. In contradiction to the experiment, the models give different scales of T _c for the γ band and for α and β bands. This fact shows that the models with intralayer interactions or with the spin structure assumed are insufficient.     

Band splitting and relative spin alignment in bilayer systems

It is shown that one-particle spectra of the lower Hubbard band of bilayer correlated 2D systems with different relative alignments of the spin systems in the layers differ significantly. In particular, the bilayer band splitting differs from zero for identically directed alternating spins of different layers (F _z configuration), but tends to zero for antiparallel alignment (AF _z configuration). It is found that the type of the alignment of the ground state changes upon an increase in the doping δ from the lower AF _z configuration to the F _z configuration of the alignment observed for large values of δ. The behavior of bilayer splitting in Bi₂Sr₂CaCu₂O_8+δ suggests that the configuration of the alignment may change from F _z →AF _z simultaneously with the superconducting transition. The effects associated with the influence of spin alignment on the magnetic excitation spectrum as a method of studying the spin structure of bilayer systems are considered for homogeneous solutions of effective spin models.     

Spectroscopy of coherent dark resonances in multilevel atoms for the example of samarium vapor

A universal theory for calculating coherent population trapping resonances in multilevel atoms is suggested. The theory allows arbitrary schemes of multilevel atoms and their excitations to be calculated taking into account the influence of relaxation effects in atoms, applied magnetic field, and the Doppler effect. The experimental data obtained by high-precision diode spectroscopy of coherent dark resonances in samarium vapor are systematically analyzed using the suggested theory. In the absence of a magnetic field, the model of samarium is based on consideration of a degenerate Λ system of the 4f⁶6s²(⁷F₀) ? 4f⁶(⁷F)6s6p(³P⁰)⁹F ₁ ⁰ ?4f⁶6s²(⁷F₁) active transitions. If the fourth 4f⁶6s²(⁷F₂) level is taken into account, this Λ system becomes open. Numerical simulation of coherent population trapping resonances shows that the open character of the system decreases the contrast of resonance curves in absorption spectra without changing resonance widths. The system under applied external longitudinal and transverse magnetic fields is correctly described by 7-and 12-level models of atomic transitions, respectively.     

Features of the Formation of the Spin Polarization of an Alkali Metal at the Resolution of Hyperfine Sublevels in the <Superscript>2</Superscript><Emphasis Type="Italic">S</Emphasis><Subscript>1/2</Subscript> State

The optical orientation of the angular momenta of alkali atoms in the presence of a buffer gas (molecular nitrogen) has been studied experimentally. It has been shown that, even at a low concentration of molecular nitrogen in the cell, the excitation of ¹³³Cs atoms from the lower hyperfine level with F = 3, which belongs to the ground ²S_1/2 state, results in a larger amplitude of the magnetic resonance than the excitation from the hyperfine level with F = 4. This result has been theoretically explained under the assumption that the spin state of the alkali atomic nucleus does not change at collision with a nitrogen molecule, which is accompanied by a nonradiative transition of the alkali atom from the excited ²P_1/2 state to the ground ²S_1/2 state.     

Free Energy as a Dynamical Invariant (or Can You Hear the Shape of a Potential?)

Classical lattice spin systems provide an important and illuminating family of models in statistical physics. An interaction Φ on a lattice L?? ^d determines a lattice spin system with potential A _Φ . The pressure P(A _Φ ) and free energy F _AΦ (β)=?(1/β)P(βA _Φ ) are fundamental characteristics of the system. However, even for the simplest lattice spin systems, the information about the potential that the free energy captures is subtle and poorly understood. We study whether, or to what extent, (microscopic) potentials are determined by their (macroscopic) free energy. In particular, we show that for a one-dimensional lattice spin system, the free energy of finite range interactions typically determines the potential, up to natural equivalence, and there is always at most a finite ambiguity; we exhibit exceptional potentials where uniqueness fails; and we establish deformation rigidity for the free energy. The proofs use a combination of thermodynamic formalism, algebraic geometry, and matrix algebra. In the language of dynamical systems, we study whether a Hölder continuous potential for a subshift of finite type is naturally determined by its periodic orbit invariants: orbit spectra (Birkhoff sums over periodic orbits with various types of labeling), beta function (essentially the free energy), or zeta function. These rigidity problems have striking analogies to fascinating questions in spectral geometry that Kac adroitly summarized with the question ``Can you hear the shape of a drum?''.     

Effect of the Lattice and Spin-Phonon Contributions on the Temperature Behavior of the Ground State Splitting of Gd<Superscript>3+</Superscript> in SrMoO<Subscript>4</Subscript>

The temperature behavior of the EPR spectra of the Gd³⁺ impurity center in single crystals of SrMoO₄ in the temperature range T = 99–375 K is studied. The analysis of the temperature dependences of the spin Hamiltonian b ₂ ⁰ (T) = b₂(F) + b₂(L) and P ₂ ⁰ (T) = P₂(F) + P₂(L) (for Gd¹⁵⁷) describing the EPR spectrum and contributing to the Gd³⁺ ground state splitting ΔE is carried out. In terms of the Newman model, the values of b₂(L) and P₂(L) depending on the thermal expansion of the static lattice are estimated; the b₂(F) and P₂(F) spin-phonon contributions determined by the lattice ion oscillations are separated. The analysis of b ₂ ⁰ (T) and P ₂ ⁰ (T) is evidence of the positive contribution of the spin-phonon interaction; the model of the local oscillations of the impurity cluster with close frequencies ω describes well the temperature behavior of b₂(F) and P₂(F).     

Spin observables in <Emphasis Type="Italic">np</Emphasis> elastic scattering in the energy range 200–600 MeV. Complete experiment

A survey of available experimental data on the measurement of spin observables in neutron-proton (np) elastic scattering in the neutron energy range 200–600 MeV is presented. Sixteen spin observables (the polarization of recoil particles P _0n00, the analyzing power A _00n0, the spin correlation parameters A _00nn , A _00ss , A _00sk , and A _00kk , the spin transfer parameters K _0nn0, K _0ss0, and K _0sk0, the depolarization parameters D _0n0n , D _0s0s , and D _0s0k , and the three-spin parameters N _0nkk , N _0skn , N _0ssn , and N _0sns for energies of 200–590 MeV and scattering angles in the center of mass system of 60°–164°) were studied in experiments using polarized neutron beams and polarized proton targets at the Paul Scherrer Institute. The results of these investigations present a complete set of precision data on np elastic scattering which, along with the complete set of data for proton-proton (pp) elastic scattering obtained earlier, provides a basis for unambiguous determination of the amplitudes of the scattering matrix for nucleon-nucleon (NN) elastic scattering for the channel with the isotopic spin I = 0 and makes it possible to describe NN interaction in a model-independent way.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

Spin orbit interaction and polarization of slow neutrons

It is shown that the spin orbit (LS) interaction of an anomalous magnetic moment is twice that of a Dirac moment. In neutron scattering this interaction leads to an imaginary spindependent scattering amplitude. Possible experiments are discussed, where interference ofLS scattering and nuclear scattering in crystals without inversion symmetry leads to detectable neutron polarization.     

Mechanisms of ionization of <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript>-centers in laser media on the basis of LiF crystals

F₂ color centers with a superhigh concentration (5000-cm^–1 absorption coefficient at 450 nm) were formed by high-density electron beams in a layer of LiF crystals of micrometer thickness. The F₂-centers excited by high-power nanosecond wide-band optical pulses (the “soft” pumping regime) efficiently amplified the laser radiation and showed high stability under these conditions. A low stability of F₂-centers to laser radiation (the “hard” excitation regime) is explained by the dissociation of (F ₂ ⁺ , F^–) pairs induced by two-step ionization of F₂-centers: (2hν > 4.5 eV) → F₂ → (F₂)* → F ₂ ⁺ + e; F + e → F^–; F ₂ ⁺ + F^– → 3F.     

The effects of the composition,temperature and geometry on the hysteretic properties of the Ising-type barcode nanowire

In the present study, a theoretical approach to investigate the magnetic hysteresisproperties in barcode nanowire are used and applied to study Ising system on hexagonalstructure. The hysteresis behaviors of Ising-type barcode nanowire (IBN) are studiedwithin the effective-field theory with correlations. The effects of the composition(p),temperature (T) and geometry (interlayer length (d), shell length(s), andwire length (r)) on the hysteresis behaviors are examined indetail. The phase diagrams are presented in the five different planes, namely(p,T),(d,r),(d, T), (r, T) and (s, T) as function of coercive field (H _C ) and remanence(M _r ), and investigatedsoft/hard the magnetic characteristics of the system. We find that the hysteresis loopsareas decrease case as the temperature, wire and lengths increase. Moreover, whenp increasesthe hysteresis loop areas increase. Moreover, H _C exhibits an increasein around d =1 value, then H _C does not change withthe increasing d values. Theoretical results have qualitativelycompatible with some experimental works of multilayer nanowire.     

Self-referencing measurement of an ultrashort pulse by the standard shear interferometry method

A new method for the self-referencing measurement of the amplitude-phase shape of an ultrashort pulse is proposed. The method uses a two-frequency characteristic of the pulse, which is defined as S(F ₁)S(F ₂), where F is the frequency, S(F) is the complex Fourier spectrum of the pulse, and F ₁ and F ₂ are two independent variables. It is shown that this characteristic can be generated as a two-dimensional polychromatic light wave upon generation of the sum frequency of two crossed spectral decompositions of one and the same pulse, as well as upon space-time Fourier transform of radiation of the noncollinearly generated second harmonic of the pulse. In an orthogonal system of transverse coordinates F ₁ + F ₂ and F ₁ ? F ₂, at any given value of F ₁ + F ₂, the radiation frequency of this wave in the direction of the second coordinate F ₁ ? F ₂ does not change. Therefore, the phase structure of the two-frequency characteristic can be reconstructed by the standard method of lateral shear interferometry in the direction of this coordinate. In the reconstructed two-dimensional phase structure of the two-frequency characteristic, any section by the plane F ₁ = const or F ₂ = const yields the phase structure of the spectrum of the pulse under study. This makes it possible to reconstruct the amplitude-phase shape of the pulse.     

Quantifying Correlations via the Wigner-Yanase-Dyson Skew Information

In this paper, based on a discussion about the Wigner-Yanase-Dyson (WYD) skew information, the measure F_a,α(ρ_ab) for correlations in terms of the WYD skew information is introduced and discussed. The following conclusions are obtained. For a classical-quantum state ρ_ab, F_a,α(ρ_ab)=0 if and only if ρ_ab is a product state; F_a,α(ρ_ab) is locally unitary invariant and convex on the set of states with the fixed marginal ρ_a; F_a,α(ρ_ab) decreases under local random unitary operation on H_b; For a quantum-classical state ρ_ab, F_a,α(ρ_ab) decreases under local operation on H_b; Lastly, F_a,α(ρ_ab) is computed for the pure states and the Bell-diagonal states, respectively.     

Effect of doping by boron,carbon, and nitrogen atoms on the magnetic and photocatalytic properties of anatase

The effect of doping of titanium dioxide with the anatase structure by boron, carbon, and nitrogen atoms on the magnetic and optical properties and the electronic spectrum of this compound has been investigated using the ab initio tight-binding linear muffin-tin orbital (TB-LMTO) band-structure method in the local spin density approximation explicitly including Coulomb correlations (LSDA + U) in combination with the semiempirical extended Hückel theory (EHT) method. The LSDA + U calculations of the electronic structure, the imaginary part of the dielectric function, the total magnetic moments, and the magnetic moments at the impurity atoms have been carried out. The diagrams of the molecular orbitals of the clusters Ti₃ X (X = B, C, N) have been calculated and the pseudo-space images of the molecular orbitals of the clusters have been constructed. The effect of doping on the nature and origin of photocatalytic activity in the visible spectral range and the specific features of the generation of ferromagnetic interactions in doped anatase have been discussed based on the analysis of the obtained data. It has been shown that, in the sequence TiO_{2 ? y} N _y → TiO_{2 ? y} C _y → TiO_{2 ? y} B _y (y = 1/16), the photocatalytic activity can increase with the generation of electronic excitations with the participation of impurity bands. The calculated magnetic moments for boron and nitrogen atoms are equal to 1 μ_B, whereas the impurity carbon atoms are nonmagnetic.     

Low-energy Ce spin excitations in CeFeAsO and CeFeAsO<Subscript>0.84</Subscript>F<Subscript>0.16</Subscript>

We use inelastic neutron scattering to study the low-energy spin excitations of polycrystalline samples of nonsuperconducting CeFeAsO and superconducting CeFeAsO_0.84F_0.16. Two sharp dispersionless modes are found at 0.85 and 1.16 meV in CeFeAsO below the Ce antiferromagnetic (AF) ordering temperature of T _N ^Ce ? 4 K. On warming to above T _N ^Ce ? 4 K, these two modes become one broad dispersionless mode that disappears just above the Fe ordering temperature T _N ^Fe ? 140 K. For superconducting CeFeAsO_0.84F_0.16, where Fe static AF order is suppressed, we find a weakly dispersive mode center at 0.4 meV that may arise from short-range Ce-Ce exchange interactions. Using a Heisenberg model, we simulate powder-averaged Ce spin wave excitations. Our results show that we need both Ce spin wave and crystal electric field excitations to account for the whole spectra of low-energy spin excitations.     

Grundzustand eines Fermi-Gases mit hard-sphere-Wechselwirkung

The decomposition of the ground state wave function of a Fermi gas interacting via hard core potentials into cluster functionsS _n leads to a systematic expansion of wave function and energy in powers of the parameterc=P _F r _c (r _c =hard core radius,P _F =Fermi momentum). For instance,S _n has the order of magnitudec ^n-λ-1, if λ=number of Fermion coordinates with distances smaller thanr _c . The first three energy terms agree with the ones given by other authors. Any occurrence of singular terms in the intermediate steps of the derivation can be avoided     

X-ray emission and X-ray photoelectron spectroscopic studies of fullerene fluoride C<Subscript>60</Subscript>F<Subscript>24</Subscript>

The structure of the fullerence fluoride C₆₀F₂₄ of the T _h symmetry contains two types of chemically different carbon atoms, namely, atoms of isolated double bonds and atoms of CF groups. X-ray photoelectron and x-ray emission spectroscopic studies of C₆₀F₂₄ revealed a difference in the widths of the x-ray bands corresponding to these types of atoms. Nonempirical quantum-chemical calculations performed for C₅₉NF ₂₄ ⁺ ions with a hole in the C 1s core level of the fullerence fluoride showed that the difference in the bandwidths may be due to the fact that the vibrational states of the system are different when 1s electrons are removed from chemically nonequivalent atoms.     

Dissipative Evolution of the Qubit State in the Tomographic-Probability Representation

We consider the evolution of qubit states for the Demkov problem in the presence of dephasing processes in the spin tomographic-probability representation. We present an explicit solution of the spin tomogram in terms of the ₁ F ₂ hypergeometric function. We calculate the tomographic Shannon and q entropies through the solution of the master equation in the form of tomographic-probability distribution of the qubit states obtained.