Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Near-threshold <Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis>-meson photoproduction on nuclei

On the basis of the first-collision model that relies on the nuclear spectral function and which includes incoherent processes involving charmonium production in proton–nucleon collisions, the photoproduction of J/ψ mesons on nuclei is considered at energies close to the threshold for their production on a nucleon. The absorption of final J/ψ mesons, their formation length, and the binding and Fermi motion of target nucleons are taken into account in this model along with the effect of the nuclear potential on these processes. The A dependences of the absolute and relative charmonium yields are calculated together with absolute and relative excitation functions under various assumptions on the magnitude of the cross section for J/ψN absorption, the J/ψ-meson formation length, and their inmedium modification. It is shown that, at energies above the threshold, these features are virtually independent of the formation length and the change in the J/ψ-meson mass in nuclear matter but are rather highly sensitive to the cross section for J/ψN interaction. The calculations performed in the present study can be used to determine the unknown cross section for J/ψ-meson absorption in nuclei from a comparison of their results with data expected from experiments in the Hall C of the CEBAF (USA) facility upgraded to the energy of 12 GeV. It is also shown that the absolute and relative excitation functions for J/ψ mesons in photon–nucleus reactions at subthreshold energies are sensitive to the change in the meson mass and, hence, carry information about the properties of charmonium in nuclear matter.     

Tevatron and LHC potential for observing <Emphasis Type="Italic">χ</Emphasis><Subscript>b</Subscript>

Results of recent studies that indicate that allowance for the relative motion of quarks in mesons leads to an increase in the cross sections for the process e ⁺ e ^? → J/ψη _c are confirmed. It is shown that the same effect also leads to an increase in the width of scalar and tensor mesons with respect to their decay to two vector mesons, so that the decays χ _b0,2 → 2J/ψ can be used to observe these mesons at the Tevatron collider and LHC.     

Depolarizing collisions in ytterbium vapor: Isotropic and anisotropic relaxation

Isotropic depolarizing collisions are studied using a stimulated photon echo with a specific polarization of the excitation radiation pulses in a mixture of ytterbium with krypton for the J = 1 ? J = 0 transition of ¹⁷⁴Yb. The difference between the relaxation rates of orientation and alignment γ _b ⁽²⁾ ? γ _b ⁽¹⁾ of the ³ P ₁(6s6p) ¹⁷⁴Yb level is measured as a function of the krypton pressure. The collision photon echo at the J = 1 ? J = 0 transition induced by the anisotropic relaxation is studied for the Yb + Xe mixture. The power of the collision echo increases from zero with the addition of a buffer gas to ytterbium, reaches an optimal level, and decreases with an increase in the buffer gas pressure. The polarization of this collision-induced echo differs from the polarization of the conventional echo. The experimental results are in qualitative agreement with theoretical predictions.     

Invariant surfaces and orbital behaviour in dynamical systems of 3 degrees of freedom. II

Two formal integrals of motion besides the Hamiltonian are found in a system of three degrees of freedom with three unperturbed frequencies ω₁, ω₂, ω₃ which are close to, or exactly at, the double resonance 6:4:3. The integrals are truncated at various orders and they are used to find theoretical invariant surfaces on a surface of section.The theoretical invariant surfaces are then compared with the empirical results. The agreement is improved as the order of the integrals increases from the 5th up to the 11th degree. This is surprising because theoretical considerations indicate that one formal integral breaks down beyond order 6, because of the second resonance 4:3. (However it is possible to construct one further integral by a different method). As expected the agreement is worse when the perturbation becomes large. A check of the constancy of the truncated integrals along various orbits shows that the relative variations become smaller as the order increases; they become larger as the perturbation increases.     

Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy

The low-energy constants, namely the spin stiffness ρ _s , the staggered magnetization density ? _s per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J ₁ and J ₂ in the spatial 1- and 2-directions, respectively. For each considered J ₂∕J ₁, the aspect ratio of the corresponding linear box sizes L ₂∕L ₁ used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρ _s1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J ₂∕J ₁. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ? _s and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.     

Equilibrium magnetic and orbital states of the manganites with four manganese atoms in the unit cell

The carrier energy spectrum and the total energy of various magnetic and orbital crystal-structure configurations of the manganites R _1?x A _xMnO₃ (R=La, Pr, Nd, Sm, etc.; A=Ca, Sr, Ba) with four manganese atoms in the unit cell have been calculated for the electron doping region x>0.5. The equilibrium magnetic and orbital configurations of the model are determined by minimizing the total energy of the system with respect to the angles θ _i ^s , φ_i, and θ _i ^o , which define the directions of the local manganese magnetic moments and the type of orbital mixing of the e _g electrons in the manganites. Assuming the parameters of the Heisenberg exchange interaction to be 0.018t<J _AFM<0.022t, the Hund exchange interaction to be J _H=2.5t, and the Jahn-Teller splitting to be Δ=1.5ty, the model with four manganese atoms in the unit cell predicts the experimentally observed magnetic phase alternation sequence G-C-A with increasing doping level y=1?x. For the values J _AFM<0.018t and y<0.28, this model allows the existence of a collinear phase H not observed earlier.     

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J(z), the stress intensity factor K(z) and the tri-axial stress constraint level T _z (z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J(z) and T _z (z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.     

Structure of geodesics in the regular Hayward black hole space-time

The regular Hayward model describes a non-singular black hole space-time. By analyzing the behaviors of effective potential and solving the equation of orbital motion, we investigate the time-like and null geodesics in the regular Hayward black hole space-time. Through detailed analyses of corresponding effective potentials for massive particles and photons, all possible orbits are numerically simulated. The results show that there may exist four orbital types in the time-like geodesics structure: planetary orbits, circular orbits, escape orbits and absorbing orbits. In addition, when \(\ell \), a convenient encoding of the central energy density \(3/8\pi \ell ^{2}\), is 0.6M, and b is 3.9512M as a specific value of angular momentum, escape orbits exist only under \(b>3.9512M\). The precession direction is also associated with values of b. With \(b=3.70M\) the bound orbits shift clockwise but counter-clockwise with \(b=5.00M\) in the regular Hayward black hole space-time. We also find that the structure of null geodesics is simpler than that of time-like geodesics. There only exist three kinds of orbits (unstable circle orbits, escape orbits and absorbing orbits).     

Emergent nesting of the Fermi surface from local-moment description of iron-pnictide high-T<Subscript>c</Subscript> superconductors

We uncover the low-energy spectrum of a t-J model for electrons on a square lattice of spin-1 iron atoms with 3d _xz and 3d _yz orbital character by applying Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of one hole roaming over a 4 × 4 × 2 lattice. Hopping matrix elements are set to produce hole bands centered at zero two-dimensional (2D) momentum in the free-electron limit. Holes can propagate coherently in the t-J model below a threshold Hund coupling when long-range antiferromagnetic order across the d + = 3d _{(x + iy)z} and d ? = 3d _{(x ? iy)z} orbitals is established by magnetic frustration that is off-diagonal in the orbital indices. This leads to two hole-pocket Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate spin-density wave (cSDW) that exists above the threshold Hund coupling results in emergent Fermi surface pockets about cSDW momenta at a quantum critical point (QCP). This motivates the introduction of a new Gutzwiller wavefunction for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta indicates that the dispersion of the nested band of one-particle states that emerges is electron-type. Increasing Hund coupling past the QCP can push the hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy level, in agreement with recent determinations of the electronic structure of mono-layer iron-selenide superconductors.     

Fluctuations and waves in a spatially distributed system with the 1/<Emphasis Type="Italic">f</Emphasis> spectrum

A spatially distributed system with the 1/ _f spectrum of fluctuation power is modeled by two nonlinear stochastic equations. The numerical methods show the formation of 1/ _f and 1/ _k spectra of extreme fluctuations against the background of the formation and motion of waves under the effect of white noise. The distribution of extreme fluctuations corresponds to the maximum of entropy, which testifies to their stability. Under an external periodic perturbation in the system, it is possible to observe space?time stochastic resonance.     

Rotationstemperaturen von H2 bei Beschuß mit 15 keV-Elektronen

Rotational temperatures have been determined from the intensities of the vacuum ultraviolet H₂(2p ¹ Π _u →1s ¹ Σ _g ⁺ ) emission lines, excited by 15 keV electron impact. Their experimental values for the unperturbed 2p ¹ Π _d rotationallevels verify theoretical predictions, and show that the fast electron impact populates 2p ¹ Π _d out of the ground state byΔJ=0, analogous to the valid optical selection rule.     

Manifestation of the vibronic analogue of the Fermi resonance in quasi-line spectra of porphyrins: Experiment and theoretical analysis

The quasi-line low-temperature (4.2 K) fluorescence excitation spectra of two porphyrins, meso-tetraazaporphin and meso-tetrapropylporphin introduced into an n-octane matrix are measured in the range of the S ₀ → S ₂ electronic transition. A characteristic feature of these spectra is that a conglomerate of quasi-lines—a structured complex band—is observed instead of one 0–0 quasi-line of the S ₀ → S ₂ transition. In this band, the intensity distributions for the two main types of impurity centers considerably differ from each other. The occurrence of such conglomerates is interpreted as a result of nonadiabatic electronic-vibrational interactions between vibronic S ₂ and S ₁ states (the complex vibronic analogue of the Fermi resonance). The frequencies and intensities of individual transitions determined from the deconvolution of complex conglomerates are used as the initial data for solving the inverse spectroscopic problem: the determination of the unperturbed electronic and vibrational levels of states involved in the resonance and the electronic-vibrational interaction matrix elements between them. This problem is solved with a method developed previously. The energy intervals between the S ₂ and S ₁ electronic levels of the two main types of impurity centers formed by molecules of a given porphyrin in the crystal matrix are found to significantly differ from each other (～100 cm^?1). At the same time, the energies of the unperturbed vibrational states of the S ₁ electronic level partcipating in the resonance are very close to each other for these two types of impurity centers.     

Strong short-range magnetic order in a frustrated FCC lattice and its possible role in the iron structural transformation

The magnetic properties of a frustrated Heisenberg antiferromagnet with the fcc lattice and exchange interaction between the nearest (J ₁) and next-to-nearest (J ₂) neighbors are studied in this work. For the collinear phase with the wave vector Q= (π,π,π), the equations of the self-consistent spin-wave theory are obtained and solved numerically for the sublattice magnetization and the averaged short-range order parameter. The dependence of the Néel temperatureT _N on the ratio J ₂/J ₁ is found. It is shown that, in the case of a sufficiently strong frustration, strong short-range magnetic order persists over a wide temperature range above T _N. The possible application of this result to the mechanism of structural phase transition from α-Fe to γ-Fe is considered.     

Photon motion in Kerr–de Sitter spacetimes

We study the general motion of photons in the Kerr–de Sitter black-hole and naked singularity spacetimes. The motion is governed by the impact parameters X, related to the axial symmetry of the spacetime, and q, related to its hidden symmetry. Appropriate ‘effective potentials’ governing the latitudinal and radial motion are introduced and their behavior is examined by the ‘Chinese boxes’ technique giving regions allowed for the motion in terms of the impact parameters. Restrictions on the impact parameters X and q are established in dependence on the spacetime parameters \(M, \Lambda , a\). The motion can be of orbital type (crossing the equatorial plane, \(q>0\)) and vortical type (tied above or below the equatorial plane, \(q<0\)). It is shown that for negative values of q, the reality conditions imposed on the latitudinal motion yield stronger constraints on the parameter X than that following from the reality condition of the radial motion, excluding the existence of vortical motion of constant radius. The properties of the spherical photon orbits of the orbital type are determined and used along with the properties of the effective potentials as criteria of classification of the KdS spacetimes according to the properties of the motion of the photon.     

Neutral Particle Motion around a Schwarzschild Black Hole in Modified Gravity

We investigate circular motion of neutral test particles on equatorial plane near a black hole in scalar-tensor-vector gravity. We consider three cases (i) α < G/G_N (ii) α = G/G_N and (iii) α > G/G_N to find the regions where motion can exist. The corresponding effective potential, energy, angular momentum and center of mass energy are evaluated. Further, we define four different cases for α > G/G_N and identify stable and unstable regions of circular orbits. It is found that circular orbits having zero angular momentum exist at r = αGNM due to repulsive gravity effects. We conclude that the structure of stable regions for α < G/G_N as well as α = G/G_N case is completely different from that of α > G/G_N.     

The analysis of the densities of <Emphasis Type="Italic">s</Emphasis>-wave neutron resonances separated with respect to spin

The density ratio of s-wave neutron resonances z=ρ(J₁)/ρ(J₂) was analyzed on the basis of the experimental data for 22 atomic nuclei and the Gilbert-Cameron formula for ρ(J). Here, J₁=I_x—1/2 and J₂=I_x+1/2, where I_x denotes the spin of the target nucleus in the ground state. Our aim was to verify whether the factor η(I_x), as a multiplier, can be applied in the expression describing ρ(J₁), with the assumption that ρ(J₂) values remain unchanged, or whether the factor 1η(I_x) can be applied, as a multiplier with ρ(J₂), while the ρ(J₁) values remain unchanged. The final conclusions, e.g., the confirmation or the negation of the fact that it may be necessary to apply the η(I_x) factor, depend on the values of “real” errors Δz of the z variable, which can be calculated if the optimal values of Δρ(J₁) and Δρ(J₂) are known.     

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.     

Bestimmung von Moleküleigenschaften des Tl205F19 aus kombinierten Stark-Zeeman-Effekt-Messungen mit der Molekularstrahlmethode

An electric Molecular-Beam-Resonance-Spectrometer has been used to measure simultanously the Zeeman- and Starkeffect splitting of the hyperfinestructure of TlF. Electric fourpole lenses served as focusing and refocusing fields of the spectrometer. A homogenous magnetic field (Zeeman-Field) was superimposed to the electric field (Stark-Field) in the transition region of the apparatus. The observedΔm _J =±1 -transitions were induced electrically. Completely resolved spectra of Tl²⁰⁵F¹⁹ in theJ=1 rotational, andυ=0 vibrational state have been measured. The obtained quantities are: The rotational magnetic momentμ _J of Tl²⁰⁵F¹⁹ in the stateJ=1,υ=0, and the difference of the magnetic shielding (σ _1,±1?σ _1,0) of both nuclei as well as the difference of the molecular susceptibility (ξ _1,±1?ξ _1,0) in the states (J, m _J)=(1,±1) and (J, m_J)=(1, 0). The sign of the rotational magnetic moment could be determined unambigously by the influence of offdiagonal matrix elements. The numerical values for Tl²⁰⁵F¹⁹ in the stateJ=1 andυ=0 are:μ _J =?29,153(21) · 10^?6 μ _Bohr (σ _1,±1?σ _1,0)^Tl=?0,002291 (33) (σ _1,±1?σ _1,0)^F=?0,000206(9) (ξ _1,±1-ξ _1,0)=+3,02(15) · 10^?30erg/Gauß² The quantities in brackets are root-mean-square deviations in units of the last digit. From these data and the known values for the spin-rotational interaction constants a number of expressions are derived which characterise the electronic charge distribution in the molecule.     

Low-energy singlet sector in the spin-1/2 <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Heisenberg model on a square lattice

Based on a special variant of the plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of a spin-\(\frac{1}{2}\) Heisenberg antiferromagnet on a square lattice with nearest-heighbor and frustrating next-nearest-neighbor exchange couplings J ₁ and J ₂. It is well known that a nonmagnetic phase arises in this model for 0.4 ? J ₂/J ₁ ? 0.6, sandwiched by two Néel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J ₂ ≈ 0.64 J ₁ from the non-magnetic phase to the Néel one. A large gap (? 0.4J ₁) is found in the singlet spectrum for J ₂ < 0.64J ₁, which excludes a gapless spin-liquid state for 0.4 ? J ₂/J ₁ ? 0.6 and the deconfined quantum criticality scenario for the QPT to another Néel phase. We observe a first-order QPT at J ₂ ≈ 0.55J ₁, presumably between two nonmagnetic phases.