Spherical magnetic multipole moments system of currents

Concepts of spherical magnetic multipoles that represent distributions of electric currents over a spherical surface are introduced. Vector potentials of magnetic multipoles meet solenoidal- and harmonic-field conditions outside of the spherical surface and are continuous on it. Within the sphere, the vector potential of currents flowing outside of it is represented by the sum of vector potentials of basis magnetic multipoles with coefficients expressed by spherical multipole moments of system of currents. This expansion of the vector potential is in many respects analogous to the multipole expansion known from electrostatics. The first three terms of the expansion represent components of the well-known magnetic moment, the next five terms represent components of the magnetic quadrupole moment, etc. Possible applications of the magnetic spherical multipole technique are discussed. Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 66–72, October, 1999.     

Vacuum Nodes and Anomalies in Quantum Theories

We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple geometric terms. We analyse in detail two different archetypical systems: i) the planar rotor with a non-trivial magnetic flux Φ and ii) the Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any reflection invariant potential V is encoded in the nodal structure of the unique vacuum for θ=π. In the second case we prove that the nodes of the first Landau level for unit magnetic charge appear at the crossing of the two non-contractible circles α₋, β₋ with holonomies h _α-(A)=h _β-(A)=−1 for any reflection invariant potential V. This property illustrates the geometric origin of the quantum translation anomaly. Received: 6 April 1999 / Accepted: 21 October 2000     

On the behaviour of Er3+ ion in tetragonal crystalline field

Crystal field parameters for ErGaG and Er³⁺ YAlG and used to compute the temperature dependence of Schottky specific heat, paramagnetic susceptibility, magnetic anisotropy,μ _eff and quadrupole splitting in the range 10–400 K. The hyperfine interaction parametersA andB for¹⁶⁶Er and¹⁶⁷Er in both the systems are also obtained and in turn used to estimate the nuclear specific heat contribution. The studied parameters compare well with the available experimental results.     

Higher multipole polarizabilities of hadrons from compton scattering amplitudes

Starting with partial wave projections of the Compton scattering invariant amplitudes free of kinematical singularities or zeros, generalized electric and magnetic multipole polarizabilities of spin-0 and $\text{spin}\text{-}\text{1}\text{2}$ hadrons are introduced as threshold limits of the non-Born parts of the corresponding electric and magnetic Compton multipoles. These objects, which enter the higher low-energy theorems for elastic γ-hadron scattering, are shown to be acceptable quantum field theoretical generalizations of the usual static multipolar polarizabilities encountered in classical electrodynamics or non-relativistic quantum mechanics. Using the analyticity properties of the amplitudes, sum rules for the generalized electric and magnetic quadrupole polarizabilities of the proton and the pions are written down and evaluated numerically within the two-particle unitarity approximation.     

Intrinsic <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">K</Emphasis></Subscript> factors of odd-mass <Superscript>167–179</Superscript>Lu isotopes

In this paper, g _K -factors of the intrinsic magnetic moments and effective spin gyromagnetic factors (g _s^eff) of the ^167–179Lu isotopes have been studied within the Tamm-Dancoff approximation (TDA) (Kuliev et al, Sov. J. Nucl. Phys. 9, 185 (1969)) by using a realistic potential such as Woods-Saxon potential for the first time. The effects of the spin-spin and spin-isospin interactions on magnetic moments were investigated. The results of the theoretical calculations are compared with the experimental data for related nuclei. The experimental values of g _K and g _s^eff were computed from the observed magnetic moments (Georg et al, Eur. Phys. J. A3, 225 (1998)) using the spin matrix elements. The theoretical predictions for the g _K factors exhibit good agreement with the experimental g _K factors with increasing mass number A of the lutetium isotopes. The strongest influence of the neutron-proton spin interaction occurs at q = −1. Sufficient agreement between the calculated and the experimental values of g _K is obtained for κ = (45/A) MeV and q = −1.     

Electric multipole interaction of pairs in solids: Ce in LaCl3

The electric multipole interaction (EMI) is studied in general for the case of two rare earth (RE) ions interacting in host crystals possessing C_3h symmetry at the ion sites. The particular case of Ce³⁺ substituted for La³⁺ in LaCl₃ is used as an example. The splitting of two degenerate levels of such a system is studied as an application of elementary group theory, and a notation is proposed for the resulting levels. The angular dependence of the splitting due to the first term of the EMI, namely, the electric quadrupole-quadrupole interaction (EQQ), is obtained for one of the levels of the system under consideration. The ground quartet is studied for the nearest neighbor configuration (nn), and all of the multipoles in the expansion for EMI are kept. The shielding effects, which are very important in this problem, are assumed to depend on one parameter. This makes possible the study of the variation of the splittings with respect to such a parameter. The importance of terms beyond the quadrupole is brought out.     

Äquivalente Operatoren der Wechselwirkung zwischen Atomen und elektromagnetischem Feld

As well-known the dynamical interaction theory of molecules or atoms with the electromagnetic field may be based alternatively on one of two HAMILTON ians, ^IH or ^IIH. where the vector potential appears in the interaction term of ^IH while this of ^IIH is expressed in terms of the electric and the magnetic field strength coupled to atomic multipoles. Using a calculus of transversal functional derivation with respect to a vector function we show that we can go from ^IH to ^IIH by a comperatively simple canonical transformation which may be interpreted within the classical theory as well as within as the quantized theory. The equivalence of both HAMILTON ians is lost if, as customary in quantum optics, only a few atomic levels are taken into account. We give a plausible argument that in this case the multipole HAMILTON ian ^IIH is more suitable.     

Anomalies in orientation interaction of slow neutrons with nuclei and the problem of neutron molecule existence

Based on the Dirac equation, the features of long-range electromagnetic orientational interaction of slow neutrons with even-even and even-odd nuclei are considered. This interaction is controlled by a narrow potential barrier arranged beyond the nucleus. The barrier height is U _tot = 20–40 eV and depends on Z, A, and the nucleus magnetic moment μ_nucl. The barrier formation is associated with the ponderomotive nonlinear interaction of the anomalous neutron moment with the nucleus electric field. The barrier transparency for thermal neutrons is D(E) ≈ 0.8–0.95. For cold neutrons, the barrier transparency and their reaction cross sections with nuclei sharply decrease and, at E → 0, their cross sections tend toward zero. It was shown that the combined effect of the magnetic dipole-dipole and ponderomotive interaction of the neutron and even-odd nucleus results in the formation of removed symmetrically positioned potential wells for neutrons beyond the nucleus. The presence of these wells results in the possible existence of short-lived or virtual nucleus-neutron molecules and the “neutron halo” effect beyond the nucleus.     

Three-dimensional Gross-Neveu model under the condition of Lorentz invariance violation

A 3-D Gross-Neveu model with Lorentz-violating term b _μ is studied. The effective potential V _eff with a real or imaginary Lorentz-violating term b _μ is calculated. The gap equation is obtained and the influence of the presence of an additional term b _μ on the symmetry of the theory is examined.     

Relaxation of a quadrupolar nucleus in a strong magnetic field

Longitudinal relaxation of spin systems (S = 1, 3/2, 3) containing isolated quadrupolar nuclei are studied. The characteristic features of the relaxation behavior are identified in strong magnetic fields in the presence of chemical shift anisotropy. Two mechanisms are established that favor involvement of high rank multipoles in the relaxation process: an autocorrelation mechanism and a cross correlation mechanism. Multipoles of odd rank are involved in the relaxation of nuclei with spin S > 1 as a result of the autocorrelation mechanism (in this case, due to quadrupole interactions). The cross correlation mechanism, due to correlations between the chemical shift anisotropy and the quadrupole interactions, favors the appearance of multipoles of even rank. Expressions are presented for the multipole cross relaxation and longitudinal relaxation rates for spin systems with S = 1, 3/2, 3. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 1, pp. 18–25, January–February, 2006.     

Investigation of Hyperfine Interactions in GdNiIn Compound

Perturbed gamma–gamma angular correlation technique was used to measure the hyperfine interactions in the compound GdNiIn using the ¹¹¹InCd → and ¹⁴⁰La¹⁴⁰Ce probe nuclei at the In and Gd sites, respectively. A unique quadrupole frequency with asymmetry parameter η = 0.78 was observed for ¹¹¹Cd probe at In sites for the measurements above Curie temperature. Below T _C , the spectra for ¹¹¹Cd show combined magnetic dipole and electric quadrupole interaction. Below 85 K, a unique magnetic interaction is observed at ¹⁴⁰Ce. A linear relationship between the saturated magnetic hyperfine field and the magnetic transition temperature was observed for both probes, indicating that the main contribution to the mhf comes from the conduction electron polarization.     

Theory of birefringence of sound in easy-plane rhombohedral antiferromagnets with inclusion of hexagonal anisotropy and mechanical stresses

The constructed thermodynamic theory of magnetic birefringence of transverse sound in easyplane weak ferromagnets with an axial basal anisotropy induced by boundary conditions has been generalized to the case of additional inclusion of the hexagonal anisotropy enhanced by isotropic mechanical stresses. The magnetoelastic contribution ΔC _a to the effective elastic modulus C ₄₄^eff = C ₄₄ + ΔC _a , which determines the phase velocity of the magnetic mode of the acoustic wave in a crystal, has been calculated. It has been shown that the induced anisotropy with the twofold and sixfold symmetry leads to the appearance of an additional anisotropic term of the fourfold symmetry in the contribution ΔC _a . The developed theory has made it possible to satisfactorily describe the existing experiments.     

Zn-doping effect on the energy barrier to magnetization reversal in superparamagnetic nickel ferrite nanoparticles

Measurements of ac-susceptibility and dc-magnetization were carried out on samples of Ni_1-xZn_xFe₂O₄ nanoparticles (x=0, 0.25, 0.5, 0.75) with average diameters 〈D〉≈7 nm. Values of the superparamagnetic blocking temperature T̄_B were obtained from the characteristic temperature behavior of the imaginary susceptibility χ_imag. An Arrhenius-type law, which accurately describes the relationship between the observation time τ_obs and the blocking temperature, was used to determine the effective energy barrier to magnetization reversal U_eff. A Zn-content dependence of the energy barrier is observed, where U_eff changes little for 0≤x≤0.25, it peaks at x=0.5, and decreases back upon further Zn-doping. The large increase of U_eff at x=0.5 is attributed to an enhanced magnetic anisotropy induced by the crossover between two spatial arrangements of spins in the A and B sub-lattices of the ferrimagnetic inverse spinel. PACS 75.50.Bb; 75.50.Gg; 75.30.Et     

General multipole expansion of polarization observables in deuteron electrodisintegration

Formal expressions are derived for the multipole expansion of the structure functions of a general polarization observable of exclusive electrodisintegration of the deuteron using a longitudinally polarized beam and/or an oriented target. This allows one to exhibit explicitly the angular dependence of the structure functions by expanding them in terms of the small rotation matrices d ^j _m'm(θ), whose coefficients are given in terms of the electromagnetic multipole matrix elements. Furthermore, explicit expressions for the coefficients of the angular distributions of the differential cross-section including multipoles up to L _max = 3 are listed in tabular form. Received: 19 November 2002 / Accepted: 7 May 2002     

Corrections to the Casimir–Polder potential arising from electric octupole coupling

ABSTRACT

Molecular QED theory is employed to derive a generalised formula for the dispersion potential between two molecules with mixed electric multipole polarisability tensors of arbitrary order at each centre. This expression is used to readily extract the pair energy shift between an electric dipole polarisable molecule and a mixed electric dipole–octupole polarisable one, and that between two mixed electric dipole–octupole polarisable species. This is done to see whether these interaction energies give rise to higher-order corrections to the Casimir–Polder potential, as was found in the previously calculated case of the dispersion energy shift between an electric dipole polarisable molecule and an electric octupole polarisable one. Interestingly, for orientationally averaged species, both of the computed interaction energies are independent of the octupole weight-3 term, are retarded, and may be interpreted as higher-order corrections in the fine structure constant to the leading dipole–dipole dispersion potential.     

中红外色散平坦硫系光子晶体光纤设计及性能研究

本文以自制Ge20Sb15Se65硫系玻璃为基质材料,设计一种正八边形结构色散平坦型中红外硫系光子晶体光纤,并采用多极法对其中红外色散和传输特性进行数值研究.结果表明:控制该光纤占空比(d/Λ)在0.323—0.367之间,其色散及传输特性在3—5μm范围内可调.当孔间距Λ=3.4μm,孔直径d=1.1μm时,光纤在4.1—4.9μm波段的色散值在0.8—0.8 ps·nm 1·km 1波动,且具备单模低损耗传输(Loss0.049dB/m),小模场面积(Aeff8.46μm2)特性,适合于中红外非线性应用领域.     

Formation of a quasi-uniform sequence of vortices in a periodically modulated finite-length Josephson contact

The configurations of currents and the profile of a magnetic field penetrating into a finite-length contact at I < I _C are calculated. The computational method is based on analyzing the continuous variation of the current structure leading to a decrease in the Gibbs potential. Such an approach makes it possible to find a configuration that sets in when an external field slightly exceeds H _max and trace the evolution of this configuration with increasing field. It is shown that at H > H _max boundary structures turn into quasi-uniform sequences of vortices the spacing between which oscillates about a mean value decreasing with increasing H. At some values of H, vortices with a number of fluxoids Φ₀ larger by unity start penetrating into the contact in the form of boundary sequences. As the field grows, they produce quasi-uniform sequences, etc. Vortices with the number of fluxoids Φ₀ differing by more than unity can fall into the contact at no field. The penetration of vortices with (k + 1)Φ₀ into a contact each cell of which contains kΦ₀ is fully identical to the penetration of vortices with one Φ₀ into the Meissner configuration. This statement is supported by the almost strict periodicity of mean induction b in the contact versus external field h dependence with a period of 1 along both axes and also by the form of the dependences of the magnetic field in the cells on the cell-boundary distance.     

Elastic charge density representation of the interaction via the nematic director field

The interaction between particle-like sources of the nematic director distortions (e.g., colloids, point defects, macromolecules in nematic emulsions) allows for a useful analogy with the electrostatic multipole interaction between charged bodies. In this paper we develop this analogy to the level corresponding to the charge density and consider the general status of the pairwise approach to the nematic emulsions with finite-size colloids. It is shown that the elastic analog of the surface electric charge density is represented by the two transverse director components on the surface imposing the director distortions. The elastic multipoles of a particle are expressed as integrals over the charge density distribution on this surface. Because of the difference between the scalar electrostatics and vector nematostatics, the number of elastic multipoles of each order is doubled compared to that in the electrostatics: there are two elastic charges, two vectors of dipole moments, two quadrupolar tensors, and so on. The two-component elastic charge is expressed via the vector of external mechanical torque applied on the particle. As a result, the elastic Coulomb-like coupling between two particles is found to be proportional to the scalar product of the two external torques and does not directly depend on the particles' form and anchoring. The real-space Green function method is used to develop the pairwise approach to nematic emulsions and determine its form and restrictions. The pairwise potentials are obtained in the familiar form, but, in contrast to the electrostatics, they describe the interaction between pairs (dyads) of the elastic multipole moments. The multipole moments are shown to be uniquely determined by the single-particle director field, unperturbed by other particles. The pairwise approximation is applicable only in the leading order in the small ratio particle size-to-interparticle distance as the next order contains irreducible three-body terms.     

Low-field magnetic response of multi-junction superconducting quantum interference devices

The magnetic states of multi-junction superconducting quantum interference device containing 2N identical conventional Josephson junctions are studied by means of a perturbation analysis of the non-linear first-order ordinary differential equations governing the dynamics of the Josephson junctions in these devices. In the zero-voltage state, persistent currents are calculated in terms of the externally applied magnetic flux Φ_ex . The resulting d.c. susceptibility curves show that paramagnetic and diamagnetic states are present, depending on the value of Φ_ex . The stability of these states is qualitatively studied by means of the effective potential notion for the system.     

Evidence for strong Coulomb correlations in the metallic phase of vanadium dioxide

The influence of Coulomb correlations on magnetic and spectral properties in the metallic rutile phase of vanadium dioxide is studied by state of the art LDA + DMFT method. Calculation results in strongly correlated metallic state with an effective mass renormalization m*/m ≈ 2. Uniform magnetic susceptibility shows Curie-Weiss temperature dependence with effective magnetic moment, p _eff^theor = 1.54μ_B, in a good agreement with the experimental value p _eff^exp = 1.53μ_B that is close to ideal value for V⁴⁺ ion with the spin S = 1/2, p _eff = 1.73μ_B. Calculated spectral function shows well developed Hubbard bands observable in the recent experimental photoemission spectra. We conclude that VO₂ in rutile phase is strongly correlated metal with local magnetic moments formed by vanadium d-electrons.