Lorentzian Form Research Articles

Neutron scattering intensity of isotropic Heisenberg ferromagnets for T ⩾ Tc

In a large part of the critical region the commonly used double Lorentzian form for the neutron scattering intensity S( q, ω) of an isotropic ferromagnet is inadequate. Based on a renormalization group calculation for a Heisenberg system an expression for S( q, ω) is presented, which agrees with neutron scattering results.

Hilbert-space formulation of Feshbach-Fano methods for atomic and molecular photoionization: Optimal choice of zeroth-order states in shape-resonance channels

An explicit Hilbert-space formulation is provided of Feshbach-Fano methods for ionization continua employing a novel zeroth-order state particularly well suited to shape-resonance profiles. The resulting photoionization cross sections are of Lorentzian form, with shifts and widths that are generally slowly varying functions of the energy. Fano q and ϱ parameters are avoided entirely in the development. Applications to a model problem having broad and narrow shape resonances indicate that precise crosssectional values can be obtained in this way from Stieltjes calculations employing L 2 pseudo spectra that have energy spacings considerably greater than the resonance width. The advantages of the zeroth-order state introduced here in applications to molecular ionization continua are also indicated.

Experimental synthesis of phase-diffusing optical fields

Techniques are described for synthesizing a statistically well-characterized radio-frequency noise spectrum and imposing this noise spectrum on a well-stabilized laser beam by means of extracavity phase and frequency modulation. The basis of the noise spectrum is the Gaussian noise-voltage spectrum derived from shot noise. The Gaussian property is carefully preserved at every step, ensuring that correlation functions to all orders can be represented in terms of the lowest-order correlation function, which, in turn, is the Fourier transform of the power spectrum, according to the Wiener–Khintchine theorem. The power spectrum can be measured and controlled, in a range that has Lorentzian and Gaussian forms as limiting cases, by controlling the bandwidth and amplitude of the noise voltage at the source. The objective of this methodology is the definitive experimental study of nonlinear-optical absorption processes, all such processes requiring knowledge of higher-order correlation functions for complete definition.

A 29-root soluble model for the nonlinear calculation of a four-body propagator

The time-independent mean-field theory of collisions is applied to the collision of four one-dimensional particles. Their two-body interactions are taken as separable, with Lorentzian form factors. This allows completely analytical solutions. A unique and satisfactory physical branch emerges out of 29 candidate solutions. It is very stable when the strength of the interaction is modified.

Space-time ‘bonds’, electromagnetism and graphs

By assuming familiar relational properties of local, stratified space-time measurements and using simple graphs symmetries, the laws of electromagnetism follow in their relativistic, four-dimensional form without invoking Lorentz transformations. This suggests that the topological compactification of pregeometric space-time points may be achieved through the laws of electromagnetism. The results are in agreement with those obtained using Lorentz transformations, spinors and forms.

Relativistic impulse approximation description of polarized proton elastic scattering from polarized 13C.

The elastic scattering of intermediate energy polarized protons from polarized /sup 13/C is studied within the framework of the relativistic distorted wave Born approximation using the relativistic impulse approximation to describe the projectile--target nucleon interaction. Sensitivities of observables to (1) the upper and lower components of the valence nucleon wave function, (2) the Lorentz form of the two-body interaction, (3) isoscalar three-vector currents, and (4) the individual strengths of the separate Lorentz terms in the two-body interaction are calculated and discussed. The bound state wave functions for the 1p/sub 1/2 valence neutron used in the calculations are taken from relativistic mean field theory and from traditional, nonrelativistic Woods-Saxon eigenstate solutions. Predictions obtained using either pseudoscalar or pseudovector projectile-nucleon coupling forms are compared. Possible effects on the p-arrow-right+/sup 13/C-arrow-right polarized target spin observables due to contributions of the core nucleons to the effective isoscalar three-vector current are discussed and investigated using a simple model. What can be learned from normal (i.e., perpendicular to scattering plane) and transverse (i.e., approximately perpendicular to beam, in the scattering plane) polarized target spin observables, as well as unpolarized p-arrow-right+/sup 13/C elastic scattering observables are discussed. The results suggest that new nuclear structure information, additional effectivemore » interaction phenomenology, and further constraints on the Lorentz character of the effective two-body interaction can in principle be obtained from analyses of p-arrow-right+/sup 13/C-arrow-right elastic scattering data. Experiments to obtain such data are encouraged« less

Incoherent quasi-elastic neutron scattering in a Ni35Ti65-H metallic glass hydride

The incoherent quasi-elastic neutron scattering from hydrogen absorbed in the Ni35Ti65 metallic glass has been measured. The linewidths of the spectra at momentum transfers less than 0.83 AA-1 are found to be compatible with earlier measurements of the nuclear magnetic dipolar relaxation rate, if the classic model of hopping diffusion is assumed for the motion of the hydrogen atoms. The combination of these measurements gives a value of 2.5 AA for the average jump length. At larger momentum transfers the lines depart from the Lorentzian form. The possibility that this indicates a distribution of jump rate is discussed.

Paramagnetic neutron scattering from an amorphous Fe 80Cr 5B 15 alloy

The spin dynamics of the amorphous ferromagnet Fe 80Cr 5B 15 has been investigated by means of inelastic neutron scattering. The Lorentzian form of the neutron scattering cross section describes the data above T C well. In the range of momentum transfers 0.02 Å -1< q<0.15 Å -1 the half-width of the quasielastic scattering varies as q 5 2 at T= T c. The inverse correlation length changes with temperature as (0.36±0.02) ϵ 0.73±0.02, where ϵ=( T- T C. The dynamical scaling function is found to differ quantitatively from the dynamical scaling function calculated by Résibois and Piette.

Experimental study of the critical scattering from a two-dimensional random Ising antiferromagnet.

The magnetic critical fluctuations in the d = 2 random-exchange antiferromagnet Rb/sub 2/Co/sub 0.7/Mg/sub 0.3/F/sub 4/ have been studied by neutron diffraction at temperatures both above and below the Neel temperature T/sub N/ = 40.8 K. At temperatures above T/sub N/, the line shape of the critical scattering is well described by the Lorentzian form, and the critical exponents ..nu.. and ..gamma.. for the inverse correlation length kappa/sup +/ = kappa/sub 0//sup +/chemically bondtchemically bond/sup ..nu../ and the staggered susceptibility chi/sup +/ = C/sub 0//sup +/chemically bondtchemically bond/sup -//sup ..gamma../ are in good agreement with the values for the pure d = 2 Ising model.

Neutron scattering study of the spin ordering in amorphous Tb45Fe55 and Tb25Fe75

Small-angle neutron scattering measurements (SANS) have been made on Tb45Fe55 and Tb25Fe75 as a function of temperature. The SANS results show that long-range ferromagnetic order is quenched in these alloys and is replaced by a spin-glass-like state. For T&amp;gt;Tc, where Tc is the transition temperature, both samples exhibit a conventional Lorentzian line shape (in q), but they depart from this form below Tc. We have fitted the low-temperature line shapes with the Lorentzian plus Lorentzian-squared form appropriate for random field systems. As the temperature of the Tb45Fe55 alloy is lowered, the correlation length ξ rises to a rounded maximum of about 80 Å at 250 K (Tc =298 K) and decreases to about 60 Å at 5 K. In contrast, ξ in the Tb25Fe75 alloy exhibits a cusplike form reaching a resolution limited value between 400 and 410 K before declining slowly to 55 Å at low T. In both alloys the coefficient of the Lorentzian term rises sharply as T→0, whereas the Lorentzian-squared coefficient follows approximately the square of the order parameter divided by the correlation length. Both systems thus lend support to the suppression of long-range order by the random anisotropy field.

Anisotropic spin fluctuations in the itinerant-electron ferromagnet MnP

The paramagnetic scattering cross section of the anisotropic metallic ferromagnet MnP has been measured up to the zone boundaries along the [100] and [010] directions perpendicular to the easy magnetization axis. The spectral shape functions in both directions are well fitted to a Lorentzian form at T=TC (290.5 K), 1.03TC, and 1.20TC except those close to the zone boundaries. Near TC the linewidth along [010] follows the dynamical scaling prediction for the isotropic ferromagnet Γ(q)∝q2.5. On the contrary, a unique q dependence, Γ(q)∝q3.2, along [100] was observed. However, these q dependencies deviate at small q(q&amp;lt;0.1 A−1 along [100] and q&amp;lt;0.02 A−1 along [010]), suggesting the existence of a residual linewidth of Γ0∼0.02 meV at q=0.

Kinetic theory of binary gas mixtures with large mass disparity

The Boltzmann equations for a binary mixture of gases are considered in the asymptotic limit when their molecular weight ratio and the light gas Knudsen number are small quantities. A first mass-ratio expansion reduces the cross-collision operator of the light gas Boltzmann equation to a Lorentz form, uncoupling its kinetic behavior from that of the heavy gas. The light gas distribution function is then determined to first order in the Knudsen number, independently of the degree of nonequilibrium characterizing the heavy gas, whose influence is felt only through its hydrodynamic quantities. All transport coefficients arising are determined variationally for arbitrary interaction potentials using Sonine polynomial expansions as trial functions. A remarkable feature of this analysis is that it yields binary transport information (i.e., diffusion and thermal diffusion coefficients) from considering only the Boltzmann equation for the light gas. A second mass expansion reduces the cross-collision operator of the heavy gas equation to a Fokker–Planck form. The corresponding coefficients involve integrals over the light gas distribution function determined previously and are evaluated explicitly in terms of the hydrodynamic quantities and transport coefficients of the light gas. The heavy gas distribution function can be determined by solving a Fokker–Planck equation at dilutions large enough to make heavy–heavy collisions negligible, or by a new Knudsen number expansion when the molar fraction of the heavy gas is of order 1. In this latter case, the heavy gas kinetic behavior is independent of the light gas, being characterized by the same transport coefficients of the pure heavy gas. The problem is then reduced to a set of two-fluid hydrodynamic equations.

Operational concepts and the transformation laws of space-time co-ordinates in arbitrary dispersive media

The concept of operational parameters is discussed. Operational parameters are compared with extrinsic or hidden variables. It is shown that, by applying Einstein’s synchronization conventions, the transformation properties of operational space and time parameters depend on the dispersion (energy momentum) relation of the system. In particular, with nonlinear forces acting in a medium, transformation laws need not necessarily be of the Lorentz form.

Technique of surface-wave scattering and calibration with simple liquids

Heterodyne detection of light scattered from capillary waves is used to study the surface properties of the air–liquid interface. A diffraction grating is employed to select a precise ripplon wave vector k and to provide a stable local oscillator field. The optics are designed to form a real image of the grating on the surface, thus allowing the measurements to be reproducible within 5%. The power spectrum detected in frequency domain is well fitted by a Lorentzian profile for the range of ripplon wave vectors 260≤k≤390 cm−1. The shape of the scattered spectra at each wave vector is corrected for the incident beam profile by effecting a convolution of the Lorentzian and Gaussian functional forms. The surface tensions and the kinematic viscosities of water, anisole, and ethanol are deduced from the ripplon dispersion relation corrected to the first order in damping, and found to be within 5% of the literature values. Thus we confirm the validity of approximations made for the instrumental function and the dispersion relation.

Effects of random field interactions in amorphous rare earth alloys

Recent neutron small angle scattering studies have shown that amorphous alloys of non S-state rare earth elements with Fe are not ferrimagnetic as inferred from magnetization data, but rather exhibit a spin-glass type of order. The data show no divergence in the spin correlation length below T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , and the gradual evolution of the scattering lineshape from Lorentzian to a Lorentzian plus Lorentzian squared form appropriate for a system in which random fields destroy the long range order. SANS data taken in applied fields indicate the formation of an infinite cluster in low fields which is responsible for the ferrimagnetic magnetization response and which co-exists with increasingly smaller residual clusters.

Collective modes in simple liquids: A semiempirical model.

A semiempirical model for the dynamical structure factor, S(Q,\ensuremath{\omega}), in a simple liquid is presented. This is a modification of the Lorentzian form predicted by linear hydrodynamics that enable it to be extended into the viscoelastic region while still retaining finite moments. The model leads directly to a criterion for the existence of a sound mode which includes the possibility of soft modes and dispersion gaps. By a suitable choice of parameters the experimental results for liquid Ar and molten Rb may be explained.

The structure of gauge and gravitational anomalies

It is shown how the form of the gauge and gravitational anomalies in quantum field theories may be derived from classical index theorems. The gravitational anomaly in both Einstein and Lorentz form is considered and their equivalence is exhibited. The formalism of gauge and gravitational theories is reviewed using the language of differential geometry, and notions from the theory of characteristic classes necessary for understanding the classical index theorems are introduced. The treatment of known topological results includes a pedagogical derivation of the Wess-Zumino effective Lagrangian in arbitrary even dimension. The relation between various forms of the anomaly present in the literature is also clarified.

Spin stiffness anomaly in the reentrant spin-glass (Fe0.25Ni0.75)0.75P0.16B0.06Al0.03

Low field magnetization measurements have shown that the amorphous alloy (Fe0.25Ni0.75)0.75P0.16B0.06Al0.03 becomes a demagnetization-limited ferromagnet below a Curie temperature Tc of 200 K, but that the spontaneous magnetization vanishes again below a reentrant temperature TR of 4 K. Inelastic neutron scattering measurements have been performed to study the spin-wave dynamics as the spin-glass state is entered from the ferromagnetic state. The observed spin-wave peak positions decrease in energy and the linewidths increase as the temperature is lowered towards TR. A detailed analysis based on both the double Lorentzian and damped harmonic oscillator forms of the spectral weight function shows that the spin-wave energies strongly decrease as the temperature is lowered and the excitations become heavily damped over the range of wave vectors (0.04 Å−1&amp;lt;q&amp;lt;0.18 Å−1) studied. An elastic component of the magnetic scattering, attributed to a spin-glass order parameter, is also observed.

Light Scattering From a Nematic Liquid Crystal in the Presence of an Electric Field

Abstract The intensity and spectrum of light scattered by a nematic liquid crystal of positive dielectric anisotropy (5CB) in the presence of an ac squarewave electric field have been measured. The results for the twist-bend mode agree well with the theory developed by the Orsay Group and lead to satisfactory values for elastic and viscous coefficients. The results for the splay-bend mode, however, do not, showing a strong dependence on the frequency of the applied field, with scattering no longer of Lor-entzian form. In an attempt to explain the above we examine appropriate solutions of the continuum equations including both conduction and flexoelectric effects. In line with our experimental results, it turns out that neither of these complications affects the twist-bend mode, but that both contribute to the splay-bend mode, although the influence of llexoelectricity is likely to be small. However, conduction can significantly alter the splay-bend mode, there being the possibility of a more complex behav...

Influence of collisions of atoms with walls of a storage chamber on the emission frequency of a hydrogen maser

An investigation is made of the gain profile of a maser utilizing transitions between hyperfine components of the energy levels of the hydrogen atom in a storage chamber. It is shown that deviations of the gain profile from the Lorentzian form appear at a frequency stability level of ~10−15 and they give rise to dependences of the transition frequency in the maser on the shape of the storage chamber as well as on the field configuration in the resonator.