Acoustic scattering of a high-order Bessel beam by an elastic sphere

The exact analytical solution for the scattering of a generalized (or “hollow”) acoustic Bessel beam in water by an elastic sphere centered on the beam is presented. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis and the half-conical angle of the wave vector components of the generalized Bessel beam. The sphere is assumed to have isotropic elastic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The transverse acoustic scattering field is investigated versus the dimensionless parameter ka(k is the wave vector, a radius of the sphere) as well as the polar angle θ for a specific dimensionless frequency and half-cone angle β. For higher-order generalized beams, the acoustic scattering vanishes in the backward (θ = π) and forward (θ = 0) directions along the beam axis. Moreover it is possible to suppress the excitation of certain resonances of an elastic sphere by appropriate selection of the generalized Bessel beam parameters.     

Spin-flip scattering effect on the current-induced spin torque in ferromagnet–insulator–ferromagnet tunnel junctions

We have investigated the current-induced spin transfer torque of a ferromagnet–insulator–ferromagnet tunnel junction by taking the spin-flip scatterings into account. It is found that the spin-flip scattering can induce an additional spin torque, enhancing the maximum of the spin torque and giving rise to an angular shift compared to the case when the spin-flip scatterings are neglected. The effects of the molecular fields of the left and right ferromagnets on the spin torque are also studied. It is found that τ^Rx/I_e (τ^Rx is the spin-transfer torque acting on the right ferromagnet and I_e is the tunneling electrical current) does vary with the molecular fields. At two certain angles, τ^Rx/I_e is independent of the molecular field of the right ferromagnet, resulting in two crossing points in the curve of τ^Rx/I_e versus the relevant orientation for different molecular fields.     

Acoustic beam interaction with a rigid sphere: The case of a first-order non-diffracting Bessel trigonometric beam

Mathematical expressions for the acoustic scattering, instantaneous (linear), and time-averaged (nonlinear) forces resulting from the interaction of a new type of Bessel beam, termed here a first-order non-diffracting Bessel trigonometric beam (FOBTB) with a sphere, are derived. The beam is termed “trigonometric” because of the dependence of its phase on the cosine function. The FOBTB is regarded as a superposition of two equi-amplitude first-order Bessel vortex (helicoidal) beams having a unit positive and negative order (known also as topological charge), respectively. The FOBTB is non-diffracting, possesses an axial null, a geometric phase, and has an azimuthal phase that depends on cos(?±?₀), where ?₀ is an initial arbitrary phase angle. Beam rotation around its wave propagation axis can be achieved by varying ?₀. The 3D directivity patterns are computed, and the resulting modifications of the scattering are illustrated for a rigid sphere centered on the beam's axis and immersed in water. Moreover, the backward and forward acoustic scattering by a sphere vanish for all frequencies. The present paper will shed light on the novel scattering properties of an acoustical FOBTB by a sphere that may be useful in particle manipulation and entrapment, non-destructive/medical imaging, and may be extended to other potentially useful applications in optics and electromagnetism.     

Scattering of Mathieu beams by a rigid sphere

Based on the recent results on the scattering of Bessel beams by a sphere and using the Whittaker integral, the scattering by a rigid sphere centred on a Mathieu beam is derived. The scattering field is expressed as a partial wave series involving the scattering angles relative to the beam axis and Mathieu beam parameters. Some numerical calculations are performed and it is shown that the illumination of a rigid sphere by a Mathieu beam produces asymmetrical scattering as a function of scattering angles θ and ?. The geometrical properties of the scattering Mathieu beam are noted.     

Analisis of inelastic scattering of π-mesons from nuclei within the microscopic optical potential

Cross sections of inelastic scattering of π-mesons from Si, Ni, and Pb nuclei at energy T _lab = 291 MeV are calculated using the distorted wave approximation. The microscopic direct and transition optical potentials are determined by specifying the pion-nucleon scattering amplitude and the nuclear density distribution, where we use the in-medium πN amplitude parameters obtained earlier by analyzing the elastic scattering data for the same nuclei. The cross sections are calculated on the basis of the relativistic wave equation. The deformation parameters of the nuclei are obtained by comparing inelastic scattering cross sections with the appropriate experimental data.     

Tensor interaction in heavy-ion scattering: (II). Partial-wave expansions

The turning-point-model relations between components of rank-2 tensor analysing power in polarized heavy-ion scattering, which were derived semi-classically in our previous work, are re-derived quantum-mechanically without resorting to any classical concept. Using partial-wave expansions of the scattering amplitudes, the turning-point-model relation is reduced to a relation between the diagonal and off-diagonal components of the tensor scattering amplitude for each type of tensor interaction (T_R, T_P and T_L). Numerical investigations and analytical investigations using a plane-wave expansion method show that these relations arise from universal features of heavy-ion scattering: large angular momenta and the short-range nature of the tensor potentials. An interrelation between the three types of tensor interaction is also obtained for each partial wave.     

Temperature dependence of the rho-meson mass and width

It is shown, to leading order in the virial expansion, that unitarity of the ππ scattering amplitude implies that if the ρ-meson widthΓ _ρ(T) increases with temperature, then the ρ-meson massM _ρ(T) must also increase. The temperature dependence ofM _ρ(T) is explicitly obtained from a simple, but physically motivated, parametrization of theI=J=1 ππ scattering amplitude.     

Exact solution of a model for πd induced reactions and its application to pion-nucleus reactions

Reduction techniques are applied to πd elastic scattering and π-absorption in a theory without anti-nucleons. In a one-pion approximation we derive two sets of exact coupled-channel equations for respectively the amplitudes T_πd,NN, T_{Nδ, NN} and T_{πd, πd}, T_{d, NΔ}- Alternatively we express in terms of the absorption amplitude T_{πd, NN} available solutions for a three-body problem restricted to the πd and NΔ channels. We explicitly demonstrate that our model (which comes close to the one of Thomas, Mizutani and Koltun) strictly respects the Pauli principle and avoids double-counting. Using the same technique we determine amplitudes for the (π, 2N) reaction and for π (in)elastic scattering on general nuclei in terms of amplitudes amongst the NN, NNπ channels. Both the elastic amplitude and the πA optical potential are shown to decompose into a multiple scattering part based on an input πN amplitude without the P₁₁ partial wave and calculable absorption corrections.     

Excitation of states of medium-mass nuclei in the region of giant resonances in inelastic deuteron scattering

Results are presented that were obtained by measuring a continuum in the inelastic scattering of 37-MeV deuterons on ¹²C, ⁴⁸Ti, and ^58,64Ni nuclei in the angular range 16° ≤ θ ≤ 61°. Broad excitation maxima are found for deuteron scattering angles in the range θ ≤ 21°. The region of a broad maximum includes giant resonances of target nuclei, whose levels are excited quite readily at E _d = 37 MeV. Summation of the inelastic-scattering cross sections over all final states of the excited| nucleus and the use of completeness of the wave functions for these states make it possible to express the total cross section for inelastic (incoherent) deuteron scattering only in terms of the wave functions for the ground state of the target nucleus. The corresponding quasielastic-scattering amplitude is taken in the diffraction approximation. Nucleon correlations in the target nucleus are disregarded. Upon disregarding a small contribution of multiple quasielastic scattering at small scattering angles, the cross section for incoherent deuteron scattering is represented approximately as the product of known factors—the square of the absolute value of the amplitude for diffractive quasielastic scattering and the effective number of target nucleons scattering deuterons. The results of these calculations agree qualitatively with experimental data.     

Partial differential cross section of inelastic magnetic neutron scattering in the paramagnetic phase of LaCoO3

The partial differential cross section of inelastic magnetic neutron scattering from the compound LaCoO₃ in the paramagnetic phase is studied theoretically. The contribution to scattering from the high-spin state of an ion in zero magnetic field and the modification of this contribution upon application of a magnetic field are calculated using the effective Hamiltonian for the ⁵ D term. The amplitude of the peak in the dependence of the scattering cross section on the energy of scattered neutrons, which corresponds to the transition from the low-spin to the intermediate-spin state, is estimated.     

Model calculations forI=0 andI=2S-wave pion-pion scattering

Several simple models for theS-waves in isospinI=0 andI=2 pion-pion scattering are constructed. These models are based on unitarity, analyticity in the complexq-plane (q=c.o.m. momentum), approximate crossing symmetry, and the assumption that the forces acting in theS-waves are mainly due to exchange ofρ-mesons,fmesons and a strongI=0S-wave. These models contain between one and three parameters, which are being used to obtain a best fit to Walker'sI=0 data. Our best fits are associated with anI=0 scattering lengtha ₀=0.53 μ^?1. Having fixed the parameters from theI=0 data, predictions are obtained for theI=2S-wave. Our predictions are generally characterized by a very small positiveI=2 scattering lengtha ₂? 0.08 μ^?1 and a zero of the phase shift just above threshold, at a total c.o.m. energy of 320 to 360 MeV. The cause for this behaviour is shown to be the strongS-wave in the crossedI=0 channels. Various reasons are discussed, why we might expect this zero to occur at somewhat larger or at smaller energies, even below threshold. Although because of the crudeness of these models the significance of our results is mainly qualitative, certain internal contradictions in the Walker data seem to be indicated.     

Electron mean free path and conduction-band density of states in solid argon

In this paper, we apply a theoretical model developed by Plenkiewicz et al. for analyzing the current I_t transmitted by an ultrathin dielectric film as a function of incident electron energy E for solid argon. The analysis of I_t(E) in the elastic scattering region (0–12 eV) allows one to determine the electronic conduction-band density of states and to calculate the electron scattering mean free path as a function of energy. Comparison of our results with various solid argon band structure calculations is also presented.     

Analysis of elastic scattering of pi-mesons by nuclei within the microscopic optical potential

The microscopic pion-nucleus optical potential defined by the pion-nucleon scattering amplitude and the density distribution function of the target nucleus is applied to obtain the differential cross section of the elastic pion-nucleus scattering based on the solution to the relativistic wave equation. This allow one to account for effects of the relativization and distortion by the potential field. Data on π^±-meson scattering on ²⁸Si, ⁵⁸Ni, and ²⁰⁸Pb nuclei at T _lab = 291 MeV are analyzed and the parameters of the in-medium πN-amplitude are obtained. The parameters are compared with similar parameters for scattering on free nucleons.     

Shift of the Bragg position in grazing-incidence diffraction

The intensity distribution in grazing-incidence diffraction along the grazing exit angle, a f, has been generally studied assuming the fulfilment of the Bragg condition, both experimentally and theoretically. We consider deviations of the incidence angle and detector position (θ) from the exact Bragg angle, θ _B, as well as variation of the incidence angle with respect to the surface, α _i, and lattice mismatching of layered structures. The so-called surface peak is caused by refraction and appears at the fixed angular position of the critical angle of the total external reflection, α _c. Beside it an additional peak occurs, that is explained by fulfilling the Bragg condition of the lateral wave vector components of incident and diffracted beams. This corresponds to the intersection of the truncation rod and the Ewald sphere. Therefore its angular position in the diffracted scattering fan depends on both α_i and θ ? θ _B. This additional peak is only visible if α _i is below α _C or θ > θ _B. These considerations have been verified experimentally on an InP layer.     

Angular momentum and the electromagnetic top

The electric charge–magnetic dipole interaction is considered. If Γ_em is the electromagnetic and Γ_mech the mechanical angular momentum, the conservation law for the total angular momentum Γ_tot holds: Γ_tot=Γ_em+Γ_mech= const., but when the dipole moment varies with time, Γ_mech is not conserved. We show that the non-conserved Γ_mech of such a macroscopic isolated system might be experimentally observable. With advanced technology, the strength of the interaction hints to the possibility of novel applications for gyroscopes, such as the electromagnetic top.     

Electron mean free path and conduction-band density-of-states in solid methane as determined from low-energy electron transmission experiments

Recently, Plenkiewicz et al. developed a theoretical model for analyzing the current I_t transmitted by a thin dielectric film as a function of incident electron energy E. The purpose of this paper is to apply this model to the analysis of recent I_t(E) results for solid methane. The analysis permits the determination of both the electron mean free path as a function of energy and the electronic conduction-band density-of-states in the quasi-elastic scattering region. The differences between our results and Kunz's solid methane band structure calculations are also discussed.     

Scattering from a penetrable sphere at short wavelengths

A scalar plane wave incident on a penetrable sphere is considered in the short wavelength limit. A new representation of the scattering amplitude is introduced which is particularly appropriate in this limit, and which requires only the evaluation of certain integrals. Some of these may be evaluated asymptotically by the method of steepest descent and lead to the geometrical optics field contribution. Included in this is the bow field. The remainder of the integrals are evaluated by the method of residues and lead to the diffracted field contribution. This “diffracted ray” field is known from recent investigations in diffraction theory. An essential part of the analysis is the introduction of the parameter p, the number of internal refractions that a ray which hits the sphere undergoes. The results obtained are all in agreement with that which would be expected on the basis of geometrical diffraction theory.     

Variational methods in radiative transfer problems

An efficient variational-iterative method is applied to the problem of diffuse reflection by a plane-parallel inhomogeneous atmosphere with isotropic scattering. The emergent intensity I(τ = 0; μ, μ₀) with μ = μ₀ corresponds to the maximum of an associated functional. It is, however, shown that I(τ = 0; μ, μ₀) computed by the variational method alone has relatively large errors when μ ≠ μ₀. Such deficiencies are removed by a combined variational-iterative method. The interdependence of the iterative and variational methods is also investigated. They are shown to play a complementary role to each other. The proper choice of trial functions is emphasized in light of computational efficiency and flexibility. Two distinct classes of trial functions: the polynomials, and the step functions are investigated as possible choices of trial functions. The latter choice is shown to be far more efficient in computation. Numerical results for both approximate emergent intensities and source functions are presented and found to be in good agreement with the exact solutions. Simple analytic two-step function approximations of the source function and intensities are also presented for the case of a two-layer inhomogeneous model.     

Analysis of the methods proposed for computing the scattering of atoms from a hard corrugated surface model of He/LiF (001)

It appears that the scattering of atoms on crystal surfaces is accounted for by a corrugated infinite wall model of the surface. To determine the “corrugation function” which represents best the experimental scattering intensities, it is necessary to choose among many possible versions, the simplest and most effective computational method of the theoretical scattering amplitudes. It is the purpose of this paper to analyze the relative merits of three particular versions which we call HDM, NHM and GR, and which are described in section 3. This comparison is carried out on the He/LiF(001) system for variable incident wave vector (k) and orientation (θ_i) as well as a number of Fourier components (ζ_G) used to describe the “corrugation function”. We conclude that the GR method presents advantages over the other two: (i) it reduces the computer time necessary for the HDM and NHM methods, (ii) converges and computes to within 10^?4 in unitarity the scattering amplitudes in a larger range of energies as well as angular and corrugation parameters, and (iii) it presents a great simplicity and the corrugation is very handy. The size of that range depends on the computer facilities used. In our case, the GR method works for any calculation in which kC₀ < 9 and $\text{C}{}_0\text{< 0.35}\text{A}\text{?}$ (where k is the incident wave vector and C₀ twice the amplitude of the corrugation). These characteristics prove to make the GR method a good tool for the study of surface crystallography by parametrization of the surface corrugation.     

Physical pion-pion partial-wave equations based on three channel crossing symmetry

We present a set of closed systems of partial-wave equations for pion-pion scattering valid for ?28 m_π² ? s ? 125.31 m_π². These equations give the real part of a given partial-wave amplitude in terms of scattering lengths and a convergent series of integrals over the physical values of the absorptive parts of all partial waves. Our equations are extensions of relations previously derived from fixed-t dispersion relations. The new equations are rigorous consequences of axiomatic analyticity and three channel crossing symmetry. As an application, the effect of the f⁰-meson on the I = O S-wave is evaluated.