Impulse-approximation correction in pion-nucleus optical potential

The local density approximation is used in this paper to calculate the first-order pion-nucleus optical potential. TheπN scattering matrix in nuclear medium is computed by employing separableπN scattering matrix. This nuclear-mediumπN scattering matrix, which includes impulse-approximation correction is then used to construct the pion-nucleus optical potential.π-¹²C elastic scattering results obtained by using this potential are compared with the impulse-approximation potential results.     

The study of πd scattering in the (3, 3) resonance region on the basis of three-body relativistic equations

The πd scattering in the (3, 3) resonance region is studied on the basis of three-body relativistic equations. The differential and integral cross sections for the πd scattering are calculated with the use of πN collision matrices defined by fitting phase shifts up to 300 MeV on the one hand, and, alternatively, by the solution of the inverse πN scattering problem on the other. It is shown that (i) the effect of taking fully into account relativistic pion kinematics is of the same order as the multiple scattering effect, (ii) the πd scattering is rather sensitive to the off-shell behaviour of the πN scattering matrix and (iii) the main contribution from the multiple scattering to the cross sections comes from the terms with NN rescattering. A comparison with some experimental data is carried out.     

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.     

On normalization of scattering matrices of polarized radiation

The condition of normalization of scattering matrix is derived when the polarized radiation is described by the Stokes parameters I, Q, U, V. The normalization of the matrix is based on energy conservation. It has a probabilistic meaning also. When the scattering particle is nonspherical, scattered radiation may depend not only on the angle between incident and scattered radiation but on orientation of the scattering plane also. In these cases, the known change of the Stokes parameters Q, U of the incident radiation with respect to various scattering planes influences the normalization. The derived normalization includes all elements of the first line of scattering matrix and the characteristics of polarization of the incident radiation. Dependence on this polarization is appeared because the polarization influences intensities of scattered radiation and, therefore, is included in energy conservation. The routine normalization includes the first element of the scattering matrix only. These two normalizations determine the different normalizing constants of the scattering matrix. The simple computational example of scattering by the particle that has the shape of a finite cylinder is considered. This example shows that the values of normalizing constants of the routine normalization may considerably differ from the ones of the obtained normalization. The results of the study may be useful in various investigations of radiation scattering, especially in the cases when the scattering particles are nonspherical.     

Elastic scattering of electrons by europium and ytterbium atoms

The method of relativistic optical potential is applied to studying elastic scattering of electrons by europium and ytterbium atoms in a wide range of collision energies up to 2 keV. The angular dependences of the scattering differential cross sections and the energy dependences of the scattering integral (total, elastic, momentum transfer, and viscosity) cross sections are calculated in both spin-polarized and spin-unpolarized approximations. It is shown that the spin-polarized approximation should be used to calculate the scattering cross sections at energies below 10 eV for a europium atom. The low-energy scattering of an electron by a europium atom is characterized by P-, D-, and F-wave shape resonances. For an ytterbium atom, the calculated cross sections are in good agreement with available experimental data and with those obtained by calculation in terms of the relativistic convergent close-coupling method.     

Multiple quark scattering and the changing slope of dσ/dt in the small \t\ region

The changing slope of dσ/dt at small \t\ observed in the CERN-ISR p-p scattering data can be reproduced in the Glauber multiple quark scattering model by a quark-quark scattering amplitude that is an undamped rapidly oscillating function of momentum transferred to the quark.     

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.     

Microscopic calculation of low-energy deuteron-deuteron scattering on the basis of the cluster-reduction method

The cluster-reduction method is used to solve numerically the differential equations for the s-wave Yakubovsky components characterizing the nnpp system in the S=2 spin state. Elastic deuteron-deuteron scattering is analyzed for the case where nucleon-nucleon interaction is simulated by the MT I–III potentials. Effective equations describing the relative motion of clusters is derived. The scattering length and phase shifts for low-energy deuteron-deuteron scattering are calculated.     

Scattering times in AlGaN/GaN two-dimensional electron gas from magnetotransport measurements

The various scattering times of two-dimensional electron gas were investigated in modulation-doped Al_0.22Ga_0.78N/GaN quantum wells by means of magnetotransport measurements. The ratio of transport and quantum scattering times, τ_t/τ_q∼1, shows that the dominant mobility-limiting mechanisms are short-range scattering potentials. The low-field magnetoresistance shows the weak antilocalization and localization phenomenon from which the spin-orbit scattering and inelastic scattering times are obtained. The inelastic scattering time is found to follow the T⁻¹ law, indicating that electron-electron scattering with small energy transfer is the dominant inelastic process.     

High temperature superconductivity in the mixed state and the dynamics of charge carriers

A model to calculate the temperature and magnetic field dependence of the scattering time τ_ν(H, T) of quasiparticles by bound electron states in a vortex in high-temperature superconductors is proposed. In this model, the hydrodynamic interaction of a moving gas of quasiparticles with the discrete states of the vortex velocity field is regarded as quasielastic scattering and the resulting scattering time of quasiparticles is different from scattering of individual vortices. The normalized scattering time was found to decrease exponentially with increasing temperature. This behavior is due to the suppression of the amplitude of the superconducting order parameter as the temperature increases. This model accounts for the observed temperature and field dependence of the scattering time particularly at low-field regime.     

Relationship between cross section and matrix normalization of polarized radiation scattering

A simple relationship between the total scattering cross section and the normalizing constant of the scattering matrix for the general case of an arbitrary scattering particle and elliptically polarized incident radiation is obtained. The polarized radiation is described by the Stokes parameters I, Q, U, V. The obtained relationship is a consequence of two forms of energy conservation. The first one is in terms of the total scattering cross section. The other one involves the normalizing constant of the scattering matrix. The obtained relationship contains dimensionless integrals of the radiation scattered over all directions of scattering. The integrals depend on the elements of the first row of the scattering matrix and on the relative values of the Stokes parameters of the incident radiation. In the case of cross section, the incident radiation is assumed to be a plane wave. In the case of normalization constant, the incident radiation is assumed to be a convergent beam. The possible dependence of the scattering integrals on specificities of the particle illumination is taken into account in the obtained relationship. The relationship may be helpful in the various cases. So, the relationship allows one to determine any of the two characteristics of the scattering process under investigation, cross section or normalizing constant, via the other one. The relationship can be used for obtaining the scattering integrals and for analyzing the influence of the incident radiation polarization on cross section and normalizing constant.     

Resonant multiphonon Raman scattering in AgBr

Resonant Raman scattering in AgBr single crystals is studied at low temperatures. Excitation in resonance with the indirectΓ — L exciton as intermediate state gives rise to selectively enhanced narrow two-phonon Raman scattering. The phonons involved are pairs ofLA andTO phonons of opposite wavevectors near theL-point. A simple model involving one discrete exciton level is developed to explain the resonance behaviour. The temperature dependence of the scattered intensity, that is studied for 1.8 K <T < 35 K, can consistently be interpreted within this model as being due to the lifetime of the intermediate state. Assuming that the excitons predominantly decay by one-phonon scattering with long wavelength acoustical phonons the predicted temperature dependence of the intensity is found in good agreement with the experimental result. Additional scattering peaks are believed to be due to third-order processes involving an acousticalX-phonon in addition to theL-phonons of the second-order scattering. Using an oriented sample the resonant Raman peaks are found to be polarized.     

Unitary amplitudes with cut-plane analyticity from given scattering data

We continue the study of constructing the scattering amplitude for scalar particles from elastic scattering data at a given energy. Here we require the scattering amplitude, f (z), to be analytic in a suitably cut z-plane; (z is the cosine of the scattering angle). We find that, in the elastic domain, the unitarity constraint is satisfied by a continuum of amplitudes, all corresponding to the same elastic scattering data. This continuum ambiguity in determination of f (z), which was noted earlier in formulations based on a smaller domain on analyticity, is associated with lack of knowledge of the contribution to unitarity from inelastic channels. We discuss the problem of incorporating smooth energy dependence in the determination of the scattering amplitude over some range of energy, and show that, under certain restrictions on the scattering data, there is a continuum of amplitudes having smooth energy dependence.     

Measurement of np and pp asymmetry with an accelerated polarized deuteron beam from 725 to 1000 MeV per nucleon

The accelerated polarized deuteron beam of Saturn II was used to measure the analyzing power for np elastic scattering at five energies. The left-right asymmetries ε = (L + R)/(L + R) for np and for pp elastic scattering were measured simultaneously by CH₂? carbon subtraction using one of the beam-line polarimeters. The analyzing power A_00n0(np) is given by the ratio ε_np^d/ε_pp^d multiplied by the known analyzing power for pp elastic scattering. Experimental evidence is consistent with the underlying assumption that in the kinetmatic region of the experiment the ratio of the np to pp analyzing powers for scattering of quasifree nucleons in deuterons is the same as for scattering of free neutrons and protons, respectively.     

N-point functions and low-energy scattering by N centres

The scattering of a low-energy particle by a potential of a small range is known to be described satisfactorily by the s-wave alone. In the present paper we give a method of describing low-energy scattering by N potentials with the aid of N waves. For this purpose, a special system of Laplacian eigenfunctions is suggested. The scattering amplitude depends on only N parameters, irrespective of overlapping of potentials. The physical significance of these parameters δ_λ, λ=1,2,…N, is shown by exp (2iδ_λ)=S_λ where S_λ is the eigenvalue of the S matrix. The parameters δ_λ may be obtained by direct methods and perturbation theory.The low-energy scattering by an arbitrary configuration of N centres is discussed. The differential cross-section is averaged over all orientations of the configuration and radially about the direct beam, giving it as a function of the scattering angle. This formula may be used for the phase shift analysis.     

Electromagnetic scattering as a radiation reaction problem

Electromagnetic scattering is treated as a dynamical problem, by equating the external torque exerted by the incident wave on the sphere to the self torque due to the radiated (scattered) wave. ForI _mech=0,our scattering amplitude is equal to the usualP-wave amplitude of the electromagnetic scattering on an infinitely conducting sphere. The poles of the scattering amplitude, in particular their dependence onI _mech, are studied. For example, a pole on the positive imaginary axis, which usually corresponds to a bound state, corresponds to a runaway solution in our case. Non-decaying resonances are also discussed.     

N-soliton quantum scattering in the sine-Gordon theory

The quantum treatment of soliton scattering in the sine-Gordon model, using the path integral collective coordinate method is generalized to N solitons. The solitions. The first quantum correction to the phase shift of N-soliton scattering is equal to the zero-point energy of an effective multi-soliton Hamiltonian. The energies of the oscillators of this Hamiltonian are shown to be equal to the stability angles of a complete set of solutions of the Schrödinger equation for small fluctuations around a classical N-soliton. Consequently, calculating the fluctuations and their stability angles by the inverse scattering method, we obtain the energies of the oscillators. The first quantum correction to the phase shift (the O(1) part in a development in powers of γ) is evaluated by summing the stability angles. This result is in agreement with the “exact” scattering amplitude conjectured by Faddeev, Kulish and Korepin.     

Electron scattering in CdxHg1−xTe

Experimental studies of the electron mobility in Cdinx,Hgin1?xTe/0x/0.33, 10¹⁵ cm^?3n10¹⁸ cm^?3, 4.2 K ?T ?300 K/and of the thermoelectric power of intrinsic HgTe from 300 K down to 5 K are reported. These results are interpreted in terms of calculations based on the variational solution of the Boltzmann equation. Analysis shows that in pure samples at low temperatures, the electron mobility is limited by ionized donors, heavy holes, and, in some cases, unresolved defect scattering. In the doped samples with x0&#x0306;.1, disorder scattering also becomes significant. Polar-optical phonon scattering is dominant at high temperatures. The sharp decrease of mobility in the region 20–40 K, which occurs for pure samples with x0&#x030C;.14, is explained by interband optical phonon scattering. The thermoelectric power of intrinsic HgTe is strongly affected by phonon-drag of holes at low temperatures and by electron-electron scattering at high temperatures.     

Electron scattering and transport phenomena in small-gap zinc-blende semiconductors

We give expressions for electrical conductivity, thermoelectric power and thermal conductivity of conduction band electrons in small-gap zinc-blende semiconductors, obtained by solving the Boltzmann equation by a variational procedure. The term resulting from the phonon-drag is included in the Boltzmann equation. The following electron scattering mechanisms are investigated: inter and intraband scattering by optical phonons via polar and nonpolar interactions, scattering by charged centers (ionized defects and heavy holes) and by neutral centers, as well as scattering by acoustic phonons. Particular attention is paid to the screening of the electron-optical phonon polar interaction by free carriers, which is particularly important in the case of a linear energy band. The formula for the intraband RPA dielectric function for the case of the linear band is given.The general formulation of all the problems investigated permits direct application of the results given in this paper to both intrinsic or n-type HgTe-type and InSb-type semiconductors, including mixed crystals, e.g. Cd_xHg_1?xSe near the cross point.     

Elastic scattering of slow electrons by calcium atoms into an angular range depending on the collision energy

The use of trochoidal and hypocycloidal spectrometers that are applied in modern experimental techniques for studying processes of electron scattering by atoms, ions, and surfaces is considered in some detail. The angular range of the collection of scattered electrons is determined by the operation mode of the spectrometer and depends on the collision energy. To analyze the structure of the measured energy dependence S(E), an analytical formalism reflecting both resonance and nonresonance features of low-energy scattering was used. A theoretical analysis of elastic scattering of slow (to 2 eV) electrons by Ca atoms permitted the interpretation of the observed structure of S(E) as a manifestation of the ² D shape resonance. A comparison of the theoretical values of the S(E) function with the total and differential scattering cross sections was performed.