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.     

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.     

On the theory of elastic scattering of slow particles

A theory describing scattering of particles with low energy E from an arbitrary 3D potential is proposed. An exact expression is derived for the s scattering amplitude in the limit E → 0. Phenomenological constant κ appearing in the expression for the resonance scattering amplitude is expressed in terms of the parameters typical of the given potential.     

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.     

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.     

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.     

Theory of resonant forbidden Raman scattering in semiconductors

The Raman tensors for the electric field-induced and wavevector dependent scattering from LO phonons in semiconductors have been calculated near critical points using a perturbation treatment. The resulting expressions have analytic closed forms such that the dependence of the forbidden scattering intensity on the incident photon energy and the applied d.c. electric field can be evaluated from available energy band parameters. The forbidden LO scattering intensity of GaAs in the back scattering configuration has been numerically calculated near the e₁ and E₁ gaps as functions of the incident photon energy and the dc electric field. The result shows strong interference between the two scattering processes. The allowed TO and LO Raman scattering intensities of GaAs were also calculated at a wavelength of 1.06 μm from the SHG and Faust-Henry coefficients, and compared with the forbidden LO intensity.     

Dispersion of the acoustic phonon concerned with C66 of KD2PO4 observed by light scattering

we vector dependence of the light scattering spectra of DKDP is investigated for the scattering angles π/4, π/2 and 3π/4. Brillouin shift concerned with an elastic stiffness C₆₆ is obtained from the angular dependence of the quasi-longitudinal and quasi-transverse mode frequencies in the ab plane observed in the VV scattering. The results indicate that the phase velocity associated with C₆₆ decreases slightly near T_tr in the case of π/4 scattering, but does not in π/2 and 3π/4 scatterings.     

Amplitudes of multichannel scattering on a two-dimensional potential barrier with constant height

The immersing method is applied to solve the N-channel scattering problem for concrete potential. In particular, we consider the particle scattering on a two-dimensional potential barrier, which is constant in the scattering direction and arbitrary in the cross-section direction. For this case the scattering amplitudes t _m and r _m (1,2, m= ...,N) are determined. A transition from the obtained formulas to the case of ?-potential is performed. For this case transmission amplitudes t _m and reflection amplitudes r _m are obtained. It is also shown that the product of transmission and reflection amplitudes along the channel m does not depend on the scattering channel.     

Form of the long-range potential observed in fast-neutron scattering by heavy nuclei

It is shown that the discrepancy between the results obtained for different neutron-energy ranges, when the neutron polarizability is derived from data on neutron scattering, can be removed if one assumes that a strong-interaction long-range potential of van der Waals (～r ^?6) or of Casimir and Polder (～r ^?7) is observed in fast-neutron scattering. This strong-interaction long-range potential possibly has some experimental confirmation in elastic pp scattering.     

High-spin states in 166Lu

It is shown that the discrepancy between the results obtained for different neutron energy ranges, when neutron polarizability is derived from the neutron scattering data, can be removed if one assumes that at the fast neutron scattering a strong-interaction long-range potential of Van der Waals (～ r ^?6 ) or Casimir-Polder (～ r ^?7 ) is observed. This strong-interaction long-range potential has possibly some experimental confirmation in the elastic p-p scattering.     

Theory of pion-nucleus scattering lengths

We calculate the scattering lengths for pions on light nuclei, in a multiple scattering theory given earlier. We include all effects through second order in the pion-nucleon scattering amplitudes, using a simple nuclear model. We show how to calculate the binding corrections (BC) consistently, and find large cancellations between differentBC terms. The resulting scattering lengths are smaller than those obtained from measurements of pi-atomic level shifts. The size of the difference is consistent with the contribution of pion absorption, which we estimate.     

Amplitudes of multichannel scattering on the barrier with a constant height in the scattering direction

The immersing method is applied to solve the N-channel scattering problem. In particular, we consider the particle scattering on a multidimensional potential barrier, which is constant in the scattering direction and arbitrary in the lateral direction. For this case the scattering amplitudes t _m and r _m (m = 1, 2, …, N) are determined. Transition from the obtained formulas to the case of thin potential is performed. For this case analytical expressions of transmission amplitudes t _m and reflection amplitudes r _m are obtained. We show that the product of transmission and reflection amplitudes in the channel m does not depend on the scattering channel. It is assumed that the scattering particle falls on the potential with the longitudinal wave vector k _l corresponding to the channel l.     

Improved theoretical pion-nucleus optical potentials

An approach which makes the first order pion-nucleus optical potential theoretically sound is presented. This study should permit higher order improvements to the potential to be more meaningful and the nuclear structure information extracted from pi-nucleus scattering to be more reliable. Based on multiple scattering theory, three optical potentials are constructed and studied in momentum space. These models are the popular Kisslinger potential, the local “Laplacian” potential, and an “improved off-shell potential;” the latter one is derived from absorptive separable pion-nucleon potentials which exactly reproduce on-shell πN scattering. By working in momentum space and explicitly including πN resonances and off-shell effects in the definition of the optical potential, the approach described here is capable of handling any number of pi-nucleon partial waves, is applicable over a very wide energy region, is based on a physical model for off-shell behavior, and is extended easily to include higher order effects. The optical potentials are inserted into two different relativistic wave equations to determine the total cross section and elastic differential cross section for pi-nucleus scattering. It is found that the various models for off-shell πN scattering determine significantly different πC¹² scattering, with the improved off-shell model preferred on theoretical grounds. Also discussed is the importance of properly transforming πN scattering to the pi-nucleus c.m. system, the origin of the shift in the peak position of the π^?C total cross section, and the reason for the increased diffractive nature of the differential cross section at 180 MeV.     

Temperature dependence of hole mobility in n-type InSb upon electron bombardment

The mobility of the minority carriers, in n-InSb was investigated from the photomagnetoelectric effect as a function of temperature in the range of 12–80 K prior to and after bombardment with 1 MeV average energy beta particles. The hole mobility shows a minimum near 40 K which can be due to the h-e scattering becoming predominant in the region where other scattering mechanisms are relatively weak. After bombardment the curves have the same form but higher mobilities. This is due to a decrease of h-e scattering resulting from the decrease of the electron concentration, as determined from independent measurements.     

Scattering of Hawking photons as a barrier to particle absorption by black holes

Electromagnetic scattering interactions between photons emanating from a Schwarzschild black hole and an incident charged particle should generate a repulsive force between the particle and black hole. The net scattering cross-section is calculated here as a function of the mass M of the black hole and the mass m of the particle for scenarios in which the particle is point-like and initially stationary, with proper energy ε=m, at some location far from the black hole. It follows from comparing the repulsive scattering force to the corresponding gravitational force that, in order for the particle to be drawn to the black hole, ε/Tbh must be greater than a certain lower bound that is of the order ¹⁰−3 for spin-1/2 or spin-0 particles with unit-charge. Although the scattering restriction is weaker than the requirement ε/Tbh?1 obtained independently from field-theoretic and thermodynamic treatments, the recurrence of a lower bound on the Boltzmann factor ε/Tbh in limitations on particle absorption suggests a physical unity whose nature is fundamentally thermodynamic.     

Approximate formula for second-order rayleigh scattering from N acoustical scatterers

A model of second-order multiple scattering from N Rayleigh acoustical scatterers distribted at random throughout a volume V is analyzed, physically motivated approximations being used. The result is a simple expression for the angular distribution of the total second-order Rayleigh scattered flux that is analogous to the usual formula for first-order scattering from N independent scatterers.     

Characteristics of potential-resonance elastic scattering of slow electrons by calcium atoms

The characteristics of elastic scattering of electrons by atomic systems are described by the potential resonance method in terms of the energy dependence of integral-type cross section S taken using a hypocycloidal electron spectrometer. The effect of ² D shape resonance on the run of the curve S(E) is demonstrated with scattering of slow (of energy no higher than 2 eV) electrons by calcium atoms. The energy and width of the resonance are derived from the extrema (minimum and maximum) of the experimental curve S(E). This dependence also serves to find the electron scattering differential cross sections. Two slightly differing scattering angles are taken into account. The differential cross sections derived from the experimental data qualitatively agree with theoretical results, albeit being somewhat lower.     

High energy proton-carbon scattering in the alpha-particle model

We investigate elastic and inelastic 0⁺–2⁺ high energy proton-¹²C scattering in the alpha-particle model. We use a rigid equilateral triangle nuclear wave function with a Gaussian dispersion function allowing theα-particles of the¹²C-nucleus to deviate from their most probable positions at the triangle vertices. Expressions for the differential scattering cross sections are deduced using Glauber multiple diffraction theory. Thus we need thep?α-particle scattering amplitude, which is calculated from a Gaussian nucleon-nucleon profile function. Numerical calculations show that the model reproduces the experimental results onp?α andp-¹²C scattering.     

Large-angle scattering of heavy ions: (I). General structure of elastic cross section

Closed-form expressions are derived for the differential cross section of elastic heavy-ion scattering at large angles. The derivation is based on the general form of the elastic partial-wave S-matrix in real l-space. By a generalization of analytic techniques developed in earlier work, it is shown that the large-angle scattering cross section has a universal structure involving combinations of Bessel functions and the Fourier transforms of the rapidly varying parts of the S-matrix, irrespective of their dynamical origin. Anomalous large-angle scattering is attributed to deviations of the S-matrix from its “normal strong-absorption profile”, and general conditions for backward-angle enhancement are given. Our model-independent formulation provides the framework for an “inductive” method of analyzing experimental angular distributions and excitation functions aimed at identifying, as uniquely as possible, the dynamical mechanisms that operate in large-angle heavy-ion scattering. Extensions of the formalism to inelastic scattering and transfer reactions, and applications of the analytic method, will be described in subsequent papers.