Coulomb correction to Delbrück scattering investigated atZ=94

Differential cross sections for the elastic scattering of 2.754 MeV photons by Pu were measured for angles ranging from 45 to 120° and interpreted in terms of Delbrück, nuclear Thomson, Rayleigh and nuclear resonance scattering. It is shown that the largest part of the discrepancy between experiment and the lowest-order Delbrück theory can be removed by introducing a (Zα)⁴-dependent Coulomb correction term. Evidence is obtained for additional Coulomb correction terms of higher order in (Z α).     

Delbrück scattering

The various calculations of the Delbrück scattering amplitude are presented. This is followed by some generalities on the elastic scattering of photons by heavy atoms and finally by a review of the experiments together with a comparison with the calculations.     

Elastic scattering of 2.754 MeV photons by Ta and interference between Rayleigh,Thomson and Delbrück scattering

Differential cross sections for the elastic scattering of 2.754 MeV photons by Ta have been measured for angles ranging from 30° to 150°. A comparison with lowest-order Delbrück theory reveals discrepancies of the same size as previously observed for Pb and Bi. Consideration is given to interference phenomena between Delbrück, Rayleigh and nuclear Thomson scattering.     

Delbrück scattering of 2.75 MeV photons by uranium

Elastic differential scattering cross sections from U were measured at 2.75 MeV photon energy and compared with the predictions of lowest-order Delbrück theory. Evidence for the effect of multi-photon exchange is obtained.     

Nonperturbative Time-Independent Green Function of Matrix Schrödinger Equation. General Formalism and Quasiclassical Representation

A Green function of time-independent multichannel Schrödinger equation is considered in matrix representation beyond a perturbation theory. Nonperturbative Green functions are obtained through the regular in zero and at infinity solutions of the multichannel Schrödinger equation for different cases of symmetry of the full Hamiltonian. The spectral expansions for the nonperturbative Green functions are obtained in simple form through multichannel wave functions. The developed approach is applied to obtain simple analytic equations for the Green functions and transition matrix elements for compound multipotential system within quasiclassical approximation. The limits of strong and weak interchannel interactions are studied.Alexander I. Pegarkov:On leave from Physics Faculty     

Experimental aspects of synchrotron-Čerenkov radiation

Various features of synchrotron-?erenkov radiation are illustrated in the context of the following situations: (1) The passage of high energy electrons through gases, liquids, solids, and plasmas in the presence of magnetic fields. (2) The suppression of synchrotron X-rays from high energy electrons in the earth's atmosphere and extraterrestrial environs. (3) The detection of the real part of the Delbrück scattering amplitude. (4) Vacuum polarization effects on radiation by ultra-high energy electrons in intense magnetic fields. (5) Synchrotron-?erenkov radiation by charged particles heavier than electrons.     

Delbrück scattering of 2.754 MeV photons by Bi and Th

Differential cross sections for the elastic scattering of 2.754 MeV photons by Bi and Th have been measured for angles ranging from 60° to 120°. The results deviate from the predictions of lowest-order Delbrück theory by factors between 1.1 and 1.4. The strong increase of these deviations with charge number, previously reported for Pb and U, has been confirmed. An interpretation in terms of the effect of the Coulomb correction is given.     

Azimuthal asymmetry in processes of nonlinear QED for linearly polarized photon

Cross sections of nonlinear QED processes (photon-photon scattering, photon splitting in a Coulomb field, and Delbrück scattering) are considered for linearly polarized initial photon. The cross sections have sizeable azimuthal asymmetry.     

Delbrück scattering of 2754 keV photons by Nd,Ce, I,Sn, Mo and Zn

The elastic scattering of 2754 keV photons has been investigated for charge numbers Z between 30 and 92. The lowest-order Delbrück theory was found valid for small Z. A Coulomb correction term proportional to (Zα)⁴ fits the experimental data with few exceptions.     

Elastic scattering of 1.17 and 1.33 MeV gamma rays by molybdenum,tantalum and lead

Elastic scattering cross-sections of lead, tantalum and molybdenum were determined with the help of a Ge (Li) detector for 1.17 and 1.33 MeV rays between 30° and 115°. Theoretical evaluations of the cross-sections are based on a coherent addition of the well-known nuclear Thomson scattering amplitudes, the Rayleigh amplitudes calculated by Kissel and Pratt and the Delbrück amplitudes given by Papatzacos and Mork. The fairly good agreement between experiment and theory reveals the importance of the real Delbrück amplitudes. However, the experimental results in the 30–60° range tend to lie slightly but systematically below the calculated cross-sections. Work supported in part by a grant from the National Bureau of Standards, Washington, DC under the SFCP programme.     

Small-angle scattering in a Reissner-Nordstrem field. Quasiclassical approximation

Phases, amplitude and differential cross section of charged particle scattering by a Reissner-Nordstrem black hole are obtained for small scattering angles in a quasiclassical approximation of the Klein-Gordon equation. The approximation is legitimate in the shortwave case, where the situation is considered when the Coulomb and gravitational effects are commensurate in magnitude. It is shown that for relativistic particles the angular scattering distribution differs from the Rutherford distribution in terms ^–3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 33–37, July, 1988.     

The comparison between the Mie theory and the Rayleigh approximation to calculate the EM scattering by partially charged sand

The Mie theory and Rayleigh approximation are two basic methods to study the EM scattering of uncharged spherical particle, and when the particle radius is much smaller than the incident wavelength, they are equivalent, but whether the Rayleigh approximation is still equivalent to Mie theory when we use them to calculate the EM scattering of small charged particle, there is still no any report published to discuss this problem. In this paper we make some comparisons between Mie theory and Rayleigh approximation to solve the EM scattering of partially electrification spherical particles. The results showed that the Mie theory would be more suitable to calculate the scattering of charged spherical particles.     

Delbrück scattering of 9 MeV photons from tantalum

The differential elastic scattering cross section of 9.0 MeV photons by ¹⁸¹Ta has been measured at angles between 25° and 140° and a good agreement was obtained between the measured and predicted values at θ = 35–90°. In calculating the theoretical cross sections the coherent scattering contributions of nuclear Thomson (NT), nuclear resonance (NR) and Delbrück (D) amplitudes were included while that of Rayleigh (R) scattering was excluded. The D-amplitudes were taken from a recent calculation by Mork and Papatzacos. Evidence for the contribution of the real D-amplitude is obtained.     

Elastic and Raman scattering of 8.5–11.4 MeV photons from 175Lu and 181Ta

Differential cross sections for elastic and inelastic Raman scattering from ¹⁷⁵Lu and ¹⁸¹Ta were measured. Five photon energies between 8.5 and 11.4 MeV were used and were obtained from the (n, γ) reaction on Ni and Cr using thermal neutrons. The results are compared with calculations using a modified simple rotator model (SRM) of the giant dipole resonance (GDR) in which the effect of Delbrück scattering was incorporated. In general, fair agreement between theory and experiment is obtained. A new set of GDR parameters is extracted, based on photon scattering data and, as expected, yield better agreement between experimental and predicted cross sections.     

Elastic and Raman scattering of 8.5–11.4 MeV photons from 159Tb, 165Ho and 237Np

Differential cross sections for elastic and inelastic Raman scattering from the deformed heavy nuclei ¹⁵⁹Tb, ¹⁶⁵Ho and ²³⁷Np were measured at five energies between 8.5 and 11.4 MeV. Angular distributions at four angles between 90° and 140° for both elastic and inelastic scattering at 9.0 and 11.4 MeV were also measured. The monoenergetic photons were obtained from thermal neutron capture in Ni and Cr. All the angular distributions and the elastic and Raman scattering at the higher energies are in good overall agreement with theoretical predictions. The theory is based on a modified simple rotator model of the giant dipole resonance in which the effect of Delbrück scattering was included. A trend of both the elastic and Raman scattering at lower energies to be stronger than expected are suggested by the data. However, the ratio between the Raman and elastic scattering seem to be in good agreement with theory throughout the whole energy range. This shows that there is no need to introduce a direct nonresonant component to the imaginary part of the elastic scattering amplitude to explain the experimental data.     

Scattering of electromagnetic waves by charged spheres: near-field external intensity distribution

This Letter treats the scattering of electromagnetic waves by an electrically charged spherical particle in near-field approximation. Particular attention is paid to the external intensity distribution at the outer edges of the particle. The difference between scattering by a charged sphere and an electrically neutral sphere is significant only when size parameters exceed unity.     

Dirac-delta function approximations to the scattering phase function

Dirac-delta function approximations are used to represent the single scattering phase function of large spherical particles or voids. The phase function for a spherical particle or void can be represented by a series of Legendre polynomials; however, as the diameter is increased, forward scattering becomes dominant and the number of terms in the series becomes very large. A Dirac-delta function approximation consists of a Dirac-delta function in the forward direction plus a finite series of Legendre polynomials. The Dirac-delta function accounts for strong forward scattering. Particular attention is given to large ice spheres and spherical voids in ice. The Dirac-delta function is shown effective in reducing the number of terms needed to describe the phase function.     

Numerical calculations of Delbrück scattering amplitudes

The computation of the imaginary Delbrück amplitudes with the formulae of Constantini et al. gave results whose accuracy is greater by a factor of 10 than that available in the literature. The real amplitudes were computed using the code of Papatzacos and Mork. This computation was extended to all angular and energy regions of interest, and hence may be very useful in the interpretation of scattering experiments.     

Quasiclassical approach to kinetic equations for superfluid 3hellum: General theory and application to the spin dynamics

Using the method of the quasiclassical Green function, we derive a set of kinetic equations which describe general nonequilibrium situations in the quasiclassical regime, i.e., when the external frequency and wave vector, ω and q are small compared to the atomic scale (ω ? μ, ∥ q ∥ ? pf. The equations consist of a Boltzmann equation for the quasiparticle distribution function, labeled by the energy and the direction of the momentum (particle representation), coupled to a time dependent Ginzburg-Landau equation for the order parameter. We discuss extensively the properties of these equations, and apply them to orbital and spin dynamics. Solving the Boltzmann equation in a well defined approximation, we are able to derive the expressions for the linewidths for all temperatures, with the correct identification of the phenomenological relaxation times. Furthermore, we discuss the connection between various relaxation times used in non-equilibrium situations, and we give a detailed comparison of the particle representation with the excitation representation which is used frequently in other work on non-equilibrium phenomena in superfluid ³He and in superconductors.     

Quasiclassical approach to the interpretation of the Barkas effect

A correction to the Bohr formula making it possible to explain the difference between the stopping powers of positively and negatively charged particles (the Barkas effect) is obtained in the quasiclassical approximation taking into account the difference between electron motion in a hydrogen atom as a function of the charge sign of the moving particle. The influence on the atomic electron of the moving particle leads to a change in the contribution of the adiabatic interaction, in the case of which the energy is not transferred in the majority of collisions, which is the reason for a decrease in the energy losses of slow particles compared with Bohr theory. The results of calculations show that the energy losses per path length unit can be represented in the form of the product of two functions, namely, the energy loss function (in accordance with Bohr theory) and the dynamic function taking into account corrections related to correction of the electron position in the target atom during the collision. Calculations carried out within the framework of classical dynamics make it possible to qualitatively estimate differences between the interaction of protons and antiprotons with target material atoms.