Relativistic calculations of inelastic collisions between electrons and atoms

The Feynman S-matrix formalism is used to consider the inelastic collisions of electrons with a hydrogen atom. The two leading Feynman diagrams are calculated, and the 1s-2s transition is treated in detail. Results are given for scattering amplitudes at energies of 1.0–8.0 (atomic units) and for various scattering angles, as well as the differential cross sections for direct scattering in the energy region 1.36–118.5 keV. On the basis of comparison with nonrelativistic calculations, we conclude that relativistic effects are appreciable and increase with energy. Total cross sections are calculated in both nonrelativistic and relativistic approximations. The difference between them increases with energy and is 15–20% for energies of 20–50 keV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 7–12, August, 1977.     

Gauge-Independence and the Two-Body Problem in QED

I describe a gauge-independent approach to the relativistic two-body bound state and scattering problems in quantum field theory. The basic tool is an ordinary three-dimensional equation involving a potential operator V which gets contributions from both irreducible and reducible diagrams. In QED the resultant V is independent of the choice of covariant gauge used for the photon propagator, unlike the kernel in the Bethe–Salpeter equation. As an illustration, a problem concerning spin-independent level shifts in two-body bound states is analyzed.     

Magnetoresistivity of metals II. Application to point defects in copper

The general theory given previously is applied to copper single crystals containing various kinds of point defects. The matrix elements of the scattering potential with Wannier functions, which determine the transition probability, are chosen such as to satisfy the charge neutrality condition (Friedel's sum rule) and to give a prescribed electrical resistivity in zero magnetic field. Numerical calculations are carried out for the Fermi surface due toShoenberg andRoaf. The computed Kohler and rotation diagrams for magnetoresistivity, transverse-even effect, and Hall effect at low temperatures are in satisfactory agreement with measurements. The influence of different anisotropic scattering mechanisms and of the anisotropic Fermi surface is discussed in terms of the Kohler diagrams and rotation diagrams.     

qqq→qqq Reaction in Quark-Gluon Matter

Thermalization of quark matter and antiquark matter can be influenced by the scattering processes from quark-quark-antiquark to quark-quark-antiquark in quark-gluon matter, and the scattering amplitudes of such processes are the basis of studying thermalization. According to the perturbative QCD, a Fortran code for deriving individual squared amplitudes of all the qqq→qqq scattering Feynman diagrams and interference terms between different diagrams at order α⁴_s is written and corresponding squared amplitudes and interference terms are derived.     

Experimental Determination of the Useful Reflection Coefficient of Non-Cooperative Targets for a Time-of-Flight Laser Rangefinderx

An experimental verification of the reflection properties of non-cooperative targets for a time-of-flight laser rangefinder is proposed. Indeed, knowing the light scattering physical properties of usual targets is necessary to determine the optical power budget of such a device. The useful reflection coefficient (RC) is contained at between 0.6 and 0.7 at the wavelength λlD (=820 nm), polar diagrams presenting almost a lambertian shape for incident angles lower than 60°. The useful RC thus corresponds to the value of the lambertian RC increased by the contribution of the specular RC.Presented at the 7th International Workshop on Multiple Scattering Lidar/Light Experiments (MUSCLE7). July 21–23 1994, Chiba, Japan.     

Tensor polarized γ-deuteron Compton scattering in effective field theory

The differential cross section for γ-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams. At 90° photon scattering angle, only the pion term contributes at this order to the tensor polarized differential cross section. This provides a clean way to study the photon pion dynamics in the two nucleon sector. The effect is measurable for photon energies between 40 and 80 MeV provided the uncertainty in the measured cross sections are ≲ 7%.     

Dimension of an optimum impurity cluster and multiple-occupancy corrections in the theory of scattering of vibrational excitations in a solid solution

A relationship is derived for the correlation length L determining the size of the region in a solid solution in which excitations are scattered coherently. The correlation length depends on the fraction of impurity atoms x in the solid solution and the lattice dimension d. In the physical analysis of single-particle scattering processes in the solid solution and calculations, it is sufficient to take into account clusters with the number of cells n corresponding to the correlation volume L ^d . A theoretical analysis is illustrated by calculations of the spectral functions of the solid solution at different values of x and n. The multiple-occupancy corrections (polynomials in powers of x) to scattering diagrams are calculated using the method of sequential breaking apart of the interaction lines in the diagrams for the self-energy part. The method used was previously applied to the case of scattering by a single impurity. In this paper, the efficiency of the method is checked for scattering by multi-impurity clusters. It is demonstrated that the method can be useful in analyzing and estimating the contributions of scattering diagrams.     

On the re-summation of enhanced pomeron diagrams

Dominant contributions of enhanced pomeron diagrams to elastic hadron–hadron scattering amplitude are re-summed to all orders. The formalism is applied to calculate total hadronic cross sections and elastic scattering slopes. An agreement with earlier results is obtained.     

The QCD scattering amplitude from area behaved Wilson loops

We explicitly construct the dominant saddle-point trajectory in the sum-over-path representation of meson scattering amplitudes in large N QCD for area-behaved Wilson loops and show that it dominates in the Regge regime. The graphic representation of the leading trajectory is very similar to the diagrams widely used to illustrate meson scattering.     

Binary collision expansion and partial green's functions of Kadanoff-Baym

A new formula for the binary collision expansion of the unitary operator U (t₂, t₁) is proposed. The formula is applied to the expansion of the partial Green's functions of Kadanoff-Baym in powers of the correct binary scattering amplitude. It is shown that certain linked diagrams of left-multidentate structure should be taken into account. The duration of the binary collision is seen to play an important role in the rigorous formulation. Upon neglecting this duration, a useful approximation is found for the analysis of correlations on a macroscopic time scale.     

Light scattering by single erythrocyte: Comparison of different methods

In this paper we investigate the capabilities of different light scattering programs for light scattering simulation of the single human red blood cell, also known as erythrocyte. Knowledge of the scattering properties can help to solve the inverse problem of classifying erythrocytes according to size and shape using measured scattering diagrams. We compare the different programs by presenting the corresponding scattering diagrams. Then we give an overview of computation times and point out the different characteristics of the methods.     

Bremsstrahlung contribution to deep inelastic electron-photon scattering

A comparison is made between the contributions of multiperipheral and bremsstrahlung diagrams to two-photon scattering in the deep inelastic regime. The bremsstrahlung diagrams are seen to dominate the cross section for high values of the scaling variable.     

Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies

Light scattering by a small spherical particle with low dissipation rate is discussed according to the Mie theory. It is shown that near plasmon (polariton) resonance frequencies one can see non-Rayleigh anomalous light scattering with quite unusual scattering diagrams. PACS 42.25.Fx; 42.65.Es; 46.40.Ff; 78.67.Bf     

Connected kernel methods in nuclear reactions: (I). Derivation of the connected kernel equations

A set of connected kernel equations for the scattering operator are derived. The equations connect only the two cluster channels and generalize the equations of Lovelace (for N = 3) and Sloan (for N = 4) to arbitrary N. This is done by summing all disconnected diagrams explicity by induction. Methods for handling multiple summations over partitions are developed and presented. The resulting equations are similar to those given by Bencze but have a different Born term. An error in Bencze's derivation is pointed out but we show that only the two cluster connected part of the Born term contributes on-shell so his final equation is correct and equivalent to ours.     

Diagrammatic techniques in the Martin-Schwinger-Puff many-body theory

In an attempt to understand the connection between the Martin-Schwinger-Puff Green's function approach to the many-body problem and the diagrammatic approach of Brueckner and Goldstone, the perturbation expansion of the Green's function theory is studied. This expansion leads naturally to a representation of the theory by two sets of time-dependent diagrams—the kinetic energy diagrams and the potential energy diagrams. Rules are given for writing each time-dependent diagram as a sum of time-independent diagrams. Complications arise in the application of these rules to bubble diagrams. A special simple treatment of these diagrams is then proposed. There exists a simple relation between families of kinetic diagrams and potential diagrams. This relation stems from a rather general thermodynamic identity. Both the relation and its thermodynamic origin are described. As a consequence of these studies, some connections between the Brueckner-Goldstone theory and the Green's function theory are made.     

A new technique for the evaluation of Feynman diagrams in the high energy,large momentum transfer limit

The problem of finding scattering amplitudes in the high energy, large momentum transfer limit is reconsidered. We propose a novel technique of evaluating Feynman diagrams in this regime with higher order perturbative corrections in mind. The relation to other methods is discussed and the ladder diagrams in φ³ theory, recalculated up to sixth order, serve as examples.     

On the microstructure of electrodeposited Fe−P alloys investigated with SAXS

Small angle X-ray scattering of Fe_1–x P _x , 0.05<x<0.25 suggests the existence of some volume percent of small domains with an electron density different from that of the matrix. The experimental diagrams can be described assuming three kinds of scatterers with different diameters not only in amorphous but also in microcrystalline material or in material including both phases. The diameters of the scatterers of one class are independent of composition and the microstructural state. The effect of annealing on a suitably defined inhomogeneity parameter indicates a different nature of the three classes of scattering centers. More information in this respect results from additional measurements of other physical properties.     

Processes at high energy and large momentum transfer: the momentum-space approach to the asymptotics ofφ 3 ladder diagrams

The Sudakov method is extended to study the scattering amplitudes in the high-energy and large-momentum-transfer limit. The behaviour of arbitraryφ ³ ladder diagrams in the leading logarithm approximation is reconsidered. This leads to a simple physical picture of the asymptotic behaviour: the leading-term contributions are related to the different paths along which the large momentum is transferred through the ladder diagrams.     

Near-threshold amplitude of pion-deuteron scattering: One-loop contributions

The one-loop expression for the absorptive correction to the πd scattering length is discussed. Relevant Feynman diagrams are calculated both in the relativistic and in the nonrelativistic formalism. A simple expression is obtained for the one-loop correction that arises in the πd scattering length owing to the Fermi motion of the nucleons in the deuteron. This correction includes absorption effects. Fulfillment of the unitarity relation is verified explicitly.     

Microwave scattering diagrams of three-layered SiC-metamaterial/gyrotropic ferrite-SiC cylinders

We present here for the first time the rigorous solution of the boundary diffraction problem of microwave scattering by a multilayered 2D cylinder. The cylinder layers may be made of isotropic, uniaxial anisotropic, electrically and (or) magnetically gyrotropic materials. The number and thickness of the layers may have arbitrary values in our solution. We calculated scattering diagrams (a radial component of real part of the Poynting vector) inside and outside of cylinder using the solution. Here we present scattering diagrams from a three-layered cylinder made of SiC and metamaterial or saturate magnetized ferrite. Diagrams were computed for wave incidence angles θ=π/2,π/3,π/6 inside of metamaterial/ferrite layer at a distance of 1 mm and outside of cylinder at a distance of 2.5 mm from the cylinder axis.