Scattering Cross-Sections in Quantum Gravity—The Case of Matter-Matter Scattering

Viewing gravitational energy-momentum PG<sup style='margin-left:-7px;'>μ as equal by observation, but different in essence from inertial energy-momentum PI<sup style='margin-left:-7px;'>μ naturally leads to the gauge theory of volume-preserving diffeomorphisms of a four-dimensional inner space. To analyse scattering in this theory, the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity.

First Born Double Differential Cross-Section for Ionization of H (3d) by Incident Electron Impact

Double differential cross section (DDCS) of First-Born approximation is calcu-lated for the ionization of metastable 3d-state hydrogen atoms by electron impact energy at 150 eV and 250 eV. A multiple scattering theory is applied in the present study. The present results are compared with the other related the-oretical results for the ionization of hydrogen atoms from different metastable states and ground-state experimental results. The findings demonstrate a strong qualitative agreement with the existing results. The obtained results have an extensive scope for further study of such an ionization process.

IR LASER BACKSCATTERING FROM AN ARBITRARILY SHAPED DIELECTRIC OBJECT WITH ROUGH SURFACE

The backscattering of light wave from arbitrarily convex dielectric objects withrough surface is investigated and formulas for calculating the backscattering cross-section of bothcoherent and incoherent fields are obtained.In the infrared wave-band,the influence of the ge-ometry,permittivity and statistical characteristics of the rough surface on LRCS is analyzed,byusing rough sphere and ellipsoids as examples.

Variations in Optical Scattering and Backscattering by Organic and Inorganic Particulates in Chinese Lakes of Taihu, Chaohu and Dianchi

This study presents an investigation of the scattering and backscattering properties of the particulates in three Chinese inland lakes(the Taihu Lake, the Chaohu Lake and the Dianchi Lake) based on in situ measurements taken at 119 sites. We modeled the particulate scattering spectra using a wavelength-dependent power-law function, finding that the power-law exponents in the Taihu Lake and the Chaohu Lake differ from those in the Dianchi Lake but are similar to the values in the U.S. coastal waters. In contrast to the open ocean, the backscattering properties in the three lakes can not be determined only from chlorophyll-a concentration. The backscattering ratio spectra exhibit a wavelength dependence feature in all three lakes, generally decreasing with the increasing wavelength. Analysis results of the correlations between the backscattering ratio and the individual water quality parameters clearly show that there are distinctive relations among the three lakes, attributed primarily to different compositions of optically active materials in the three lakes. Analysis of the mass-specific scattering and backscattering coefficients shows that the coefficients at wavelength 532 nm in the Taihu Lake and Chaohu Lake are similar, but they are apparently different from those in the Dianchi Lake. Lastly, Model I multiple linear regressions were adopted to partition the mass-specific cross-sections for scattering and backscattering into organic and inorganic cross-sections to further interpret the scattering and backscattering properties. The relative contribution of organic and inorganic particulates to scattering and backscattering is clearly different among the three lakes. The scattering and backscattering properties of the particulates in the three inland lakes vary significantly based on our collected data. The results indicated that the existing semi-analytical water quality retrieval models of the Taihu Lake can not be applied perfectly to the Chaohu Lake and the Dianchi Lake.

Positron-Lithium Atom and Electron-Lithium Atom Scattering Systems at Intermediate and High Energies

The coupled-channel optical method is used to study positron scattering by atomic lithium at energies ranging from the ionization threshold to 60eV, The present method simultaneously treats the target channels and the positronium （Ps） channels in the coupled-channel method together with the continuum effects via an ab-initio optical potential. Ionization, elastic and inelastic cross sections in target channels, and the total cross section are also reported and compared with other theoretical and experimental data. A comparative study with the corresponding electron-lithium data is also reported.

The First Born Triple Differential Cross-Section for Ionization of H(3P) by Electron Impact in the Asymmetric Coplanar Geometry

First Born triple differential cross sections (TDCS) for ionization of metastable 3P-state hydrogen atoms by electrons are calculated for various kinematic conditions in the asymmetric coplanar geometry. A multiple scattering theory is used in this study. The present results are compared with other existing related theoretical results for ionizations of hydrogen atoms from metastable 2S-state and 2P-state, showing a good qualitative agreement. There is no available theoretical study for ionization of metastable 3P-state hydrogen atoms by electrons. We are expecting that the present results provide a wide scope for further study of such ionization problems.

Phonon Mediated Electron-Electron Scattering in Metals

It is shown that the linear resistivity dependence on temperature for metals above the Debye’s temperature mainly is caused by electron-electron scattering of randomly moving electrons. The electron mean free path in metals at this temperature range is in inverse proportion to the effective density of randomly moving electrons, i.e. it is in inverse proportion both to the temperature, and to the density-of-states at the Fermi surface. The general relationships for estimation of the average diffusion coefficient, the average velocity, mean free length and average relaxation time of randomly moving electrons at the Fermi surface at temperatures above the Debye’s temperature are presented. The effective electron scattering cross-sections for different metals also are estimated. The calculation results of resistivity dependence on temperature in the range of temperature from 1 K to 900 K for Au, Cu, Mo, and Al also are presented and compared with the experimental data. Additionally in temperature range from 1 K to 900 K for copper, the temperature dependences of the mean free path, average diffusion coefficient, average drift mobility, average Hall mobility, average relaxation time of randomly moving electrons, and their resultant phonon mediated scattering cross-section are presented.

Elastic cross sections for electron-carbon scattering

We used the close-coupling optical （CCO） approach to investigate the open-shell carbon atom. The elastic cross sections have been presented at the energies below 90eV, and the present CCO results have been compared with other theoretical results. We found that polarization and the continuum states have significant contributions to the elastic cross sections. The present calculations show that the CCO method is capable of calculating electron scattering from open-shell atoms.

Scattering of Electromagnetic Waves by Drift Vortex in Plasma

In a quasi-two-dimensional model, the scattering of incident ordinary electromag- netic waves by a dipole-electrostatic drift vortex is studied with first-order Born approximation. The distribution of the scattering cross-section and total cross-section are evaluated analytically in different approximate conditions, and the physical interpretations are discussed. When the wavelength of incident wave is much longer than the vortex radius （kia〈〈1）, it is found that the angle at which the scattering cross-section reaches its maxim depends significantly on the approximation of the parameters of the vortex used. It is also found that the total scattering cross-section has an affinitive relation with the parameters of the plasma, while it is irrelevant to the frequency of the incident wave in a wide range of parameters of the vortex. In a totally different range of parameters when incident wave is in the radar-frequency range （then kia 〈〈 1, the wavelength of incident wave is much shorter than the vortex radius）, the numerical procedure is conducted with computer in order to obtain the distribution and the total expression of the scattering crosssection. Then it is found that the total scattering cross-section in the low frequency range is much larger than that in high frequency range, so the scattering is more effective in the low frequency range than in high frequency range.

Electron Scattering by C4H10 and C6H6 in the Energy Range 100-1000 eV

We investigate the applicability of the independent atom model （IAM） to elastic electron scattering from complex polyatomic molecules, namely C4H10 and C6H6, in the energy range 100-1000eV. The cross sections of the elastic electron scattering are calculated by employing the IAM together with the relativistic partial waves. The incorporation of both the modified absorption potential and the extended structural factor in the IAM makes the elastic differential cross sections and momentum transfer cross sections have a good agreement with the available experimental data. The present simple model seems to be insensitive to the complexity of the target molecules so that the proposed procedure can be quite useful for calculation of electron scattering from bio-molecules.

NEW APPROACH TO ELECTROMAGNETIC SCATTERING FROM A CONDUCTIVE DISC-RING STRUCTURE

A one-dimensional modified integral equation for electromagnetic scattering from a metallic concentric disc-ring structure is derived by using Fourier expansion and separating the contribution of charge density from conventional EFIE. In the case of normal incidence, the derived equation is very simple and easy to be solved numerically regardless of the electric dimension of the structure. The comparison between the data of RCS of a disc by using this method and analytical method shows the effectiveness of this approach. Numerical results are also given for current distributions and the scattered fields for a disc-ring structure.

Influence of the ordered structure of short-chain polymer molecule all-trans-β-carotene on Raman scattering cross section in liquid

We measured the resonant Raman spectra of all-trans-β-carotene in solvents with different densities and concentrations at different temperatures. The results demonstrated that the Raman scattering cross section （RSCS） of short-chain polymer all-trans-β-carotene is extremely high in liquid. Resonance and strong coherent weakly damped CC bond vibrating properties play important roles under these conditions. Coherent weakly damped CC bond vibration strength is associated with molecular ordered structure. All-trans-β-carotene has highly ordered structure and strong coherent weakly damped CC bond vibrating properties, which lead to large RSCS in the solvent with large density and low concentration at low temperature.

RESEARCH ON ELECTROMAGNETIC SCATTERING FROM PARTIALLY COATED CONDUCTING CYLINDERS

In this paper,moment methods are applied to solving the electromagnetic scatteringproblems(for both E-and H-polarizations)involving partially coated conducting cylinders.Thecomputer programs have been compiled for general use.They can be used to solve the electro-magnetic scattering from uncoated,partially coated or entirely coated cylinders of arbitrary crosssectional shape.Numerical examples are also presented to show the validity and versatility of themethod.

RADAR CROSS-SECTION COMPUTATIONS OF ARBITRARILY COMPLICATED TARGETS BY APPLYING THE PANEL METHOD

The present paper deals with the method for the radar cross-section (RCS)computations of arbitrarily complicated targets based on the work by D. Klement et al.(1988).This method is convenient in use, fast in operation and precise in calculating RCS of a complicatedtarget. With this method, the RCS of classic scatterers, for example, a cone and a cylinder, arecomputed with the result of good agreement with experimental data. Furthermore, the RCS’of an aircraft model at various attitudes are calculated with the result of good agreement withexperimental data also.

Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 1

We demonstrate a possibility of computation of inelastic scattering cross-section in a multi-peripheral model by application of the Laplace method to multidimensional integral over the domain of physical process. Founded the constrained maximum point of scattering cross-section integral under condition of the energy-momentum conservation. The integrand is substituted for an expression of Gaussian type in the neighborhood of this point. It made possible to compute this integral numerically. The paper has two parts. The hunting procedure of the constrained maximum point is considered and the properties of this maximum point are discussed in the given part of the paper. It is shown that virtuality of all internal lines of the “comb” diagram reduced at the constrained maximum point with energy growth. In the second part of the paper we give some the arguments in favor of consideration of the mechanism of virtuality reduction as the mechanism of the total hadron scattering cross-section growth, which is not taken into account within the framework of Regge theory.

Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 2

We demonstrate a new technique for calculating proton-proton inelastic cross-section, which allows one by application of the Laplace' method replace the integrand in the integral for the scattering amplitude in the vicinity of the maximum point by expression of Gaussian type. This, in turn, allows us to overcome the computational difficulties for the calculation of the integrals expressing the cross section to sufficiently large numbers of particles. We have managed to overcome these problems in calculating the proton-proton inelastic cross-section for production (n ≤ 8) number of secondary particles in within the framework of φ3 model. As the result the obtained dependence of inelastic cross-section and total scattering cross-section on the energy √s are qualitative agrees with the experimental data. Such description of total cross-section behavior differs considerably from existing now description, where reggeons exchange with the intercept greater than unity is considered.

Triple Differential Cross-Sections for Ionization of H(3d) by Incident Electron

Triple differential cross sections (TDCS) are estimated for the ionization of metastable 3d-state hydrogen atoms by electron at 250 eV for various kinematic conditions pursuing a multiple scattering theory. The present new results are compared with the theoretical results of hydrogenic different metastable states as well as the hydrogenic ground state experimental data. Obtained new finding results are in good qualitative agreement with those of compared theories. The present results give an immense opportunity for experimental trial in the field of ionization problems.

Double Differential Cross-Section for the Ionization of Hydrogenic 2S Metastable State

Double differential cross-sections of first Born estimation for ionization of hydrogenic 2S state by electrons are assessed for various kinematics situations in the asymmetric coplanar geometry. A final state wave function of multiple scattering theory is followed in this study. The present outcomes are compared with those of hydrogenic ground state, 2P state and ground state experimental results. Obtained findings show a good qualitative agreement with existing results.

Neutron-Nucleus Total Elastic Scattering

Using an exact and complete Yukawa Potential Energy (YPE), the neutron-triton and neutron-helium elastic total scattering cross section is estimated and extrapolated to zero energy. The estimated value agrees pretty well with the experimental value and the procedure can be extended to any neutron-nucleus total scattering. The results are extended to the case of 4He, 7Li, 9Be and 27Al nuclei also.

Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory.Part 3

We develop a new method for taking into account the interference contributions to proton-proton inelastic cross-section within the framework of the simplest multi-peripheral model based on the self-interacting scalar φ3 field theory, using Laplace’s method for calculation of each interference contribution. We do not know any works that adopted the inter- ference contributions for inelastic processes. This is due to the generally adopted assumption that the main contribution to the integrals expressing the cross section makes multi-Regge domains with its characteristic strong ordering of secon- dary particles by rapidity. However, in this work, we find what kind of space domains makes a major contribution to the integral and these space domains are not multi-Regge. We demonstrated that because these interference contributions are significant, so they cannot be limited by a small part of them. With the help of the approximate replacement the sum of a huge number of these contributions by the integral were calculated partial cross sections for such numbers of secondary particles for which direct calculation would be impossible. The offered model qualitative agrees with experimental dependence of total scattering cross-section on energy with a characteristic minimum in the range ≈ 10 GeV. However, quantitative agreement was not achieved;we assume that due to the fact that we have examined the simplest diagrams of theory.