<Emphasis Type="Italic">K</Emphasis><Superscript>±</Superscript><Emphasis Type="Italic">p</Emphasis> elastic scattering in the QCD inspired eikonalized model

Based on our previous study of the QCD inspired eikonalized model for describing vector meson photoproduction, pp, and \(\bar p\) p elastic scattering at high energies, we apply the mode to high energy K ^± p elastic scattering. The total cross section σ _tot(s), differential cross section dσ/dt, the ratio of the real part to imaginary part of the forward scattering amplitude ρ(s), and nuclear slope parameter function β(s) are calculated in the model. Our results show that the theoretical prediction for σ _tot(s) is in a good agreement with the experimental data within error bars of the data. For the other theoretical predictions there are no data to test the predictive power of the model. We need the corresponding experimental data to examinate the validity of our QCD inspired eikonalized model. However, our calculations clearly show that the Odderon exchange in the process makes a significant contribution to the observable of ρ(s) and β(s). Therefore, we may conclude that there is a good opportunity to find the QCD Odderon in the K ^± p elastic scattering at high energies.     

Many-particle effects in resonant inelastic scattering of an X-ray photon by an atom

The influence of many-particle effects on the shape and values of the double differential cross section for the resonant inelastic scattering of a linearly polarized X-ray photon by a free atom near the K and KL₂₃ ionization thresholds has been theoretically analyzed for the neon atom. The calculations have been performed using the nonrelativistic Hartree-Fock approximation for single-electron wavefunctions and the dipole approximation for the anomalous dispersion component of the cross section. The analytical structure of the contact part of the scattering cross section has been obtained beyond the dipole approximation. The effects of the radial relaxation of electron shells, spin-orbit and multiplet splitting, and configuration interaction in the doubly excited atomic states, as well as the Auger and radiative decays of the produced vacancies, are taken into account. The nature and role of the effect of correlation amplitudes, which is responsible for the appearance of the nonzero amplitudes of nonradiative transitions between intermediate and final single-electron states of the same symmetry that are obtained in different Hartree-Fock fields, have been analyzed also. The calculations are predictive and, for an incident-photon energy of 5.41 keV, agree well with experimental results for the Kα X-ray emission spectrum of the neon atom.     

Analysis of <Emphasis Type="Italic">p</Emphasis><Superscript>10</Superscript>B scattering within Glauber theory

The differential cross sections for p ¹⁰B scattering are calculated at the energies of 197, 600, and 1000 MeV within Glauber theory. The contributions of single and double collisions are taken into account in the multiple-scattering operator. The contributions of proton collisions with nucleons belonging to various (1s, 1p) shells are estimated in the single-scattering cross sections. A comparison with experimental data and with the result of calculations in the distorted-wave Born approximation (DWBA) at 197 MeV showed that the differential cross sections for p ¹⁰B scattering are adequately described in the region forward scattering angles.     

Elastic scattering of a photon by an atom with an open shell

In the nonrelativistic approximation, the absolute values and the forms of the differential cross sections of the anomalous elastic scattering of a linearly polarized x-ray photon by manganese and copper atoms in the energy region of the ionization threshold of the 1s shell are calculated for the wave functions of one-electron states. We take into account the multiparticle effects of relaxation of atomic shells in the field of core vacancies, multiplet splitting, the configuration interaction, and Auger and radiative decays of vacancies, as well as the processes of double excitation/ionization of the ground state of the atom. The calculation results are in good agreement with the synchrotron experiment.     

Streuung von 25 keV-Elektronen an Gasen

The differential cross section of neon, argon, krypton, and xenon for the elastic scattering and for the excitation of optical transitions has been measured. For neon and argon the elastic angular distribution can be described by the cross section calculated according toWentzel andLenz. For krypton and xenon there are considerable deviations from the Wentzel-Lenz cross section. In these cases it is better to calculate the elastic differential cross section from Slater eigenfunctions, from Thomas-Fermi-Dirac or from Hartree-Fock electron density distribution. The differential cross sections for the excitation of optical transitions, so far as measured here, obey for?<? _c the dipol approximation, i.e. for angles not to small the inverse square angular dependence is valid.? _c is higher for the heavier rare gases. The oscillator strengths for some transitions have been determined from the scattering measurements in satisfactory agreement with theoretical values.     

Theoretical study of photoionization of the isoelectronic sequence Rb<Superscript>+</Superscript>, Sr<Superscript>2+</Superscript>, and Y<Superscript>3+</Superscript>

The photoionization cross sections for the 4p shell of ions of the Kr isoelectronic sequence Rb⁺, Sr²⁺, and Y³⁺ are calculated. The configuration interaction theory and the perturbation theory are used to describe the many-electron effects. The relativistic effects are taken into account in the Pauli-Fock approximation. The calculated resonance structure of photoionization cross sections for the 4p shell in the region below the 4s threshold associated with the autoionization of the 4s-np singly excited states and the 4p4p-nln′l′ doubly excited states reproduces the results of recent measurements of total photoabsorption cross sections for the Rb⁺, Sr²⁺, and Y³⁺ ions. It is found that, as the nuclear charge in the isoelectronic sequence increases, the ratio between the direct and correlation parts of amplitudes of the 4s-(n/?)p transition changes and, as the consequence, the minimum of the photoionization cross section of the 4s shell shifts from the continuous spectrum to the region of states of discrete spectrum. This accounts for the strong changes in the shape of the 4s-np resonances in the photoionization cross sections for the 4p shell of Rb⁺, Sr²⁺, and Y³⁺, as well as the distinction between the shapes of the 4s-6p _1/2 mirror resonance in the partial 4p _1/2 and 4p _3/2 photoionization cross sections for the Y³⁺ ion which do not suppress each other in the total photoionization cross section, as is the case for similar resonances in Rb⁺ and Sr²⁺.     

Two-photon excitation and ionization of the 1<Emphasis Type="Italic">s</Emphasis> shell of the argon atom

The nonrelativistic absolute values and the form of the cross section for two-photon one-electron excitation and ionization of the 1s shell of the Ar atom are calculated in the second order of the quantum-mechanical perturbation theory by taking into account both the many-body effects of relaxation of the atomic core in the fields of arising virtual vacancies and the decay of vacancies via the autoionization Auger and (or) radiative channels. The appearance of the Cooper minimum in the two-photon absorption cross section is established. The calculations are carried out for the linear and circular polarizations of photons of an incident laser beam. The calculated results may be used for predictions.     

Neutron scattering in argon and <Emphasis Type="Italic">ne</Emphasis> interaction

As a preparation for the new experiment to measure the ne scattering length a_ne the total neutron cross section of gaseous argon has been obtained by the time-of-flight method at the Dubna booster IBR-30 in the energy range from ～5 eV to ～30 keV. A combined one-level analysis of the newly obtained and other known data on cross sections of Ar and ³⁶Ar has made it possible to improve some neutron parameters and calculate the scattering cross section σ_s and the scattering length a separately for ³⁶Ar and ⁴⁰Ar at any energy.     

Anomalous elastic scattering of X-ray photons by the molybdenum atom

The differential cross section for elastic scattering of an X-ray photon by the molybdenum atom is calculated in the region of the ionization threshold of the 1s shell. The calculation is performed in the nonrelativistic approximation taking into account the rearrangement of electron shells of the atomic core in the field of the virtual 1 s vacancy and processes of one-photon virtual excitation (ionization) of the ground state. Good agreement with experimental results is obtained     

Elastic Scattering of Two Photons by a Multicharged Atomic Ion

The elastic scattering of two X-ray photons by a multicharged atomic ion has been studied theoretically. A pronounced resonance structure and strong angular anisotropy of differential scattering cross section have been predicted in the energy range of a scattered photon from ?ω–I_1s to ?ω+I_1s (where is the energy of the incident photon and is the ionization energy threshold of the shell of the ion). The absolute value of the observed cross section has been quantitatively estimated.     

Notes on number density fluctuations and the scattering cross section for electromagnetic waves scattered from a thermal nonequilibrium plasma

The scattering cross section and the Doppler spectrum for electromagnetic waves scattered by the electron density fluctuations of a plasma, where the mean kinetic temperature of the electronsT _e may differ from that of the ionsT _i , has been obtained among others byFejer, Buneman, Renau, Camnitz andFlood, andSalpeter. These authors use different methods of approach to calculate the autocovariance of the electron number-density fluctuations (from the mean) and then obtain the scattering cross section. Because of the differing results, the methods, concepts, and derivations of the scattering cross section are carefully examined in this paper. It is shown that the short-time dynamical considerations incorporated in the formulation of the statistical theory of the electron number-density fluctuations of the plasma as used by several authors (for instanceFejer, Buneman, Salpeter,) leads to results of limited validity. In addition, a fundamental error in calculating the electron density fluctuations leads these latter authors to an incorrect scattering cross section. The theory of scattering of electromagnetic waves from a plasma, where the electrons arenot in thermal equilibrium with the ions but statistical equilibrium exists, is developed in a general way. The covariance of the number-density fluctuations from the mean of the charged species of the plasma and the scattering cross sectionσ(q) are obtained. In particular it is shown that for a wavelength λ much greater than the effective Debye lengthd, the backscattering cross section increases and approaches complete incoherent scattering asT _e /T _i increases. This result is explained by noting that in the case of thermal equilibrium, the predicted value of the back-scattering cross section is smaller than that of the backscattering cross section from completely uncorrelated electron density fluctuations because the electrostatic interaction between the charged particles of the plasma, which is a function ofT _e andT _i , introduces a certain amount of organization in otherwise completely uncorrelated electron density fluctuations. When the mean temperature of the electrons increases relative to that of the ions, the organization introduced in the fluctuations diminishes because of the increasing thermal agitation of the electrons relative to that of the ions, and the backscattering process approaches that of incoherent backscattering (Thomson-type scattering). The spectrum function of incoherent scattering of electromagnetic waves from a nonequilibrium plasma is obtained and some cases of current interest are plotted.     

Messungen des van der Waals-Potentials zwischen Alkaliatomen

Total collision cross sections for the interaction between alkali atoms have been measured using a modulated atomic beam technique. Since the determination of the density in the scattering chamber is the main source of error in absolute scattering measurements, particular attention is given to this problem: The cross section for partnersA andB is measured first withA as beam particles anB as target particles, and then withB as beam particles andA as target particles. The data are used to deduce the long rangevan der Waals (inverse sixth power) potential constants, which can be compared with theoretically calculated values of different authors. The interaction constants resulting from the present measurements are in good agreement with those calculated byFontana, while other calculations give much larger values.     

Maximum coefficient of light extinction in a nonabsorbing dispersive medium

The maximum value of the light extinction coefficient μ, which can be observed in a dispersive medium with a relative refractive index n of the scattering particles, is studied within the framework of a quasi-crystalline approximation for nonabsorbing dispersive media consisting of monodisperse spherical scatterers. A change in the diffraction parameter x of the scattering particles and their volume concentration c _v is accompanied by nonmonotonic variations of the extinction coefficient, and the function μ(x, c _v ) exhibits several maxima. The dimensions and concentrations of particles are determined, for which the extinction coefficient reaches the absolute maximum μ^max. The μ^max value exhibits a monotonic growth with increasing relative refractive index n of the scattering particles. The conditions of validity of the Ioffe-Regel criterion of radiation localization have been studied. It is established that the localization in nonabsorbing dispersive media can be observed only for n ? 2.7. The intervals of x and c _v in which the criterion of radiation localization is satisfied in dispersive media consisting of particles with n = 3.0 and 3.5 are determined.     

Resonant scattering of an X-ray photon by a heavy atom

The influence of many-body and relativistic effects on the absolute values and shape of the double differential cross section for the resonant scattering of a linearly polarized X-ray photon by a free xenon atom near the K-shell ionization threshold has been theoretically analyzed. The evolution of the spatially extended structure of the scattering cross section to the K _{α, β} structure of the X-ray spectrum of the xenon atom emission has been demonstrated. The calculations have been performed in the dipole approximation for the anomalous dispersion component of the total inelastic scattering amplitude and in the impulse approximation for the contact component of this amplitude. The contribution of the Rayleigh (elastic) scattering component is taken into account using the methods developed in Hopersky et al., J. Phys. B 30, 5131 (1997). The effects of the radial relaxation of the electron shells, spin-orbit splitting, double excitation/ionization of the atomic ground state, as well as the Auger and radiative decays of the produced main vacancies, are considered. Using the results obtained by Tulkki, Phys. Rev. A 32, 3153 (1985) and Biggs et al., At. Data Nucl. Data Tables 16, 201 (1975), the nonrelativistic Hartree-Fock wavefunctions are changed to the relativistic Dirac-Hartree-Fock wavefunctions of the single-particle scattering states when constructing the process probability amplitude. The calculations are predicting and are in good agreement with the synchrotron experiment on the measurement of the absolute values and shape of the double differential cross section for the resonant scattering of an X-ray photon by a free xenon atom reported by Czerwinski et al., Z. Phys. A 322, 183 (1985).     

Merging of X-Ray photons in the field of a light atomic ion

The process of merging of three X-ray photons into one photon in the field of a light atomic ion is theoretically studied. A pronounced resonance structure and a strong angular anisotropy of the differential cross section for merging are predicted in the region of the incident photon energy ?ω ? I _1s /2 (I _1s is the threshold energy of ionization of the -shell of the ion). The magnitude of the observed merging cross section is estimated.     

Dipolsummenregel bei nichtlokalen Potentialen

The integrated cross section of photonuclear reactions is considered in the electricdipole approximation. The nucleon-nucleon potential used is well-behaved and nonlocal. We use the Tabakin potential, which matchesS-, P- andD-wave phase shifts up to 320 MeV without generating strong short-range correlations.     

Verhältnis des differentiellen (e,N)- zum totalen (γ,N)-Wirkungsquerschnitt

The ratio of the differential cross section for the (e, N)-process to the total (γ,N) -cross section is derived with the use of the relativistic Coulomb Eigenfunctions for the continuous spectrum. For electric and magnetic dipole transitions the Born approximation, the Coulomb correction, the effect of screening and that of finite nuclear size are calculated. In this angular distribution there should be no interference of electron waves scattered by different multipoles, where the inelastically scattered electrons are detected. Numerical calculations have been done for nuclei withZ=6, 29, and 82 and scattering anglesθ=1Ω, 132Ω, 160Ω and 180Ω of the electron. The result of this theory is compared with the experiments of W.C.Barber et al.     

Compton and double-compton scattering processes at colliding electron-photon beams

Radiative corrections to the Compton scattering cross section are calculated in the leading and next-to-leading logarithmic approximations in the case of colliding high-energy photon-electron beams. Radiative corrections to the double-Compton scattering cross section in the same experimental setup are calculated in the leading logarithmic approximation. We consider the case where no pairs are created in the final state. We show that the differential cross section can be written in the form of the Drell-Yan process cross section. Numerical values of the K-factor and the leading-order distribution on the scattered electron energy fraction and scattering angle are presented.     

Saturation Approach in Top Production

The reduced cross section for the top production, in deep inelastic scattering, determined when we use the Kharzeev–Levin–Nardi (KLN) model of the low x gluon distributions. With respect to this model, a compact formula for the ratio R^t(τ) provided that it is approximately independent of τ behavior at low- τ values. For the top production where Q_sr_⊥ ? 1, the model reduced to color transparency.