Elastische und unelastische Streuung von Elektronen an Gasen

The theoretical differential cross section for the elastic scattering and for the excitation of optical transitions in helium by electron impact has been refined in Born approximation by use of the two parameter Eckart eigenfunction for the ground state and for the excited states. The angular distributions of 25 kev electrons scattered elastically and inelastically by helium were measured in the angular range 2·3·10^?4≦?≦4·10^?2. The intensity distribution of the elastically scattered electrons is in accordance with the theoretical curve for?>7·10^?3 and is disturbed at smaller angles by the primary beam. Normalization of the experimental values to the theoretical elastic differential cross section leads to agreement between the experimental differential cross section for the excitation of the 2¹ P and 3¹ P state and the scattering formulae given in this paper. There are small systematic deviations (<20%) for the 2¹ P differential cross section in the angular range 3·10^?3<?<1·10^?2 only. The oscillator strength of these two transitions has been determined from the scattering measurements:f ₂₁=0·312±0·04 andf ₃₁=0·0898±0·006.     

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.     

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.     

Quasielastic kaon knockout from a proton and momentum distribution of virtual kaons in the proton

The momentum distribution of kaons in the proton and the coupling-constant ratio fKΛN/fKΣN are determined on the basis of the ³P₀ quark model of meson-baryon coupling. The longitudinal cross section for kaon electroproduction is calculated. The results of the present study are compatible with available experimental data, but more detailed data on the longitudinal cross section would make it possible to refine the absolute values of the coupling constants fKΛN and fKΣN.     

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.     

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.     

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.     

Elastic scattering of 0.5 MeV gamma rays by heavy elements

The absolute differential cross sections for the elastic scattering of 0.511 MeV gamma rays were measured in the angular range 0.5? to 10? for the elements withZ=72 toZ=92. The experimental method, employing annihilation radiation in coincidence, permits the investigation at very small momentum transfer. In general the results obtained are in very good agreement with the predictionZ ² r ₀ ² for the differential Rayleigh cross section atθ=0? and with the form factor theory, using Hartree-Fock-Slater wave functions, for the investigated angular range. However, for the elements lead, bismuth and thorium we found marked deviations from the form factor predictions, occurring at very small scattering angles. This is attributed to an outer atomic charge distribution different from the other investigated elements, which is also indicated by considerably greater metallic radii. Also effects due to the crystalline structure cannot be excluded. — Further, an elastic, resonance-like andZ-dependent scattering effect by bound electrons is discussed which is due to the formation of an intermediate, bound positronium state by electron-positron pairs.     

Zur Theorie der Vorwärtsasymmetrie bei der Photospaltung des Deuterons

The forward asymmetry in the differential cross section for the photo disintegration of the deuteron has been calculated on the basis of a phenomenological theory for energies up to 80 MeV. The formulas for this asymmetry, which come from theE1-E2-andM1-M2-interference, are given, assuming the validity ofSiegert's theorem. TheE2-andM2-amplitudes are calculated approximately, using the Hulthén wavefunction with a 4% D-state admixture for the ground state and scattered waves determined by the phase shifts given by Marshak for the final states. The contribution of theM1-M2-interference turns out to be unimportant for the asymmetry, theE1-E2-interference giving the main effect. In the differential cross section,dσ/dΩ=a + b sin ² ? + c cos ? + d cos ? sin ² ?, we have obtained a very low value forc and the ratioc/d is approximately equal toa/3b. This is in contradiction to the assumptionc/d=a/b made in the previous analysis of the experimental data. This ratio seems to be insensitive to the value of the D-state admixture. For the lover energiesE _γ=10 MeV andE _γ=20 MeV the theoretical values for “d” are in agreement with the experimental ones. For the energies 54 and 80 MeV we have made a comparison of the theoretical differential cross sectiondσ/dΩ, taking into account the values for “a” and “b”, obtained in a former work ie, with the measureddσ/dΩ.     

Inelastische Positronenstreuung am Atomkern

The ratio of the total and differential cross section for the inelastic positron-nucleus scattering (ē, N)-process to the total (γ, N) -cross section is derived in Born approximation for electric and magnetic dipole transitions. The result agrees with that obtained for the (e, N)-processes. Using the relativistic Coulomb Eigenfunctions for the continuous spectrum of the positrons, the Coulomb correction, the effect of screening and that of finite nuclear size agree with the (e, N)-process, when the annihilation of positrons with atomic electrons is neglected, and for positron energiesE _1,2 ⁺ >10 MeV. The effect of finite nuclear size is only calculated in Born approximation. ForE _1,2 ⁺ ≦2 MeV only the Coulomb correction differs from that obtained for the (e, N)-process. In the angular distribution for the (ē, N)-process there should be no interference of positron waves scattered by different multipoles, where the inelastic scattered positrons are detected. Numerical calculations have been carried out for nuclei withZ=6.29 and 82 and scattering angles ?=1°, 132°, 160° and 180° of the positron. This theory can be compared with the experiments in progress by W.C.Barber et al. using positrons for the inelastic scattering process at nuclei. The two-and three-virtual quanta-exchange effect in the (ē, N)-cross section is below 1.3% for positron energies between 10≦E ₁ ⁺ ≦300 MeV, and decreases rapidly for higher energies. This theory is also valied for inelastic scattering processes with positiveμ-mesons at nuclei; one has only to change the mass in the following equations.     

Spectral characteristics of a barrier discharge in cadmium dihalide vapor-inert gas mixtures

Spectral characteristics of a barrier-discharge plasma produced in atmospheric-pressure mixtures of cadmium diiodide and cadmium dibromide vapors with neon, krypton, and xenon at a repetition rate of sine voltage pulses up to 130 kHz are studied. The emission from the discharge is studied within the spectral range 200–900 nm with a resolution of 0.05 nm. Emission of exciplex molecules CdI(B → X) and CdBr(C, B → X), and cadmium and inert gas atoms is revealed, as well as emission of exciplex molecules XeI(B → X, A) and XeBr(B → X, A) in xenon-containing mixtures. The emission of xenon halides prevails in the spectra at a mixture temperature up to 200°C. With a further temperature increase, the emission of cadmium halides becomes dominating. It is ascertained that the most intense emissions of CdI(B → X) and CdI₂/CdBr₂/Xe/Kr and CdBr(B → X) molecules are observed, respectively, in CdI₂/CdBr₂/Xe/Kr and CdI₂/CdBr₂/Xe mixtures. The cadmium dihalide-inert gas mixtures are of interest for the use as a radiating gas in a multiwavelength and broadband excilamp emitting in the UV and visible spectral ranges.     

Über die Berechnung der Photoerzeugung von π0 aus Streudaten

The cross section forπ ⁰-production is calculated from the results of the dispersion relation approach ofChew, Goldberger, Low andNambu and compared with the experimental data. The predictions are made using the measured values of all scattering phase shifts. A fit of the theoretical result toσ(90?) between 260 and 370 MeV givesf ²=0,082. There is no systematic deviation from the predictions forσ (90?) up toE _γ =450 MeV. The general behavior of the asymmetry coefficientB is correct. A quantitative comparison which would show the contribution of the unknown electric dipole termN ⁽⁺⁾ ofChew et al. is only reasonable after the calculation ofB and the measurements have been improved.C/A depends strongly on the small phases up to 240 MeV. The effects of the small phases are pretty large forσ(l50?) but there is no discrepancy similar to the results forπ ⁺-production above 290 MeV. The formula for the cross section does not reduce to the results of the phenomenological theories ofBrueckner-Watson, Sachs et al. andFeld, if the simplifications made by these authors are taken into account. The origin of the differences is discussed.     

Role of the nuclear and electromagnetic interactions in the coherent dissociation of the relativistic <Superscript>7</Superscript>Li nucleus into the <Superscript>3</Superscript>H + <Superscript>4</Superscript>He channel

The differential cross section in the transverse momentum Q and a total cross section of (31 ± 4) mb for the coherent dissociation of a 3-A-Ge V/c ⁷Li nucleus through the ³H + ⁴He channel have been measured on emulsion nuclei. The observed Q dependence of the cross section is explained by the predominant supposition of the nuclear diffraction patterns on light (C, N, O) and heavy (Br, Ag) emulsion nuclei. The contributions to the cross section from nuclear diffraction (Q ≤ 400 Me V/c) and Coulomb (Q ≤ 50 Me V/c) dissociations are calculated to be 40.7 and 4 mb, respectively.     

Energieverteilung und Wirkungsquerschnitt der Photoprotonen aus N15

The energy spectra of photo protons from highly enriched N¹⁵ were investigated with the bremsstrahlung from the Heidelberg betatron running at six different endpoint energies between 19 and 30.5 MeV. The protons were detected at 90° to theγ-beam by means of a CsJ-spectrometer with pulse shape discrimination. The energy spectra show pronounced maxima atE _p =3.2; 4.6; 9.5 and 13.3 MeV. Proton yields are given as a function of endpoint energy, the yield value atE ₀=30.5 MeV being (7.0±0.8) μb/MeV · ster. Because the first excited state in the daughter nucleus C¹⁴ lies 6.09 MeV above the groundstate, the cross section for groundstate transitions of the process N¹⁵(γ, p)C¹⁴ could be derived from the upper 6 MeV of the single proton spectra. The main contribution to the cross section comes from the region between 18 and 26 MeV excitation energy with maxima at 19.5; 20.4; 22.7 and 24.5 MeV. A “pygmy resonance” occurs at 15.2 MeV with further less pronounced structures at 13.6 and 17.0 MeV. The integrated cross section for groundstate transitions up to 30.5 MeV is (22±3) MeVmb assuming isotropic angular distribution. The ratios of protons from transitions to excited states and from the (γ, n p)-reaction to those of groundstate transitions rise from 0.45 atE ₀=24.5 MeV to 0.70 atE ₀=30.5 MeV.     

The effect of hadronic rindler horizon on hadronization process

In this study by extending the recent suggested mechanisms to hadronization processes, the information loss for QCD matter in hadronic Rindler horizon is found. We notice that for all finite values of quark and gluon energies, all information from all hadronization processes experiences some degree of loss. Then the effect of hedonic Rindler horizon on three jet cross section is explored. It is found that the three jet cross section is rising at y_cut =?0.0002 exhibits a turn-over at moderate value of y_cut =?0.01 and then rapidly decreases as y_cut increases. This model is consistent with OPAL data. Finally, different channels for producing Higgs boson near hadronic Rindler horizon are studied. It is shown that the cross section of Higgs boson produced via gluon fusion and quark interaction near a single Hadronic Rindler Horizon is much larger for higher center of mass energies. This is because an increase in the energy of hadronic Rindler horizon raises the temperature, thus intensifying the thermal radiation of QCD matter.     

Relationship between <Emphasis Type="Italic">T</Emphasis>-invariance and formation mechanisms for <Emphasis Type="Italic">T</Emphasis>-odd and <Emphasis Type="Italic">T</Emphasis>-even asymmetries in the angular distributions of fission fragments of oriented nuclei

The T-invariance condition was analyzed for the amplitude T _b,a of multiparticle multistep elastic or inelastic a → b nuclear reactions. This condition leads to the equality of the amplitude T _b,a to the amplitude \({\tilde T_{\bar a,\bar b}}\) of \(\bar b \to \bar a\) time-reversed reaction, for which the reaction operator \(\tilde T\) coincides with the inverse-reaction (b → a) operator. It is shown that, in the case where the original, inverse, and time-reversed reactions are governed by a common T-invariant mechanism, the coefficients D of asymmetries appearing in the differential cross sections for these reactions can be represented in the form of a unified scalar (pseudoscalar) function of arguments equal to the momentum and spin vectors of particles of the initial and final channels of the reactions under analysis. It is also shown that the use of the T-invariance condition for the coefficients D of asymmetries in the differential cross section for the original nuclear reaction that are different in P- and T-parity makes it possible to separate mechanisms leading to nonzero coefficients D for a number of the asymmetries under analysis from the remaining mechanisms leading to zero coefficients D of these asymmetries. It is proven that there exist such asymmetries in the differential cross section for the original reaction whose coefficients vanish for all possible T-invariant mechanisms of their appearance, so that, upon proving experimentally the appearance of nonzero coefficients of these asymmetries in the differential cross section for the original reaction, this fact can be used to assess features of T-noninvariant interactions in nuclear systems.     

Die Feinstruktur desL-MM-Auger-Elektronenspektrums von Argon und derK-LL-Spektren von Stickstoff,Sauerstoff und Methan

The fine structure ofL-MM Auger electron spectrum of argon andK-LL spectra of the gases N₂, O₂ and CH₄ was investigated with an electrostatical spectrometer. The ionisation was caused by the continuous X-radiation from a tungsten target. From the results of Auger electron energies measured, the binding energies of the electrons of the inner shells were calculated. The results obtained with argon agreed exactly with the known values. Further it could be shown, that the value of 400 eV for the binding energy of a 1s-electron in the N₂-molecule, so far obtained, must be replaced by the value (409,4±1,0) eV. A comparison between the relative intensities of fine structure lines and the theory of the Auger process given byAsaad andBurhop could not be carried out, because the Auger electrons, having in our experiment an angular distribution relativ to the incident X-ray beam, could only be measured between an angular range of 49,3° and 61,0°.     

<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.     

Vergleich der Photoerzeugung von π0 am Proton mit der Voraussage nach der Dispersionstheorie

The real parts of the photoamplitudesE 1S _1/2,M 1P _1/2,M 1P _3/2 have been calculated from the angular distribution of the reactionγ+p→p+π⁰ recently measured byGoldansky et al. at 160 to 240 MeV. One of the solutions fits pretty well to the theoretical prediction for theM 1P _3/2-amplitude according to the dispersion method ofChew, Goldberger, Low andNambu. There is a discrepancy forM 1P _1/2 ifα ₁₁ is taken from the effective range formula, but the positive values ofα ₁₁, necessary to give agreement, are not excluded by the results of the phase shift analysis, especially sincePontecorvo et al. have recently found positive values at higher energies. The prediction for the real part of theE 1 S_1/2-amplitude agrees with the experimental data, if pretty large recoil corrections are added which had been neglected byChew et al.     

Effects of radial relaxation and intershell correlations during resonance inelastic photon scattering by an atom

The absolute value and shape of the double differential cross section of the resonance inelastic scattering of a linearly polarized photon in the ionization threshold energy range of the subvalence s shell of the free neon or argon atom are calculated in the nonrelativistic approximation for one-electron wavefunctions and in the dipole approximation for the anomalously dispersive scattering probability amplitude. The effects of radial relaxation, intershell correlations, bremsstrahlung, spin-orbit splitting, and a finite decay width of s vacancies are taken into account. The effects of radial relaxation and intershell correlations substantially affect the near-threshold scattering intensity: they decrease the contribution of the leading Compton anomalously dispersive component of the total cross section calculated in the one-electron approximation by several times. The calculation results have a predictive character.