Photon interaction cross-sections and anomalous scattering factors of Cu and Ag

Total attenuation cross sections of copper and silver have been measured in the energy range 5 to 85 keV in a narrow beam good geometry set up using X- andγ-rays emitted from radio isotopes, by employing a high resolution hyper pure germanium detector. From the measured values, the photoeffect cross-sections have been derived by subtracting a small contribution of the sum of the theoretical coherent and incoherent scattering cross sections. The photoeffect cross-sections so obtained are found to be in better agreement with the unrenormalized values of Scofield [10]. These photoeffect cross-sections have been used to evaluate the dispersion corrections (also called anomalous scattering factors)f ⁺ andf″ for the forward Rayleigh scattering amplitude by a numerical evaluation of the dispersion integral that relates them at the energies at which the cross-sections have been measured. To thef ⁺ values so obtained, the relativistic corrections proposed by different investigators are included separately and the valuesf′ so obtained are compared with the available data and discussed. Possible conclusions are drawn from the present study.     

Coulomb “flux corrections” and total cross sections for pion-nucleus interactions in the Δ-resonance region

A relativistic generalization of the Blair model is shown to give large flux corrections (up to 20%) to pion-nucleus cross sections in the Δ-resonance region. Total cross sections for heavy nuclei are calculated and used in the evaluation of these corrections. The formulas also apply to incident high energy protons.     

Elastic scattering of electrons by europium and ytterbium atoms

The method of relativistic optical potential is applied to studying elastic scattering of electrons by europium and ytterbium atoms in a wide range of collision energies up to 2 keV. The angular dependences of the scattering differential cross sections and the energy dependences of the scattering integral (total, elastic, momentum transfer, and viscosity) cross sections are calculated in both spin-polarized and spin-unpolarized approximations. It is shown that the spin-polarized approximation should be used to calculate the scattering cross sections at energies below 10 eV for a europium atom. The low-energy scattering of an electron by a europium atom is characterized by P-, D-, and F-wave shape resonances. For an ytterbium atom, the calculated cross sections are in good agreement with available experimental data and with those obtained by calculation in terms of the relativistic convergent close-coupling method.     

Modeling of a microscopic optical pion-nucleon potential at energies in the (3, 3)-resonance region and nuclear-matter effect on the pion-nucleon amplitude

Differential cross sections for elastic pion scattering on a number of nuclei at energies between 130 and 290 MeV are calculated. For this purpose, use is made of a microscopic optical pion-nucleus potential that was obtained on the basis of the Glauber theory of high-energy scattering and which is determined by the density distribution of pointlike target nucleons and by the pion-nucleon scattering amplitude. The calculation of the cross sections in question is based on solving the respective relativistic wave equation. Three parameters of the pion-nucleon amplitude are fitted in performing a comparison with experimental data. These are the total cross section for pion-nucleon scattering, the ratio of the real to the imaginary part of the forward pion-nucleon scattering amplitude, and the slope parameter. The resulting values of these parameters are then compared with their counterparts for scattering on free nucleons. The character of nuclear-matter-induced changes in these parameters is studied.     

Recoil corrections to elastic electron scattering in the Breit approximation

Recoil corrections to the cross sections for elastic electron scattering from spin-0 nuclei are investigated in the Breit approximation. The form of the scattering amplitude in first- and second-Born approximation is investigated in detail using time-dependent perturbation theory, and it is found that the center-of-mass (CM) frame is particularly convenient to work in. Transformation equations relating the lab and CM frames are developed. Those parts of the second-Born amplitude which correspond to the Breit amplitude are isolated, and the Breit equation with the electromagnetic Breit interaction is investigated in detail. Corrections to the scattering cross sections which are inversely proportional to the nucleus mass (recoil corrections) are calculated. Numerical results are presented for the particular case of ¹⁶O.     

M X‐ray production cross sections for heavy elements by proton impact

We present in this paper, M‐shell ionization cross sections and M X‐ray production cross sections calculated within the Energy loss, Coulomb deflection, Perturbed Stationary State and Relativistic effects (ECPSSR) theory for elements with 72 ≤ Z ≤ 90 for protons with 0.1–4.0 MeV energy. Our results are compared to the plane wave Born approximation (PWBA) predictions, the relativistic plane‐wave Born approximation including corrections for binding and Coulomb deflection effect (RPWBA‐BC) results and the ECPSSR calculations from earlier works. On the other hand, semiempirical and empirical M X‐ray production cross sections are deduced from the polynomial fitting of the available experimental data collected from different sources. A comparison is made between the different sets of results. The differences between the above calculations and the experimental results are pointed out and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Total toK-shell photoelectric cross section ratios in Zr,Ag, Ta,and Th

Total photon atomic cross sections in elements Zr, Ag, Ta and Th were determined around theirK-edges in the energy region 6 to 400 keV with a good geometry set-up using proportional counter or Ge(Li) detector system. From these values the photoelectric cross sections were obtained by subtracting the theoretical values of coherent and incoherent scattering cross sections. The resulting photoelectric cross sections were fitted to curves above and below theK-edge for each element and extrapolated on either side and the total toK-shell photoelectric cross section ratios were determined with an error not exceeding 2%. The ratios were compared with the theoretical values obtained by Grodstein and others, as also from the empirical relation of Hubbell. The present values show good agreement with those of Scofield. A definite trend of decrease of the ratio as the energy increases is observed in the case of Th unlike in the previous experimental studies.     

Calculation of the photoionization cross sections for the ions of the rubidium isoelectronic sequence by the Dirac-Fock method

The photoionization cross sections for the ground and some excited states of 11 ions of the rubidium isoelectronic sequence from Rb through Ag¹⁰⁺ are calculated by the relativistic Dirac-Fock self-consistent field method. The energy dependence of the photoionization cross sections and the changes in the threshold values along the isoelectronic sequence are considered. The influence of the exchange effect and the choice of gauge on the calculated values of photoionization cross sections is examined. For practical use, the calculated cross sections are approximated by an analytical expression. Along with the total photoionization cross sections, the asymmetry parameter in the angular distribution of photoelectrons and the degree of their polarization are also calculated.     

Relativistic effects in exclusive pd breakup scattering at intermediate energies

The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is achieved by constructing a dynamical unitary representation of the Poincaré group on the three-nucleon Hilbert space. The exclusive breakup reaction at 508 MeV is calculated based on a Malfliet–Tjon type two-body interaction and the cross sections are compared to measured cross sections at this energy. We find that the magnitude of the relativistic effects can be quite large and depends on the configurations considered. In spite of the simple nature of the model interaction, the experimental cross sections are in surprisingly good agreement with the predictions of the relativistic calculations. We also find that although for specific configurations the multiple scattering series converges rapidly, this is in general not the case.     

The study of πd scattering in the (3, 3) resonance region on the basis of three-body relativistic equations

The πd scattering in the (3, 3) resonance region is studied on the basis of three-body relativistic equations. The differential and integral cross sections for the πd scattering are calculated with the use of πN collision matrices defined by fitting phase shifts up to 300 MeV on the one hand, and, alternatively, by the solution of the inverse πN scattering problem on the other. It is shown that (i) the effect of taking fully into account relativistic pion kinematics is of the same order as the multiple scattering effect, (ii) the πd scattering is rather sensitive to the off-shell behaviour of the πN scattering matrix and (iii) the main contribution from the multiple scattering to the cross sections comes from the terms with NN rescattering. A comparison with some experimental data is carried out.     

低能质子引起的金LX射线相对产生截面

对于能量为０．５－１ＭｅＶ的入射质子，在计算中采用ＡｕＬ１次壳层荧光产额的实验值代替相应的Ｄｉｒａｃ－Ｈａｒｔｒｅｅ－Ｓｌａｔｅｒ值时，使用ＲＰＷＢＡ－ＢＣ（经结合能和库仑歪曲修正的相对论平面波玻恩近似）电离截面计算得到的金原子ＬＸ射线相对产生截面与测量值相符。以前报道的对ＲＰＷＢＡ－ＢＣ截面的各种修正都是不需要的     

N‐shell ionization cross sections by proton impact in the BEA

The N‐subshell ionizations cross sections of heavy elements by proton impact have been calculated in the binary‐encounter approximation. The momentum distribution of target electrons is taken into account by the use of the nonrelativistic and relativistic hydrogenic models and the Hartree–Fock–Roothaan and the relativistic Hartree–Fock–Roothaan methods. The obtained subshell ionization cross sections are compared with the experimental data and other theoretical calculations. The electronic relativistic effect and the wave‐function effect on N‐shell ionization cross sections are discussed.     

解相对论Dirac方程计算低能电子弹性散射截面的分波法

本文给出一个基于解相对论Dirac方程计算低能电子弹性散射截面的方法,比较Thomas-Fermi-Dirac(TFD)势及Hartree-Fock(HF)势对散射截面计算的影响,计算了C、Al、Cu、Ag、Au等多种元素在0.01~10keV能量范围的弹性散射截面,比较分析Mott模型、Pendry模型以及屏蔽的Rutherford截面之间的差异。     

Nucleon photoabsorption and quark structure

The electromagnetic excitation of nucleon resonances is stidied discussing retardation effects and relativistic corrections in the integrated photo-absorption cross sections. The retardation effects are calculated using the constituent quark model (CQM), while the relativistic corrections are evaluated in the framework of a bag model with massless quarks. The influence of three-body forces on the theoretical strength is also analyzed.     

Classical and quantum scattering by a Coulomb potential

For relativistic energies the small-angle classical cross section for scattering on a Coulomb potential agrees with the first Born approximation for quantum cross section for scalar particle only in the leading term. The disagreement in other terms can be avoided if the sum of all corrections to the first Born approximation for large enough Coulomb charge contains the classical terms which are independent of that charge. The difference in classical and quantum cross sections may be partly attributed to the fact that the relativistic quantum particle can rush through the field without interaction. We expect that smaller impact parameters and spin facilitate this effect. The text was submitted by the authors in English.     

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.     

Resonant Raman Scattering of synchrotron X-rays by xenon: Test of angular and polarization dependence of RRS

Using monochromatized synchrotron radiation with variable photon energyE _i=33.94keV...34.54keV, Resonant Raman Scattering (RRS) by free Xenon atoms (B _1s=34.566keV) was investigated. The measured double-differential RRS cross sections are in excellent agreement with those calculated in the non-relativistic dipole approximation, modified by some relativistic corrections, and including the interference corrections predicted by Tulkki and Åberg. Within the experimental error of 5 % the RRS cross section is found to be independent of the scattering angle and of the polarization of the incident photons.     

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

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.     

Analisis of inelastic scattering of π-mesons from nuclei within the microscopic optical potential

Cross sections of inelastic scattering of π-mesons from Si, Ni, and Pb nuclei at energy T _lab = 291 MeV are calculated using the distorted wave approximation. The microscopic direct and transition optical potentials are determined by specifying the pion-nucleon scattering amplitude and the nuclear density distribution, where we use the in-medium πN amplitude parameters obtained earlier by analyzing the elastic scattering data for the same nuclei. The cross sections are calculated on the basis of the relativistic wave equation. The deformation parameters of the nuclei are obtained by comparing inelastic scattering cross sections with the appropriate experimental data.