Estimation of backscattering factor for low atomic number elements and their alloys

The single elastic scattering theory of Everhart was adapted to determine the angular and energy distribution of electrons backscattered from low atomic number solid materials (Z < 40–45). This distribution and the classical ionization cross-section expression of Gryziński were used in the calculations of the backscattering factor, r, in quantitative AES analysis. The values of r were found to be in reasonable agreement with the results of the Monte Carlo calculations and the existing experimental data. Everhart's theory was extended for the case of mixtures, and that made possible the determination of the backscattering factor for binary alloys. It was found that neglecting the concentration dependence of r in quantitative AES analysis apparently enriches the surface with the component having the lower atomic number. The experimental data on surface composition of binary alloys measured by AES are discussed in view of the presented theory.     

Effect of focusing of primary electrons on their reflection from a crystal and on the associated Auger emission

The orientational dependence for different groups of secondary electrons — quasi-elastically scattered, inelastically reflected with excitation of a plasmon and with ionization of the core level M _4.5, and the Auger electrons M _4.5 VV — are measured in the primary electron energy range 0.6–1.5 keV. The data are obtained for a Nb (100) single crystal by varying the azimuthal angle of incidence of the primary beam, with complete collection of secondaries. A relationship is established between the processes of focusing and defocusing of the electrons that have penetrated into the crystal in the 〈110〉 and 〈133〉 directions, which differ substantially in the atomic packing density. Specific details of the Auger orientation effect, due to the focusinginduced variation of the flux density of the reflected electrons, are identified and explained. The contributions, both of anisotropy of ionization of the core level and of variation of the backscattering intensity, to the angular dependence of Auger emission and reflection with ionization loss are estimated. The possibilities of using such orientational dependences for an element-sensitive analysis of the local atomic structure of surfaces are assessed. Zh. Tekh. Fiz. 67, 117–123 (August 1997)     

Cross sections for single and double ionization of atomic helium under impact by fast multiply charged ions

Expressions for the cross sections for single and double ionization of atomic helium in collisions with fast multiply charged ions are obtained in the collision parameter range υ ²≫Z≳υ, υ ₀<c, where Z and υ are, respectively, the ion charge and ion velocity, υ ₀ is the characteristic velocity of electrons in the atomic helium ground state, and c is the velocity of light. Zh. Tekh. Fiz. 68, 1–7 (March 1998)     

Contribution of backscattered electrons to the total electron yield produced in collisions of 8–28 keV electrons with tungsten

It is shown experimentally that under energetic electron bombardment the backscattered electrons from solid targets contribute significantly (∼80%) to the observed total electron yield, even for targets of high backscattering coefficients. It is further found that for tungsten (Z = 74) with a backscattering coefficient of about 0.50, about 20% of the total electron yield is contributed by the total secondary electrons for impact energies in the range of 8–28 keV. The yield of true backscattered electrons at normal incidence (η ₀), total secondary electrons (δ) and the total electron yield (δ _tot) produced in collisions of 8–28 keV electrons with W have been measured and compared with predictions of available theories. The present results indicate that the constant-loss of primary electrons in the target plays a significant role in producing the secondary electrons and that it yields a better fit to the experiment compared to the power-law.      

Investigation of the passage of 100–1000-MeV/nucleon superheavy ions through homogeneous media

This work is a continuation of the experimental and theoretical investigations of the effect of the Z ₁ ³ correction to the stopping power of ions on the passage of heavy ions ⁴⁰Ar, ⁵⁶Fe, ¹⁹⁷Au, ¹³¹Xe, and ²³⁸U with energies of about 1 GeV/nucleon through a homogeneous medium. The previously observed systematic deviations of the calculations based on the first Born approximation to the scattering of a particle by the atomic electrons in the medium from the experimental values of the total ionization ranges of the nuclei and their stopping powers is confirmed. The discrepancy increases with the atomic number of the projectile nucleus. It is shown that the Z ₁ ³ correction in the form proposed by Jackson and McCarthy eliminates, especially for ions with Z ₁>50, the systematic discrepancy between the computed and experimental values. For the experimental energy range relativistic Mott scattering of a particle by the atomic electrons in the target makes the dominant contribution to the observed Z ₁ ³ effect. Zh. éksp. Teor. Fiz. 115, 404–415 (February 1999)     

Role of the electron forward-focusing effect in the formation of Kikuchi patterns of single-crystal silicon

Kikuchi patterns produced by quasi-elastic backscattering of electrons with energies of 0.6–2 keV from a thin Si(111)7×7 near-surface layer are studied. It is shown that experimental data obtained for silicon, just like those for metals, can be described satisfactorily by calculations made in single-scattering cluster approximation, as well as in terms of a model taking phenomenologically into account the forward-focusing of backscattered electrons as they escape from the crystal. It has thus been demonstrated that the forward-focusing effect at an energy E=2 keV plays a dominant role in the formation of Kikuchi patterns, which permits their use for visualization of the atomic structure of a surface. The dependences of the focusing efficiency on the parameters of the atomic chains along which electrons propagate have been established for the closest-packed crystal directions. Fiz. Tverd. Tela (St. Petersburg) 39, 752–757 (April 1997)     

Annihilation of a relativistic positron and K-electron to yield a photon and second K-electron

We study the annihilation of a fast positron and a K-electron resulting in the emission of a photon and a second K-electron. It is assumed that all electrons and positrons move in the Coulomb field of the nucleus and that the Coulomb parameter αZ is much less than unity (α=1/137 is the fine-structure constant and Z is the atomic number). The electron-electron interaction, which is responsible for the ejection of the electron by the atom, is taken into account in the first order of perturbation theory. We calculate the differential and total cross sections of the process and construct the ratio of the cross sections of double and single ionization as a function of the energy of the incident positron. Finally, we establish the high-energy limit of this ratio, equal to 0.34/Z ². Zh. éksp. Teor. Fiz. 113, 786–804 (March 1998)     

X-ray converters for radiation treatment of thin films

The energy absorbed in thin films of selected materials bombarded by x rays emitted in the braking of low-energy electrons (E ₀<500 keV) in converters with various atomic numbers (Z=29–73) is calculated by the Monte Carlo method. The program takes into account both of the K-shell ionization mechanisms that lead to emission of characteristic photons as a result of electron impact and as a result of the photoelectric effect, and the characteristic radiation is shown to make a large contribution to the absorbed energy in thin films. Calculations show that the proper choice of material and thickness of the converter affords a two-to fivefold increase in the energy of the x radiation absorbed in thin films of semiconductor materials. Zh. Tekh. Fiz. 68, 99–101 (November 1998)     

Double atomic photoeffect in the relativistic domain: Angular and energy distributions of photoelectrons

We study the double ionization of the atomic K-shell by a single photon in the relativistic energy domain. The differential and total cross sections of the process are calculated. It is shown that the ratio of the cross sections of double and single ionization increases with the photon energy, tending to the limit 0.34/Z ², where Z is the atomic number or the nuclear charge. The formulas are found to be valid for Z≫1 and αZ≪1, where α=1/137 is the fine-structure constant. Zh. éksp. Teor. Fiz. 114, 1537–1554 (November 1998)     

Albedo factors of 279, 320, 511 and 662 keV backscattered gamma photons

The backscattered peak and albedos are important for the estimation of exposure distribution and for better understanding the phenomenon of the backscattering of gamma photons. To characterize the backscattering probability of gamma photons interacting with different atomic numbers (Z), number (A _N), energy (A _E) and dose (A _D) albedos are experimentally evaluated. The response function converts the observed pulse-height distribution of a NaI(Tl) scintillation detector to a true photon spectrum. For each of the incident gamma photon energies, the number and energy albedos show an increase with the increasing target thickness, and finally saturate. The energy albedos are found to be decreasing with the increase in the atomic number of the target material and incident gamma photon energy. The dose albedos do not differ significantly from the energy albedos for the chosen incident gamma photon energies.     

Electrical conductivity of germanium with dislocation grids

Samples of n-type germanium with a donor concentration N _d=2.4×10¹⁶ cm⁻³ are plastically deformed to a degree of strain equal to 18–40% to detect static conduction by electrons trapped on dislocations in a system of dislocation grids. In samples with 20%<δ<31%, which retain an electronic type of conductivity, the conductivity for T<8 K, which is weakly temperature-dependent, is associated with conduction by electrons trapped on dislocations. The nonmonotonic dependence of the conductivity at 4.2 K on the degree of strain as the latter increases from 18% to 40% attests to the existence of an energy gap between the donor and acceptor dislocation states in strongly plastically deformed germanium. Zh. éksp. Teor. Fiz. 115, 115–125 (January 1999)     

Spin-orbit coupling constant and <r −3> in transuranic ions

The spin-orbit coupling parameter ζ, the quantum average <r ^?3>, and binding energy ? E for atomic number Z = 92, 94, 96 and net ionic charge approximately 1 and 5, have been calculated for the 5f electrons. The potential assumed in the one-electron wave function calculation is that given by the Thomas-Fermi model of a positive ion.

It is shown that the ratio ζ/<r ^?3> is fairly insensitive to changes in the surroundings of the ion, and can be used for estimating one of the parameters with the experimental value of the other.

The 5g electrons are shown to be effectively free in the considered range of Z and n.

The behaviour of the wave function as a function of n and Z is discussed.     

Electron shake process following inner‐shell ionization

Electron shakeup and shakeoff probabilities accompanying inner‐shell ionization of atoms were calculated for K‐, L‐ and M‐shell electrons using hydrogenic wavefunctions. The dependence of shake probabilities on atomic number Z is estimated. It is found that both shakeoff and shakeup probabilities are proportional to 1/Z². Based on this Z‐dependence, the shakeup‐plus‐shakeoff probabilities are expressed in a simple analytical form with two parameters. Copyright © 2004 John Wiley & Sons, Ltd.     

K-shell ionization of atoms and ions by relativistic projectiles

We evaluate the total cross section for the single K-shell ionization of atoms and ions by the impact of relativistic electrons. The study is performed to leading orders of the QED perturbation theory with respect to the parameters αZ and 1/Z. The results obtained are in good agreement with experimental data for different atomic targets. In the case of moderate values of the nuclear charge Z, the total cross section is described by a simple analytic formula. The K-shell ionization by relativistic heavy particles is also considered.     

On the role of correlation energy produced by the spin-spin interaction in the formation of binding energy for two-electron atomic systems

An algorithm is proposed for computing the correlation energy produced by the spin-spin interaction V _SS of electrons in He-like atomic systems. The algorithm takes into account the singular nature of V _SS and the formation of a compact finite motion of electrons in the range of distances Ze ²/mc ² < r ₁₂ < ħ/mc between the electrons under the action of the magnetic fields of spins for a singlet ground state. Good agreement with experimental values of the ionization potential is attained for a wide set of two-electron atomic systems without resorting to variational procedures, but only using hydrogen-like wavefunctions and correctly taking into account the singular nature of the spin-spin interaction of electrons.     

Influence of photo and Auger electrons of the elements with high atomic numbers on formation of carbon x‐ray fluorescence intensity

The x‐ray fluorescence radiation of carbon was studied in the presence of elements with high atomic numbers in the material irradiated. It was found that photo and Auger electrons of such elements originating from ionization of shells remote from nucleus (L‐, M‐ and N‐shells) effectively excite atoms of carbon. Hence, using a matrix with Z > 30, the influence of the electrons should be considered, and using a matrix with Z > 50 this influence becomes decisive. Calculations of carbon x‐ray fluorescence intensity were executed for different x‐ray tube anodes. Their correctness is confirmed by agreement with experimental results. Copyright © 2005 John Wiley & Sons, Ltd.     

Measurement of the bremsstrahlung spectra generated from thick targets with <Emphasis Type="Italic">Z</Emphasis>=2–78 under the impact of 10 keV electrons

We present new experimental data on thick target bremsstrahlung spectra generated from the interaction of energetic electrons with bulk matter. The ‘photon yields’ in terms of double differential cross-sections (DDCS) are measured for pure elements of thick targets: Ti (Z = 22), Ag (Z = 47), W (Z = 74) and Pt (Z = 78) under the impact of 10 keV electrons. Comparison of DDCS obtained from the experimental data is made with those predicted by Monte-Carlo (MC) calculations using PENELOPE code. A close agreement between the experimental data and the MC calculations is found for all the four targets within the experimental error of 16%. Furthermore, the ratios of DDCS of bremsstrahlung photons emitted from Ag, W and Pt with those from Ti as a function of photon energy are examined with a relatively lower uncertainty of about 10% and they are compared with MC calculations. A satisfactory agreement is found between the experiment and the calculations within some normalizing factors. The variations of DDCS as a function of Z and of photon energy are also studied which show that the DDCS vary closely with Z; however, some deviations are observed for ‘tip’ photons emitted from high Z targets.     

Light element depth distribution by the intensity ratio of incoherent and coherent scattering

A method is proposed for analyzing the distribution of elements with a small atomic number Z < 9 over the depth of the substrate. The method is based on measuring the ratio of incoherent and coherent scattering peaks intensities at different exit angles of X-rays from the sample surface. Varying the beam exit angle at a constant scattering angle makes it possible to vary the depth of radiation penetration into the sample by almost two orders of magnitude and, correspondingly, to vary the information averaging zone. Mathematically, the method reduces to the numerical solution of integral equations of the first kind, in which the impurity distribution profile is given by the model function. Experimental measurements were performed on model samples of beryllium (Z = 4) and aluminum (Z = 13) foils and real coatings of boron (Z = 5) and titanium nitride. The adequacy of the received solutions to the certified characteristics is shown.     

Electron-pair densities of group 2 atoms in their and terms

Electron-pair intracule (relative motion) and extracule (center-of-mass motion) densities are studied in both position and momentum spaces for the ¹ P and ³ P terms of the group 2 atoms Be (atomic number Z =4), Mg (Z =12), Ca (Z =20), Sr (Z =38), Ba (Z =56), and Ra (Z =88). In position space, the ¹ P - ³ P difference in the intracule densities shows that the probability of a small interelectronic distance is larger in the triplet for all the six atoms, as reported for the lightest Be atom in the literature. The position-space extracule density clarifies that the triplet electrons are more likely to be at opposite positions with respect to the nucleus than the singlet electrons for all the atoms. In momentum space, the singlet generally has a larger probability of a small relative momentum between two electrons as a na?ve manifestation of the Fermi hole in the triplet. The extracule density in momentum space shows that the ¹ P term has a distribution larger in a large center-of-mass momentum region than the ³ P term. Received: 26 August 1998 / Received in final form: 1 February 1999     

Hot-electron-pumped K-shell X-ray laser

Amplified spontaneous inner-shell emission produced via an ultrafast burst of high-energy electrons from a femtosecond laser-produced plasma is proposed as a novel electron-pumped x-ray laser. In this scheme, a population inversion of the upper laser level is created via impact ionization of atomic inner shells by electron bombardment. Based on the requirement of a positive gain coefficient for amplifying spontaneous K _α line emission, a simple pumping threshold is found for the incident electron flux, and feasibility of the scheme is assessed for a range of low-Z elements. Published in English in the original Russian journal. Edited by Steve Torstveit. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 10, 771–776 (25 May 1998)