Inner-shell Ionization Cross Sections Research Articles

Multiple ionization and capture in relativistic heavy-ion atom collisions

We show that in relativistic heavy-ion collisions the independent electron model can be used to predict cross sections for multiple inner-shell ionization and capture in a single collision. Charge distributions of 82- to 200-MeV/amu Xe and 105- to 955-MeV/amu U ion beams emerging from thin solid targets were used to obtain single- and multiple-electron stripping and capture cross sections. The probabilities of stripping electrons from the K, L, or M shells were calculated using the semiclassical approximation and Dirac hydrogenic wave functions. For capture, a simplified model for electron capture was used. The data generally agree with theory.

Multiple ionization in relativistic heavy-ion-atom collisions.

We show that in relativistic heavy-ion collisions the independent-electron model can be used to predict cross sections for multiple inner-shell ionization in a single collision. Charge distributions of 430- and 955-MeV/amu ${\mathrm{U}}^{90+}$, ${\mathrm{U}}^{89+}$, ${\mathrm{U}}^{83+}$, and ${\mathrm{U}}^{68+}$ beams emerging from thin solid targets were used to obtain single- and multiple-electron stripping cross sections. The probabilities of stripping electrons from the K, L, or M shells were calculated using the semiclassical approximation and Dirac hydrogenic wave functions. The data generally agree with theory. An influence of the Auger effect is seen in ${\mathrm{U}}^{68+}$ collisions.

Description of the polarization effect in inner-shell ionization via a variational perturbed stationary state.

A one-parameter, polarized, variational wave function, correlated to a projectile, is described and used as the initial state in calculations of inner-shell excitation probabilities and ionization cross sections for collisions with heavy charged particles. The Rayleigh-Ritz variational principle is used to determine the parameter. The minimized energy gives the binding effect as a function of projectile position. Existing computer codes can be adapted to incorporate the variational wave function. Early treatments of polarization as a negative binding effect give results remarkably similar to the new ones. The new results do not show the abrupt cessation of the polarization effect caused by the use of an impact-parameter cutoff in the original description. The polarization of the wave function does not give a negative binding effect. Agreement with measured K-shell ionization cross sections is improved.

Coulomb effect and threshold effect in electronic stopping power for slow protons.

We show how the electronic stopping power for slow protons is influenced by the deceleration and deflection of the projectile in the field of the target nucleus (Coulomb effect) and by the fact that in insulators a finite energy is also required for excitation of the outermost electrons (threshold effect). Estimates are derived from the Fermi-Teller description of the stopping process, from a modified local-density approximation, and from measured inner-shell ionization cross sections. It is found that the introduction of an energy threshold reduces at low energies the stopping cross section by a large factor and hence leads to an appreciable deviation from ${v}_{1}$ proportionality.

Measurement of Carbon/Metal Ratio in a Single Grain of Nonstoichiometric Titanium Carbide

The carbon/metal ratio, x, was measured at several points in a single grain ofTiCx 1 μm in diameter in a nickel-bonded composite, TiC /Ni-Mo, by electron energy loss spectroscopy. Cross sections for inner-shell ionization of Ti and C were taken from elemental film values. A value of x=0.81 ±0.02 was obtained at the center of the grain. This result is significant for interpreting mechanical properties of the material, as they should depend on x.

Electronic Relativistic Effect in Inner-Shell Ionization Cross Section and Electron Momentum Distribution

The inner-shell ionization cross section by charged-particle impact is expressed in the form of the momentum distribution of the target electron. Based on this approximation, the correction factor for the electronic relativistic effect is obtained as the ratio of the relativistic to nonrelativistic momentum distribution at the momentum corresponding to the minimum momentum transfer in the ionization process. It is found that for K -, L 1 - and L 3 -shell ionization cross sections the correction factor obtained from the momentum distribution is in good agreement with the exact relativistic calculation.

Application of relativistic electrons for the quantitative analysis of trace elements

Particle induced X-ray emission methods (PIXE) have been extended to relativistic electrons to induce X-ray emission (REIXE) for quantitative trace-element analysis. The electron beam (20 ≤ E 0≤ 70 MeV) was supplied by the Darmstadt electron linear accelerator DALINAC. Systematic measurements of absolute K-, L- and M-shell ionization cross sections revealed a scaling behaviour of inner-shell ionization cross sections from which X-ray production cross sections can be deduced for any element of interest for a quantitative sample investigation. Using a multielemental mineral monazite sample from Malaysia the sensitivity of REIXE is compared to well established methods of trace-element analysis like proton- and X-ray-induced X-ray fluorescence analysis. The achievable detection limit for very heavy elements amounts to about 100 ppm for the REIXE method. As an example of an application the investigation of a sample prepared from manganese nodules — picked up from the Pacific deep sea — is discussed, which showed the expected high mineral content of Fe, Ni, Cu and Ti, although the search for aliquots of Pt did not show any measurable content within an upper limit of 250 ppm.

Characteristic x-ray production by electron bombardment of argon, krypton, and xenon from 4 to 10 keV

As part of an experiment to study atomic-field bremsstrahlung produced by electron bombardment of rare-gas atoms in the 4- to 10-keV energy range, we have determined the characteristic x-ray production cross section for the $K$ shell of argon and the $L$ shells of krypton and xenon. We compare our results for the inner-shell ionization cross section with the Bethe theory, the plane-wave Born approximation of McGuire, and the classical binary encounter theory as well as with previous experiments. Using the observed validity of classical scaling over this energy range, and the known average $K$-shell fluorescence yield for argon, we have determined the average $L$-shell fluorescence yield for xenon and krypton.

K-Shell Vacancy Production in Light-Element Atoms with α Particles and N7+ Ions of 5,6, and 7 MeV/amu

K-shell ionization cross sections of five elements in the range from Ca to Cr have been measured for α-particle and N 7+ -ion bombardments at projectile energies of 5, 6 and 7 MeV/amu. Contributions from the binding energy effect, the polarization effect and the electron transfer effect to these inner-shell ionization are investigated. From the ( Z p / Z s )-dependence of the inner-shell ionization cross section, where Z p is the projectile charge and Z s is the effective atomic number of target atoms, it is found that the binding energy effect and the polarization effect cancel out each other in the present impact-energy region and the charge-transfer cross section is proportional to ( Z p / Z s ) 5 .

Energy-loss effect in inner-shell Coulomb ionization by heavy charged particles

The influence of the energy loss of slow projectiles during inelastic collisions on the inner-shell ionization cross sections is treated analytically. The result agrees with available experimental cross sections for $K$-shell ionization by protons. Residual trends in the data may gauge the quality of wave functions employed in calculations of Coulomb ionization cross sections.

Sum-rule-constrained classical binary-collision model for inner-shell ionizations

A model calculation of cross sections for inner-shell ionization by electrons is described. This model is based on the classical binary-collision model and modified with the application of several sum rules. It is found that the model predicts quite accurately generalized oscillator strengths and cross sections for inner-shell ionization of atoms. A comparison is made with experiment and other theoretical results.

Coulomb-deflection effect in inner-shell ionization by heavy charged particles

K-shell x-ray production cross sections were measured for /sub 28/Ni(K) in collision with /sup 1//sub 1/H ions of kinetic energies 55 to 300 keV, /sup 2//sub 1/H ions of 100 to 300 keV, and /sup 4//sub 2/He ions of 200 to 300 keV; for /sub 46/Pd(K) with /sup 1//sub 1/H ions of 215 to 300 keV, and for /sub 47/Ag(K) with /sup 1//sub 1/H ions of 200 to 300 keV. L-shell x-ray cross sections were measured for /sub 47/Ag(L) in collision with /sup 1//sub 1/H ions of kinetic energies 35 to 300 keV, with /sup 2//sub 1/H ions of 60 to 300 keV, with /sup 4//sub 2/He ions of 110 to 300 keV, and for /sub 79/Au(L) with /sup 1//sub 1/H ions of 140 to 300 keV. The collisions conditions were such that the effect of the projectile energy loss during the ionizing collision became significant for the K-shell ionizations, but remained unimportant for the L-shell ionizations. The measurements extend the experimental range of the Coulomb-deflection variable dq/sub 0S/ over previous measurements for the shells S=K by a factor of approx.1.2, and for S=L by a factor of approx.2. This permits a decisive test of current theories for the effectmore » of the deflection of the projectile in the Coulomb field of the target nucleus on inner-shell ionization cross sections.« less

Effects of coulomb repulsion in the inner-shell ionization cross-section by protons, deuterons and alpha-particles

A critical survey has been made of the currently accepted BEA theory for inner-shell atomic-ionization processes. This review has led to the introduction of an effective ion energy which accounts for the slowing-down of the ion in the nuclear Coulomb field. The effect of the ion deflection, also due to the nuclear Coulomb field, is analysed. Relativistic effects in the collision of ions withK-shell electrons have been taken into account. A tentative qualitative explanation for the experimentally observed nonexistence of a threshold energy for ionization is given in the framework of the BEA theory. Ionization cross-sections for Rb, Sr, Zr, Cd, In, Sb, W by protons in the energy range from 500 keV to 3 MeV have been measured. Also measurements of ionization cross-sections by deuterons in the energy range from 800 keV to 2.6 MeV on Rb, Sr, Zr, Cd, Sb and by He ions in the energy range from 1.4 MeV to 2.8 MeV on Cd and Sb have been performed. Results are compared with those of other authors and in the context of the corrections introduced in the BEA theory.

Fitted inner-shell proton ionization cross sections from Ca to Sn for 0.2–2 MeV incident energy

Experimental proton ionization cross section values pertaining to all elements from Ca to Sn at various incident energies in the range 0.2–2 MeV are fitted to an empirical law in an attempt to obtain a set of “most reliable” values to be used in PIXE analysis and in comparisons with theory. A theoretical justification based on the results of the PWBA and BEA models is given. Results are presented in a table for various incident energies and a method of interpolation to obtain values at energies intermediate to those tabulated is suggested.

Electron capture from inner shells by fully stripped ions

Cross sections for electron capture from inner atomic shells by fully stripped ions, of velocities high compared to the electron velocities in the inner-shell orbits, are calculated in the second Born approximation. The theory of Drisko for electron capture by protons from hydrogen is generalized to projectiles and targets of arbitrary atomic numbers ${Z}_{1}$ and ${Z}_{2}$, respectively. For ions of low velocity, the effects of binding and Coulomb deflection are accounted for in a manner similar to that of Brandt and his co-workers in the theory for direct ionization to the continuum of the target atom. The results are in good agreement with experimental capture cross sections, whereas the Oppenheimer-Brinkman-Kramers approximation overestimates such cross sections. The contribution of electron capture to inner-shell ionization cross sections increases with increasing $\frac{{Z}_{1}}{{Z}_{2}}$ and brings them into agreement with experiment.

Minima in generalized oscillator strengths for initially excited hydrogen-like atoms

Generalized oscillator strengths for transitions from an initially excited state of a hydrogenic atom to final states (either discrete or continuum) have complicated structures, including minima and shoulders, as functions of the momentum transfer. Extensive calculations reveal certain systematics of these structures. Some implications of the minima to the energy dependence of the inner-shell ionization cross section of heavy atoms by proton impact are discussed.

Inner-shell ionization by electrons in the 300–600 keV region

A measuring set-up at a Cockcrof—Walton accelerator is described for the determination of electron impact inner-shell ionization cross-section detecting the X-rays by Si(Li) solid-state detector. The K-shell electron impact ionization cross-sections for Ag in the region from 300 to 600 keV were determined and compared with the earlier experimental and the calculated theoretical values.

Glauber cross sections for inner-shell ionization in multielectron targets by electron impact

Total cross sections for $K$-shell ionization of the ground state of multielectron targets by electron impact have been computed using the single-particle Glauber approximation. Various hydrogenic product wave functions are used to describe both the bound and continuum electron. Projectile-target electron exchange effects are simply approximated by limiting the region of integration over ejected electron momenta so as to avoid double counting. Using this exchange approximation and choosing reasonable effective charges initially and finally for the target, agreement is obtained with existing helium data at projectile energies above 100 eV. The effects of changing various parameters are shown and discussed, and comparisons are made with Born approximations. For $Zg3$ differences between our Glauber and Born total cross sections are small.

Abstract: Cross sections for ionization of inner-shell electrons by electron impact

Auger electron spectroscopy (AES) has been used extensively for qualitative surface analyses in recent years. There have, however, been relatively few attempts at quantitative surface analyses on account of lack of knowledge of key parameters (such as electron attenuation lengths, inner‐shell ionization cross sections, and backscattering factors) as a function, where appropriate, of material, incident electron energy, Auger electron energy, and instrumental characteristics. A review of experimental electron attenuation length data in the energy range relevant to AES and to x‐ray photoelectron spectroscopy (XPS) was given in a previous paper1 together with a method to predict attenuation lengths in other materials. We give a summary here of an analysis2 of available data concerning cross sections for ionization of inner‐shell electrons by electron impact. Cross‐section data of this type is also required in correction procedures for quantitative analysis by electron probe microanalysis.3 necessity the analy...

X-ray production cross sections, intensity ratios, and centroid energy shifts ofAg KandLandAu Lx rays produced byO16beams of 12-50 MeV

The 12-50-MeV $^{16}\mathrm{O}$ beam-induced $K$ and $L$ x rays of Ag and the $L$ x rays of Au from thin targets were studied with a Si(Li) detector. Absolute $K$ and $L$ x-ray production cross sections were derived from measured x-ray yields and compared to available theoretical calculations for inner-shell Coulomb ionization cross sections. Inclusion of Coulomb repulsion, binding, and ${(\frac{{Z}_{1}}{{Z}_{2}})}^{3}$ effects in the plane-wave Born-approximation calculations gives good agreement with experimental values of ${\ensuremath{\sigma}}_{\mathrm{KX}}$ for Ag. The agreement between theory and experiment for $L$-shell ionization is not as good, possibly owing to the effects of multiple ionization on the fluorescence yield, although the energy dependence of ${\ensuremath{\sigma}}_{\mathrm{LX}}$ for Au is well reproduced. The energies of the $\mathrm{Ag} K \ensuremath{\alpha}$ and $K \ensuremath{\beta}$ and $\mathrm{Au} L \ensuremath{\alpha}$, $L \ensuremath{\beta}$, and $L \ensuremath{\gamma}$ lines were observed to change with beam energy as did the intensity ratios of these lines. HFS calculations for the $\mathrm{Ag} K \ensuremath{\alpha}$ and $K \ensuremath{\beta}$ lines indicate that the observed shifts are probably associated with multiple $M$-, not $L$-, shell ionization.