K-Shell ionization by light ions: A graphical comparison of cross sections

Experimental K-shell ionization cross sections from the 1978 compilation by Gardner and Gray, and from some more recent publications, are presented graphically, for projectiles from ¹H up to ¹⁹F. The cross sections were normalized by dividing the experimental results by values obtained with the PWBA theory, corrected for binding, polarization, Coulomb, and relativistic effects, according to Brandt and Lapicki. The normalized cross sections are plotted versus projectile energy or versus the scaled velocity variable ξ. In spite of some obvious discrepancies between different experiments, it is found that almost all the cross sections agree with the corrected PWBA theory within 60%. The majority of those measured with H, He, or Li projectiles are between 30% below and 10% above that theory. Many of the plots versus ξ show small systematic deviations from the theory, within those 60% limits: a minimum at ξ = 0.6, a maximum at ξ = 0.3, and a steep decrease below ξ = 0.2. The last feature might be due to a deficiency of the Coulomb correction.     

Cross sections for L-shell x-ray and Auger-electron production by heavy ions

Experimental cross sections for L-shell x-ray and Auger-electron production by heavy charged particles are tabulated according to projectile energy and atomic number.     

Impact parameter method calculations for fully differential ionization cross sections

In this work, our previous fully differential ionization cross section calculations using the semiclassical, impact parameter method are improved by a new method suitable to calculate impact parameter values corresponding to different momentum transfers. This goal is achieved by two successive steps. First, using the transverse momentum balance different projectile scattering angles are calculated for the binary and recoil peak regions as a function of the transferred momentum. Then, by treating the projectile scattering as a classical potential scattering problem, impact parameters are assigned to these scattering angles. The new method, which no longer contains empirical considerations, is tested calculating by fully differential ionization cross sections for single ionization of helium produced by fast C⁶⁺ ions.     

Measurement of Sc and V K—shell ionization cross sections by slow electron impact

Electron-induced Sc and V K-shell ionization cross sections,which are scarce have been obtained from measurement of KαX-ray emission cross sections at energies from near threshold to 25keV.The influence of substrate of thin targets on ionization cross sections has been corrected using the bipartition model of electron transprot.     

Lower and upper bounds on M-shell X-ray production cross sections by heavy ions

In inner-shell ionization by heavy ions, a significant shift of X-ray lines to the higher energy side and broadening of the peaks indicate that simultaneous multiple ionization of the M and higher shells can dramatically change the values of the atomic parameters. ₁₄Si^3,4+ and ₁₆S^3,4+ ions in the energy range of 5-10 MeV were used to bombard gold (200 μg/cm²) and bismuth (80 μg/cm²) targets. Eight main M X-ray lines have been detected with a Si(Li) detector. Without a possibility for a realistic way to modify the atomic parameters and an accurate extraction of M-subshell ionization cross sections, theoretical cross sections for M-shell ionization are converted to X-ray production cross sections with two extreme choices that presume (i) no multiple ionization and (ii) the certainty that all shells outer to the M-shell are completely ionized in the full multiple ionization. These choices impose the lower and upper limits on theoretical predictions. The X-ray production data should be bracketed by the bounds calculated with any theory. We test this proposition by comparison of the measured cross sections for production of the main X-ray lines and their sum for the total M-shell X-ray production with the predictions of the First Born and ECUSAR [G. Lapicki, Nucl. Instrum. Meth. B 189 (2002) 8] theories in those two extreme limits. With the extreme assumption of no multiple ionization, the First Born approximation shows overall satisfactory agreement with the data while the ECUSAR theory drastically underpredicts our measurements. With the opposite extreme assumption of the full multiple ionization, the ECUSAR exhibits better agreement with the data than the First Born approximation. While neither agreement suggests sure preference for either of these theories, such extreme conversions - as they would have for of any ionization theories - set the lower and upper bounds on their predictions.     

Isoelectronic sequence fits to configuration-averaged photoionization cross sections and ionization energies

Hartree-Fock wave functions have been used to calculate configuration-averaged photonization cross sections and ionization energies for orbitals 1s ⩽ nl ⩽ 5g in He-like through Al-like isoelectronic sequences. The photoionization cross sections have been fitted as a function of the nuclear charge, Z, and photon energy, X, in threshold units, with average error of less than 10%. The ionization energies have been fitted as a function of Z with errors of less than 0.5%.     

Electron excitation cross sections of atomic hydrogen by fully stripped projectile ions

Electron excitation of atomic hydrogen by fully stripped projectile ions (q = 1-8) is theoretically studied by using the boundary corrected continuum intermediate state approximation in the energy range of 20-1000 keV/amu. In this formalism, we have taken a distortion effect produced by the projectile charge. The present computed results for the excited states (n = 2, 3, 4) of hydrogen atom with proton impact is only compared with experiments and other theoretical results. In addition, other results for different charge states (q = 1-8) are displayed in tabular form to get a detail view of contribution from different sub-shells. We have also studied the behavior of saturation of the cross sections which should tend to a constant value as the projectile charge increase.     

K- and L-shell ionization cross sections for protons and helium ions calculated in the ecpssr theory

Ionization cross sections for K and L subshells are tabulated according to target atomic number and incident ion energy. Proton and helium ion energies between 100 keV and 10 MeV and selected targets between C and Am for the K shell and between Ar and Am for the L subshells are used. The cross sections have been calculated in the plane-wave Born approximation (PWBA) with corrections for energy loss (E), Coulomb deflection (C), perturbed stationary state (PSS), and relativistic (R) effects (ECPSSR).     

Triple differential cross section for the ionization of helium by electronic impact

We report results of analytical triple differential cross sections (tdcs) for the single ionization of the helium iso-electronic ions by the electron impact. A two variational parameters wave function is used to evaluate the tdcs. This study shows the accuracy of the tdcs for helium atom and helium like ions in the first Born approximation (fba) at high incident energy domain. The theory is quite acceptable as a fast calculation of the triple differential cross section, particularly at high energies where other theories and methods are cumbersome. A comparison is made of our calculations with previous results of the other theoretical methods and experiment. The fba results obtained here with the two variational parameters wave function are in good agreement with the experiment data at high incident energy. The results show that the electron correlation effects are important around the maxima and influence only the extrema magnitude but not their positions. The calculations presented here are extanded to the cases where the energies of the outgoing electrons are more equal.     

Scattering of protons by hydrogen atoms at low energies: Phase shifts and differential cross sections

Phase shifts and differential cross sections for spin exchange (charge transfer) and total elastic scattering of protons by hydrogen atoms are presented for 36 and 38 values, respectively, of the collisional kinetic energy in the range 0.0001 to 10 eV (center of mass). The phase shifts are tabulated with a precision of six decimal digits. Each cross section is presented as a graph covering the complete angular range from 0 to π radians (in center-of-mass coordinates). The phase shifts were obtained via partial wave analysis within a modified Perturbed-Stationary-States theory by calculations based upon very accurate (nonrelativistic) internuclear potential energies for the 1Sσ_g and 2Pσ_u electronic states of H₂⁺. The cross sections demonstrate a transition from purely quantum behavior at very low energies (<0.1 eV) to semicllssical behavior at higher energies (>1 eV) in which protons scattered by spin exchange are angularly separated from those scattered without exchange. Thus the in-principle unobservable charge-transfer cross section becomes physically measurable at energies greater than about 1 eV.     

Low-energy electron elastic scattering cross sections for excited Au and Pt atoms

Electron elastic total cross sections (TCSs) and differential cross sections (DCSs) in both impact energy and scattering angle for the excited Au and Pt atoms are calculated in the electron impact energy range 0 ? E ? 4.0 eV. The cross sections are found to be characterized by very sharp long-lived resonances whose positions are identified with the binding energies of the excited anions formed during the collisions. The recent novel Regge-pole methodology wherein is embedded through the Mulholland formula the electron-electron correlations is used together with a Thomas-Fermi type potential incorporating the crucial core-polarization interaction for the calculations of the TCSs. The DCSs are evaluated using a partial wave expansion. The Ramsauer-Townsend minima, the shape resonances and the binding energies of the excited Au⁻ and Pt⁻ anions are extracted from the cross sections, while the critical minima are determined from the DCSs.     

L-subshell ionization cross sections of Lu,W, Au,Tl, Pb,Th and U by protons of 0.5—0.9 MeV energy

The L-subshell ionization cross sections for 0.5—0.9 MeV protons on thin Lu, W, Au, Tl, Pb, Th and U targets were extracted from the L X-ray production cross sections. The experimental cross sections were compared with other recent experimental data as well as with the results predicted by the plane wave Born approximation (PWBA) and by the perturbed stationary state theory (PSS) with the relativistic and Coulomb deflection corrections included (CPSSR). Experimental data are, on the average, still about 30% higher than those predicted by the CPSSR theory.     

Electron-impact excitation and ionization cross sections for ground state and excited helium atoms

Comprehensive and critically assessed cross sections for the electron-impact excitation and ionization of ground state and excited helium atoms are presented. All states (atomic terms) with n4 are treated individually, while the states with n5 are considered degenerate. For the processes involving transitions to and from n5 levels, suitable cross section scaling relations are presented. For a large number of transitions, from both ground and excited states, convergent close coupling calculations were performed to achieve a high accuracy of the data. The evaluated/recommended cross section data are presented by analytic fit functions, which preserve the correct asymptotic behavior of the cross sections. The cross sections are also displayed in graphical form.     

Experimental L-shell x-ray production and ionization cross sections for proton impact

Cross sections for L-shell x-ray production and ionization by protons are tabulated according to target atomic number, target type, and incident proton energy. Cross sections for production of the individual L-shell component x-rays and for ionization of the three L subshells are presented separately. Ratios of Lα to Ll x-ray production cross sections are also listed. Literature is covered from 1975 to November 1982. Experimental details pertaining to the cross-section measurements and the theoretical models employed by the experimenters for comparison with their data are included. It is intended that this information will help the reader to ascertain the most reliable cross-section values without recourse to the literature.     

Electron-impact cross sections and rate coefficients for excitations of carbon and oxygen ions

Cross sections have been compiled for electron-impact excitation of carbon and oxygen ions (C II–VI and O II–VIII). A selection has been made to recommend “best” values for use. The resulting recommended values are fitted to an analytical formula and the fitting coefficients are given in a table. The cross sections (in the form of collision strengths) and the rate coefficients calculated therefrom are shown graphically. The reliability of the recommended data is roughly estimated.     

The calculation of radial dose from heavy ions: predictions of biological action cross sections

The track structure model of heavy ion cross sections was developed by Katz and co-workers in the 1960s. In this model the action cross section is evaluated by mapping the dose-response of a detector to gamma rays (modeled from biological target theory) onto the radial dose distribution from delta rays about the path of the ion. This is taken to yield the radial distribution of probability for a "hit" (an interaction leading to an observable end-point). Radial integration of the probability yields the cross section. When different response from ions of different Z having the same stopping power is observed this model may be indicated. Since the 1960s there have been several developments in the computation of the radial dose distribution, in the measurement of these distributions, and in new radiobiological data against which to test the model. The earliest model, by Butts and Katz made use of simplified delta ray distribution functions, of simplified electron range-energy relations, and neglected angular distributions. Nevertheless it made possible the calculation of cross sections for the inactivation of enzymes and viruses, and allowed extension to tracks in nuclear emulsions and other detectors and to biological cells. It set the pattern for models of observable effects in the matter through which the ion passed. Here we outline subsequent calculations of radial dose which make use of improved knowledge of the electron emission spectrum, the electron range-energy relation, the angular distribution, and some considerations of molecular excitation, of particular interest both close to the path of the ion and the outer limits of electron penetration. These are applied to the modeling of action cross sections for the inactivation of several strains of E-coli and B. subtilis spores where extensive measurements in the "thin-down" region have been made with heavy ion beams. Such calculations serve to test the radial dose calculations at the outer limit of electron penetration. We lack data from which to test these calculations in regions close to the path of the ion aside from our earliest work on latent tracks in plastics, though it appears that the criterion then suggested for the threshold of track formation, of a minimal dose at a minimal distance (of about 20 angstroms, in plastics), remains valid.