Calculation Of Ionization Cross Sections Research Articles

Spectres auger et sections efficaces d'ionisation de la couche L 23 du magnésium et de l'aluminium sous impact de protons et d'ions lourds (10–100 keV)

A comparison of Auger structures observed on the energy distributions of secondary electrons emitted from Mg and A1 solid targets bombarded by either light particles (H + and He +) or heavy ions (Ne +, Ar +, …) is presented. With incident protons, it essentially appears a broad peak corresponding to a L 23VV transition and a weak shoulder due to the surface and bulk plasmon excitation. The Auger structures obtained with heavy ions are richer and the peaks which compose it are sharper. Such atomic-like structures correspond to Auger transitions from excited (with one or two L 23 holes) moving recoiling atoms. The experimental L 23 Mg and A1 ionization cross sections were determined from Auger spectra. In H +−Mg (or A1) collisions our results are in good agreement with the theoretical values calculated in a PWBA model. In the case of heavy ion-target interactions, we compared the experimental measurements with ionization cross section calculations obtained in a Landau-Zener model.

Multiphoton ionization spectroscopy: A theoretical analysis of the NO spectrum

The multiphoton ionization spectrum of the NO molecule is described theoretically by calculations of absorption and ionization cross-sections. Both perturbation theoretic (short-time) and rate equation (long-time) descriptions of the stepwise excitation and ionization process are considered. Under the present experimental conditions the two approaches are shown to give qualitatively similar results. Two cases of four-photon absorption are treated: in the first, called a 2+2 process, resonance occurs on absorption of the second photon; and in the second, 3+1 process, resonance occurs at the third photon level. For the wavelength range considered, there is one state, the A 2Σ+, in the former category and six possible choices for the latter. The 2+2 process is shown to have the higher intensity. For most of the resonant states, relative calculated ionization cross sections are in accord with experiment.

Ionizing Collisions of Electrons with Atoms and Molecules

Ionizing collisions of electrons with atoms and molecules are discussed. The calculations of ionization cross sections per unit energy range and its application to the calculation of total ionization cross sections, stopping power, mean energy expended per ion pair and fluoresent efficiency of electrons in the 50 eV--10 keV energy range carried out by Khare and his associates are reviewed. (auth)

Excitation of SnK- andL- and TaL-shell x rays by 1.4-4.4-MeV protons

Excitation functions and absolute cross sections for Sn $K$- and $L$-shell and Ta $L$-shell x-ray production by proton impact have been measured over the energy range 1.4-4.4 MeV with a Si(Li) detector. The results, combined with our measurements on other elements, are compared with existing theories. In the calculation of ionization cross sections from the plane-wave Born approximation, we discuss the effect of a relativistic correction for the ionization potential. The plane-wave Born approximation with the correction due to the Coulomb deflection gives the best fit for Sn $K$ x-ray production and the binary-encounter approximation is the best for Sn $L$ and Ta $L$ x-ray production. The semiclassical approximation based on the impact-parameter treatment predicts values which are not in agreement with the data on Sn $L$ x rays. The scaled universal excitation curve based on the binary-encounter approximation gives good fits to $K$-shell ionizations but seems to show some disagreement for $L$-shell ionizations. The dependence of the $\frac{K\ensuremath{\alpha}}{K\ensuremath{\beta}}$ ratio of Sn on the target thickness was investigated but it was found that the ratio is constant within the experimental uncertainty. Relative intensities for the transitions $L\ensuremath{\alpha}$, $L\ensuremath{\beta}$, $L\ensuremath{\gamma}$, and ${L}_{l}$ are also compared with the theories.

Calculations of Ionization Cross Sections of Small Molecules

Inelastic scattering of an incident electron in an EM can cause the physical disintegration of the specimen. Of all inelastic collisions, an ionizing collision generally leads to molecular dissociation (except maybe in the case of aromatic molecules). Here we outline a method developed to estimate the ionization cross sections of small molecules.

Ionization cross sections and probabilities for removal of2sand2patomic electrons in the binary-encounter approximation

Calculations of ionization cross sections have been performed for removing electrons from $2s$ and $2p$ levels in hydrogenlike atoms by heavy-charged-particle impact using the binary-encounter approximation (BEA). The ratio of $\frac{{\ensuremath{\sigma}}_{{L}_{\mathrm{II}}}}{{\ensuremath{\sigma}}_{{L}_{\mathrm{I}}}}$ is predicted to peak when the projectile has a velocity equal to 0.3 times the velocity of the atomic electron. Experimental values of $\frac{{\ensuremath{\sigma}}_{{L}_{\mathrm{II}}}}{{\ensuremath{\sigma}}_{{L}_{\mathrm{I}}}}$, in agreement with Born predictions, peak at a velocity significantly lower than that predicted by BEA calculations. By transforming to coordinate space in an approximate way, predictions for the impact-parameter dependence are made. In the $2s$ case, the ionization probability has a pronounced local minimum for impact parameters near half the atomic radius, corresponding to a node in the $2s$ wave function. The ionization probabilities for arbitrary charged particles on arbitrary targets may be easily found by applying scaling laws to values tabulated over a wide range of projectile velocities.

Calculations on the e-H cross section by the correlation method using a modified potential

A modofication on the e-H attractive potential is proposed and a study of its effect on the 1s→2s, 1s→2p and ionization cross-section calculations is made. Numerical results are compared with those previously obtained.

Zur formelmäßigen Darstellung des Ionisierungsquerschnitts für den Atom-Atomstoß und über die Ionen-Elektronen-Rekombination im dichten Neutralgas

Thomson's classical theory for the calculation of ionisation cross sections in electron-atom encounters is applied for calculating the ionisation cross section for atom-atom collisions. A very simple formula is obtained permitting a rapid calculation of the total ionisation cross sections as a function of the kinetic energyEa and the massmA of the ionizing atom, and of the binding energyEi and the number ξi of equivalent electrons in the electronic shell to be ionized. The formula is in good agreement with quantum mechanical calculations and with experimental results. It can be applied to ionization from ground and from excited states. From this formula one obtains an expression for the rate coefficient for ionization in the center-of-mass system of the colliding particles. Then, the method of detailed balancing is applied to calculate the rate coefficient for ion-electron three-body collisional recombination with a neutral atom acting as the third body. This latter formula is applicable to recombination into the ground and into excited states.

The ionization of complex ions by electron impact: I. Ionization cross sections for Fe XV and Fe XVI

Second Born and Born-exchange approximations used in calculation of ionization cross sections for Fe XV and Fe XVI

Calculations of the Energy and Angular Distribution of Electrons Ejected from Helium by Protons

Doubly differential cross sections (ddcs), for ejection of secondary electrons of various energies at various angles for helium bombarded by 50- 100-, and 150-keV protons, have been calculated and compared with the recent experimental results of Rudd and Jorgensen. Differential cross sections obtained by integrating the ddcs over all ejection angles are compared with similar results obtained from the experimental ddcs. The wave functions employed by Mapleton to calculate ionization cross sections are used in the Born approximation. General agreement between theory and experiment for the ddcs in found, but discrepancies are noted in the forward and backward directions. The integrated cross sections show good agreement over a large range of ejection energies.

The ionization of H and He + by electron impact

The ionization cross-sections of H and He + from the ground state and excited 2 s state for incident electron energies from threshold to about four times threshold energy are calculated. The strong coupling between the hydrogenic 1 s , 2 s and 2 p states is explicitly allowed for in the initial state, and the final state is taken to be an appropriate combination of Coulomb wave functions of the two outgoing electrons. Comparison with experiment for ground-state ionization shows that the method is an improvement over the Born approximation particularly for He + . New results are presented for the Born approximation in He + ionization and for the Born-Oppenheimer approximation for both H and He + ionization. Finally, conclusions are drawn from the results concerning the validity of methods for calculating ionization cross-sections from excited states.

The cross-section for ionization of O 5+ by electron impact

The calculation of ionization cross-sections is described. For O 5+ a Coulomb-Born-Oppenheimer method is used. Previous calculations for O 4+ with the distorted wave method are corrected and extended. The results are given in tables 1 to 4 and in figure 1. For O 4+ (ionization energy E i — 8·37 x 13·6 eV) the cross-section Q has its maximum at an energy of the incident electron E = 2·3 E i : Q max. = 2·74 x 10 -2 π a 2 0 = 2·42 x 10 -18 cm 2 . For O 5+ ( E i = 10·15 x 13·6 eV) the maximum is at E = 1·85 E i : Q max. = 0·97 x 10 -2 π a 2 0 = 0·86 x 10 -18 cm 2 . The corresponding reduced cross-sections Q red. = ( E i /13·6 eV ) 2 x Q /Kζπ a 2 0 ) are for O 4+ (ζ = 2): Q red. = 0·96, and for O 5+ (ζ = 1): Q red. = 1·00. The results are similar to those of Rudge & Burgess (1962) for hydrogenic ions.