Plane-wave Born Cross Sections Research Articles

Scaled plane-wave Born cross sections for atoms and molecules

Electron-atom and electron-molecule collisional cross sections are needed in the modeling and understanding of phenomena ranging from planetary atmosphere science to industrial applications of plasmas. This article reviews the Born approximation and phenomenological scaling approaches that provide accurate excitation cross sections over a range of electron impact energies. The methods are illustrated for a variety of atomic and molecular systems.

Scaling of plane-wave born cross sections for positron-impact excitations of He and H2

The scaling method applied to the plane-wave Born cross sections using electron-impact excitation of atoms (Y. Kim, Phys. Rev. A 64, 032713 (2001)) was modified for positron-impact excitations of atoms and molecules. The scaling method presented earlier using electrons as particles of incidence offers a simple yet effective tool to calculate such cross sections. We will consider here the scaling for positron scattering with relatively small amount of computational effort. The scaling Born method proposed depends on two atom (molecule) properties as the values of positronium energy and excitation energy. Numerical examples of integral inelastic cross sections of He (21P, 31P, and 41P) and H2(X1∑g+ -> B1 ∑u+) states using the new analytical representation are presented to illustrate the applicability of the improved scaling Born method for positron scattering.

An investigation of the scaling of plane-wave born cross sections for positron-H2 considering the positronium-formation channel

Cross sections for positron-H2 scattering using positronium formation have been studied using the scaled plane-wave Born approximation, originally proposed by Kim [Y. K. Kim, Phys. Rev. A 64, 032713 (2001)] for electron scattering. The modified scaling for positron scattering is simpler than the scaling for electron scattering. Moreover, the former converts the present first Born approximation into accurate results comparable to the convergent close coupling results. Comparisons to available theoretical and experimental data on positron-H2 scattering are presented.

Ionisation of phosphorus, arsenic, antimony, and bismuth by electron impact

Total ionization cross sections of neutral phosphorus, arsenic, antimony, and bismuth atoms by electron impact are reported and compared to the only available experimental results by Freund et al. [Phys. Rev. A 41, 3575 (1990)]. These calculations take into account the possibilities that some target atoms used in the experiments were in metastable states close to the ground state, the excitation-autoionization of nsnp4 excited states may be substantial, and the ions produced in experiments may be in excited, low-lying metastable states. The cross sections for direct ionization calculations are based on the BEB model by Kim and Rudd [Phys. Rev. A 50, 3954 (1994)]. Plane-wave Born cross sections scaled by the method developed by Kim [Phys. Rev. A 64, 3954 032713 (2001)] are used to determine the contributions from excitation-autoionization. The combination of the BEB model and the scaled Born cross sections is in agreement with the experimental data by Freund et al. These theoretical data are useful to experimentalists and can be used to complete data tables needed for plasma or astrophysical studies.

Scaled Born cross sections for excitations of H2 by electron impact

This article describes the scaling of plane-wave Born cross sections for the excitation of the H(2) molecule to four low-lying electronic states (B (1)Sigma(u) (+), C (1)Pi(u), B(') (1)Sigma(u) (+), and D (1)Pi(u)) by electron impact. The same BE and BEf scaling methods used on atoms were found to be equally effective for H(2) in converting Born cross sections into cross sections in good agreement with available experiments. These scaling methods are applicable only to dipole-allowed excitations. The possibility of using these scaling methods, as was done in atoms, to estimate the contribution of inner-shell excitations to the total ionization cross section via the excitation-autoionization mechanism is discussed, though this type of indirect ionization in molecules is not as common as in atoms.

Electron-Impact Cross Sections for Ground State to np Excitations of Sodium and Potassium.

Cross sections for electron impact excitation of atoms are important for modeling of low temperature plasmas and gases. While there are many experimental and theoretical results for excitation to the first excited states, little information is available for excitation to higher states. We present here calculations of excitations from the ground state to the np levels of sodium (n = 3 through 11) and potassium (n = 4 through 12). We also present a calculation for a transition from the excited sodium level 3p to 3d to show the generality of the method. Scaling formulas developed earlier by Kim [Phys. Rev. A 64, 032713 (2001)] for plane-wave Born cross sections are used. These formulas have been shown to be remarkably accurate yet simple to use. We have used a core polarization potential in a Dirac-Fock wave function code to calculate target atom wave functions and a matching form of the dipole transition operator to calculate oscillator strengths and Born cross sections. The scaled Born results here for excitation to the first excited levels are in very good agreement with experimental and other theoretical data, and the results for excitation to the next few levels are in satisfactory agreement with the limited data available. The present results for excitation to the higher levels are believed to be the only data available.

Ionization of carbon, nitrogen, and oxygen by electron impact

Total ionization cross sections of neutral carbon, nitrogen, and oxygen atoms by electron impact are presented. In our theory we have included the possibilities that (a) some target atoms used in an experiment were in metastable states close to the ground state, (b) excitation-autoionization of ${2s2p}^{m}$ exited states may be substantial, and (c) ions produced in experiments may be in excited, low-lying metastable states. The binary-encounter Bethe (BEB) model of Kim and Rudd [Phys. Rev. A 50, 3954 (1994)] is used to calculate the cross sections for direct ionization. Plane-wave Born cross sections scaled by the method developed by Kim [Phys. Rev. 64, 032713 (2001)] are used to determine the contributions from excitation-autoionization. A sum of the BEB cross sections for direct ionization weighted according to the statistical weights of the final ion states is used to modify the direct ionization cross sections. The combination of the BEB model and the scaled Born cross sections is in excellent agreement with available experimental data. The present method can easily be extended to heavier open-shell atoms.

Electron-Impact Cross Sections for Dipole- and Spin-Allowed Excitations of Hydrogen, Helium, and Lithium.

Electron-impact excitation cross sections are presented for the dipole- and spin allowed transitions from the ground states to the np 2P states for hydrogen and lithium, and to the 1snp 1P states for helium, n = 2 through 10. Two scaling formulas developed earlier by Kim [Phys. Rev. A 64, 032713 (2001)] for plane-wave Born cross sections are used. The scaled Born cross sections are in excellent agreement with available theoretical and experimental data.

Scaling of Coulomb Born cross sections for electron-impact excitation of singly charged ions

A scaling method applied to plane-wave Born cross sections for electron-impact excitation of neutral atoms is modified and applied to Coulomb Born cross sections for excitations of singly charged ions. The modified scaling for singly charged ions is simpler than the scaling for neutral atoms. Moreover, the former converts Coulomb Born cross sections into accurate results comparable to the convergent close coupling results, as is the case for the scaling for neutral atoms. Comparisons to available theoretical and experimental data on excitations of He + , Mg + , and Zn + are presented.

Ionization of boron, aluminum, gallium, and indium by electron impact

Measurements of electron impact ionization of neutral Al, Ga, and In show large cross sections compared to other elements in the same rows of the periodic table. Semiempirical and classical calculations of direct ionization cross sections are all substantially smaller. Calculations by McGuire [Phys. Rev. A 26, 125 (1982)] for aluminum that include excitations to autoionizing ${3s3p}^{2}$ doublet levels are 2.5 times higher than experiment at the peak. We report the direct ionization cross sections based on the binary-encounter-Bethe model of Kim and Rudd [Phys. Rev. A 50, 3954 (1994)], which is an ab initio theory. We add the autoionization contribution using scaled plane-wave Born cross sections as recently developed by Kim [Phys. Rev. A 64, 032713 (2001)] for excitations to the first set of autoionizing levels. Dirac-Fock wave functions are used for the atomic structure. Our results are in excellent agreement with experimental values and support substantial contributions from excitation-autoionization to the total ionization cross sections for these elements. We also compare the total ionization cross section of boron to available theories, though no experimental data are available.

Scaling of plane-wave Born cross sections for electron-impact excitation of neutral atoms

Two methods to scale plane-wave Born cross sections for electron-impact excitations of neutral atoms are shown to produce excitation cross sections comparable in accuracy to those obtained by more sophisticated collision theories such as the convergent close-coupling method. These scaling methods are applicable to integrated cross sections for electric dipole-allowed transitions. Scaled cross sections are in excellent agreement with available theoretical and experimental data for excitations in H, He, Li, Be, Na, Mg, K, Ca, Rb, Sr, Cs, Ba, Hg, and Tl, indicating the possibility of rapid and reliable calculations of excitation cross sections for many other neutral atoms.

Plane wave born cross sections including exchange forK-shell ionization of light atoms

Cross sections forK-shell ionization by electron impact have been calculated in plane wave Born approximation (PWBA) including outer screening with allowance for electron exchange in Ochkur approximation. The results agree reasonably with available experimental data.

Planewave born-approximation calculations of L-shell ionization cross sections

Simple analytical expressions used for the calculation of the planewave Born cross sections of the individual L-subshell ionization by low-energy heavy charged-particle impact are given. The formulas reproduce the numerically calculated values with deviations below 5% for all the cases of interest.

Coulomb deflection in ion-atom collisions

The Coulomb-deflection factor, defined as the ratio of the Coulomb to plane-wave Born cross sections, is derived for slow but classically moving ions, and found to be in agreement with the data for $K$-shell ionization. When the half distance of closest approach in a head-on collision, $d$, is comparable to the important impact parameters ($\ensuremath{\sim}\frac{1}{{q}_{0}}$, where ${q}_{0}$ is the minimum momentum transfer), this factor simplifies to $\mathrm{exp}(\ensuremath{-}\ensuremath{\pi}d{q}_{0})$ as it has been employed in the inner-shell-ionization theory. When the impact parameters are small on the scale of the projectile de Broglie wavelength, as they are in nuclear phenomena, the Coulomb-deflection factor tends to $\mathrm{exp}(\ensuremath{-}2\ensuremath{\pi}d{q}_{0})$. An extension of our results to screened Coulomb repulsion gives good agreement with the semiclassical calculations and the data for $K$-shell excitation in ${\mathrm{Ne}}^{+}$-Ne collisions.

Calculation of Double Differential Cross Sections for Ionizing Collisions of Electrons with Helium by Born Approximation and Binary Encounter Theory

The double differential cross sections (ddcs's) for secondary electrons resulting from ionizing collisions of electrons with helium atoms have been calculated with three kinds of approximations; the scaled Born approximation, the plane-wave Born approximation, and the binary encounter theory. The energies of incident electrons are 500 eV and 2000 eV, and the energies of secondary electrons are 5∼200 eV. While the ddcs's calculated by the scaled Born approximation excellently well reproduce the experimental ddcs's for 2000 eV electron impact, the discrepancies between theory and experiment are rather remarkably in the low and intermediate energy regions of secondary electrons for 500 eV electron impact. The ddcs's in the intermediate angular range are well reproduced by the binary encounter theory, which also yields the forward rise experimentally observed in the angular distributions. The agreement between the experimental and the plane-wave Born cross sections is very poor in the energy regions of incide...

Angular correlation of scattered and rejected electrons in ionizing collitions. II

The differential cross section σ(ε, k̂ s, k̂ e) for scattering of a fast electron with an energy loss ε in a direction k̂ s, and a simultaneous ejection of an atomic electron in a direction k̂ e, is derived with the binary-encounter theory and compared with the corresponding Born and plane-wave Born cross sections. In all cases the formulae are properly symmetrized so as to account for interference between direct and exchange scattering amplitudes. The binary-encounter and classical (Gryzinski, Stabler, Gerjuoy, etc.) collision theories are shown to be special approximations of the plane-wave Born approximation, in that all differential and total binary-encounter and classical cross- section formulae can be derived from it. It is discussed how the resulting formulae can be used in the analysis of experimental data, for example such as reported by Amaldi et al.