Modern methods for calculating photoionization and electron-impact ionization of two-electron atoms and molecules

A number of recently developed methods for calculating multifold differential cross sections for photoionization and electron impact ionization of atoms and molecules with two active electrons are reviewed. The methods are based on unique approaches to the calculation of three-body Coulomb wave functions. The exterior scaling method and the driven Schrödinger equation formalism are considered. The effectiveness of the time-dependent approaches to the scattering problem, such as the paraxial approximation and the time-dependent scaling, is demonstrated. A novel numerical method is formulated, which has been developed by the authors to solve the six-dimensional Schrödinger equation for an atom with two active electrons on the basis of the Chang-Fano transformation and the discrete variable representation. The threshold behavior manifested by the angular distributions of the two-electron photoionization of a negative hydrogen ion and a helium atom and the multifold differential cross sections for the electronimpact ionization of hydrogen and nitrogen molecules are analyzed on the basis of numerical simulations. The Wannier law for the angular distribution of double ionization is demonstrated to be incorrect even at very low energies.     

Qualitative modification of the high energy atomic photoionization cross section

It is demonstrated that the nonrelativistic high energy omega-->infinity behavior of the photoionization cross section of an nl atomic subshell, sigma(nl)(omega), for l>0 is independent of l and is given by sigma(nl)(omega) approximately 1/omega(9/2), rather than the previously generally accepted sigma(nl)(omega) approximately 1/omega(l+7/2). Furthermore, for l = 1, although the exponent does not change, the coefficient is significantly altered. This modification of sigma(nl)(omega) is due to the interchannel interaction between ns photoionization channels and l not equal0 channels in the atom. As a result, for the photoionization of l not equal0 electrons, the single-particle approximation is never correct in the omega-->infinity limit. This has important consequences for sum rule calculations.     

Scaling tests of the cross section for deeply virtual Compton scattering

We present the first measurements of the e[over -->]p-->epgamma cross section in the deeply virtual Compton scattering (DVCS) regime and the valence quark region. The Q(2) dependence (from 1.5 to 2.3 GeV(2)) of the helicity-dependent cross section indicates the twist-2 dominance of DVCS, proving that generalized parton distributions (GPDs) are accessible to experiment at moderate Q(2). The helicity-independent cross section is also measured at Q(2)=2.3 GeV(2). We present the first model-independent measurement of linear combinations of GPDs and GPD integrals up to the twist-3 approximation.     

Excitation cross section for iridium atoms by slow electrons

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 5, pp. 711–716, May, 1991.     

Asymptotic form of the high energy photoionization cross section of fullerenes

We show that the theoretical predictions on high energy behavior of the photoionization cross section of fullerenes depend crucially on the form of the function $V(r)$ which approximates the fullerene field. The shape of the high energy cross section is obtained without solving the wave equation. The cross section energy dependence is determined by the analytical properties of the function $V(r)$.     

Study of photoionization cross section of shallow donors in CdTe

The photoionization cross section of single crystals CdTe with different amounts of impurities has been studied at 4.2 K, both experimentally and theoretically. It has been found that for highly pure samples the photoionization peak is narrow. The observed behaviour can be explained with the help of a parameter χ, which is related to the region of the localization of the 1s electron of the impurity atom.     

On the total energy of two-electron atoms

Using the Multi-Configuration Dirac-Fock (MCDF) method we calculate with 9 configuration state functions the correlation energy as well as the total energy of the lowestJ=0 ground state of all two-electron systems from H^? to Thorium (Z=90). A comparison with experimental data, which are available only in the lowZ region, shows a very good agreement.     

Binary encounter approximation for the electron-impact double ionization cross section of atoms and ions

An binary encounter approximation is formulated for the direct (without any excitation of autoionization levels) double ionization of atoms and ions by electron impacts. Analytical expressions are derived for the cross section, which qualitatively represent the main dependences on the incident electron energy and atomic parameters.     

Autoionization cross section of lithium atoms excited by electron impact

We measure the full autoionization cross section of lithium atoms excited by electrons in the energy range from the first autoionization threshold at 56.39 to 600 eV. Data are obtained by determining the total intensity of electron spectrum of autoionization states 1sn ₁ l ₁ n ₂ l ₂ detected at the “magic” observation angle of 54.7°. The cross section behavior is characterized by a sharp increase to a maximum value of 1.7 × 10⁻¹⁸ cm² in the energy interval of 56.4–60 eV and a subsequent monotonic drop to a value of 10⁻¹⁸ cm² at 600 eV. We have discovered a “thin” cross section structure that reflects the presence of strong resonances of Li⁻ ions in the near-threshold area of excitation of the lowest energy autoionization states (1s2s2)2S, (1s2s2p)⁴ P, 1s(2s2p ³ P)² P), and 1s(2s2p ¹ P)² P. We have established that the contribution of autoionization to the absolute cross section of single ionization of lithium atoms does not exceed 4%. We perform a comparative analysis of the data with analogous data for potassium and cesium atoms.