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.     

原子核对光电离截面的影响

利用Dirac-Slater相对论平均自洽场理论,研究了不同原子体系光电离截面在不同核模型下的差异.考虑原子核大小时,核的尺寸效应使电子所感受到的有效核电荷减小,并进而影响到电子的概率分布及光电离截面等;对没有考虑原子核大小的点模型,由于不存在核的尺寸效应,出射光电子的波函数有较大相移,从而有可能出现Cooper极小.当入射光子的能量远大于相关电子的电离能时,不同核模型下电子束缚能及平均半径等的差异将相对减小,从而使光电离截面随入射光子能量的变化趋于一致.     

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.     

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 $V(r)$.     

Excitation cross section for iridium atoms by slow electrons

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

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.     

交换势对光电离截面的影响

利用相对论平均自洽场理论,研究了光电离截面在不同交换势下的差异,在对这种差异进行分析的基础上,对其变化规律做了较详细的理论说明.计算结果表明:光电离截面随交换系数的增大而增大;电子所感受到的平均核势场越小,交换势所起的作用则相对地有所增加,从而对光电离截面的影响更大.     

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.