Interference effects on the photoionization cross sections between two neighbouring atoms: nitrogen as an example

Interference effects on the photoionization cross sections between two neighbouring atoms are considered based on the coherent scattering of the ionized electrons by the two nuclei when their separation is less than or comparable to the de Broglie wave length of the ionized electrons. As an example, the single atomic nitrogen ionization cross section and the total cross sections of two nitrogen atoms with coherently added photoionization amplitudes are calculated from the threshold to about 60~\AA (1~\AA=0.1~nm) of the photon energy. The photoionization cross sections of atomic nitrogen are obtained by using the close-coupling R-matrix method. In the calculation 19 states are included. The ionization energy of the atomic nitrogen and the photoionization cross sections agree well with the experimental results. Based on the R-matrix results of atomic nitrogen, the interference effects between two neighbouring nitrogen atoms are obtained. It is shown that the interference effects are considerable when electrons are ionized just above the threshold, even for the separations between the two atoms are larger than two times of the bond length of N₂ molecules. Therefore, in hot and dense samples, effects caused by the coherent interference between the neighbours are expected to be observable for the total photoionization cross sections.     

相对论小分量波函数对原子光电离截面的影响

利用相对论平均自洽场理论,　研究了相对论波函数的小分量对原子光电离截面的影响。原子核尺寸效应将使波函数小分量对原子光电离截面的影响减弱。由于波函数沿径向空间被压缩,　电子离核的平均半径较小,　波函数小分量对高离化态离子光电离截面的影响比对一般原子要强得多。波函数小分量反映了相对论效应的基本特征,　从而也定性地说明了光电离过程中相对论效应的强弱。The effects of relativistic small radial component on atomic photoionization cross sections have been studied within relativistic average self consistent field theory. Relativistic effects are relatively unimportant for low photon energy, along with a review of high energy photoionization the relativistic effects are quite important. The effects of relativistic small radial component on photoionization process should show breakdown when the nuclear finite size effects is taken into account. The compression of wavefunction into the space near nucleus is so strong in highly charged ions that the electronic radius greatly decreases, and the effects of relativistic small radial component on photoionization cross sections turn to stronger than ordinary atoms. Since relativistic effects are extremely sensitive to the behavior of small radial component, the results are in good agreement with relativistic effects on photoionization cross section.     

R-matrix calculation for photoionization

We have employed the R matrix method to calculate differential cross sections for photoionization of helium leaving helium ion in an excited state for incident photon energy between the N=2 and N=3 thresholds (69～73 eV) of He + ion. Differential cross sections for photoionization in the N=2 level at emission angle 0° are provide. Our results are in good agreement with available experimental data and theoretical calculations.     

L-Shell X-Ray Production Cross Sections of Ta and Tm by Electron Impact near the Threshold Region

We present experimental measurements of L-shell production cross sections Lα, Lβ and Lγ for tantalum and thulium by electron impact at incident electron energies from about one to three times the threshold energy. From the experimental data, the total production cross section and mean ionization cross section are deduced. The influence of electrons reflected from the substrate is corrected by the electron transport bipartition model. Tile measured cross sections are compared with the theoretical predictions.     

1.0 MeV电子碰撞引起Ta 和Au 内壳电离截面的测量

无论对深入理解电子-原子的作用机制,还是在材料等领域的实际应用,电子轰击原子的内壳电离截面都具有重要意义。当前电子碰撞引起原子内壳电离的实验数据多集中在几十keV 入射能量和中小Z 靶原子,其它数据相对比较缺乏。本工作以能量为1.0 MeV电子轰击Ta 和Au 靶,通过测量靶原子特征X射线的产额,获得其K壳电离截面分别为13.3 和10.1 b,L 壳电离截面分别为554 和338 b。并将实验结果和相应的理论进行了对比,结果显示,本实验测得的K壳电离截面与Casnati、Hombourger 理论值、L 壳电离截面与Scoeld和Born-Bethe 的理论值相符。Accurate experimental data for atomic inner-shell ionization cross-sections by electrons are of basic importance both in understanding inelastic electron-atom interaction and its application. Up to now, most of available data on this process were mainly concentrated on the low and medium Z atoms by the bombardment of low energy electrons. In present experiments K-shell and L-shell ionization cross-sections of Ta and Au in collisions with 1.0 MeV eleltron were determined by measuring the characteristic X-rays emitted from the target atoms. For the present collision systems the K-shell ionization cross-sections were found to be 13.3 and 10.1 b,and the L-shell ionization cross sections were 554 and 338 b, respectively. The measured K-shell ionization cross sections are in reasonable agreement with the theoretic predictions of Casnati and Hombourger, while L-shell ionization cross sections are consistent with the theoretical results of Soc eld and Born-Bethey.     

Density Dependence of the Detailed Spectral Line Effects on the Opacity of Astrophysical Abundant Elements： oxygen

A full relativistic detailed-level-accounting approach has been developed independently to deal with the detailed spectral line effects on the opacity of the third most abundant element in stars: oxygen. The atomic energy levels and the oscillator strengths of the radiative transitions between the energy levels are obtained by carrying out the full relativistic one-configuration Dirac-Fock calculations. The photoionization cross sections are obtained via an average atom scheme with a consideration for the splitting of the ionization threshold due to the ionization stages and the term-couplings. As an example, the spectra resolved opacities and the mean opacities of oxygen are calculated to show the importance of the detailed spectral line profiles with the density of the matter.     

An alternative view of condensed-phase photoionization

This paper proposes an accurate valuable interpretation scheme to study the evolvement of the photoionization processes from the isolated to the condensed atoms by a unique ab initio method. The variations of the photoionization cross sections of the atomic sodium with the photoelectron energy and the boundary radius of the atomic configuration space are studied in this new scheme by the R-matrix method. The discrepancy in the photoionization spectra of the isolated and the condensed sodium has been explained quantitatively and understood successfully by this alternative view in detail for the first time.     

Dirac R-matrix calculations of photoionization cross sections of Ni Ⅻ and atomic structure data of Ni 

We performed R-matrix calculations for photoionization cross sections of the two ground state configuration 3s~23p~5(~2P_(3/2,1/2)~o) levels and 12 excited states of Ni Ⅻ using relativistic Dirac Atomic R-matrix Codes(DARC) across the photon energy range between the ionizations thresholds of the corresponding states and well above the thresholds of the last level of the Ni XIII target ion. Generally, a good agreement is obtained between our results and the earlier theoretical photoionization cross sections. Moreover, we have used two independent fully relativistic GRASP and FAC codes to calculate fine-structure energy levels, wavelengths, oscillator strengths, transitions rates among the lowest 48 levels belonging to the configuration(3s~23p~4, 3s3p~5, 3p~6, 3s~23p~33d) in Ni XIII. Additionally, radiative lifetimes of all the excited states of Ni XIII are presented. Our results of the atomic structure of Ni XIII show good agreement with other theoretical and experimental results available in the literature. A good agreement is found between our calculated lifetimes and the experimental ones.Our present results are useful for plasma diagnostic of fusion and astrophysical plasmas.     

Electron-impact ionization cross section calculations for lithium-like ions

The electron-impact ionization of lithium-like ions C³⁺,N⁴⁺,O⁵⁺,Ne⁷⁺,and Fe2³⁺is studied using a combination of two-potential distorted-wave and R-matrix methods with a relativistic correction.Total cross sections are computed for incident energies from 1 to 10 times of ionization energy and better agreements with the experimental results are obtained in comparison with the theoretical data available.It is found that the indirect ionization processes become significant for the incident energy larger than about four times of the ionization energy.Contributions from the exchange effects along the isoelectronic sequence are also discussed and found to be important.The present method can be used to obtain systematic ionization cross sections for highly charged ions across a wide incident energy range.     

Sequential over-barrier ionization of multi-electron atoms in the tens-to-hundreds keV/u energy range

Our previous work on the classical over-barrier ionization model for helium double ionization is extended to the complex multi-electron system of Ne.The total and q-fold ionization cross sections are calculated at energies ranging from a few tens to several hundred keV/u.The calculation results are in good agreement with the experimental data,and the energy dependence of the cross sections suggests that the multi-ionization of a strong perturbated complex atom is probably the sequential over-barrier ionization process.     

C原子、离子光电离过程的规律研究

 基于Dirac-Slater自洽场方法，计算了C原子及各价离子从低能到高能的光电离截面。通过各种理论计算结果的比较，分析了Kramers公式的适用性。定量地考察了多极效应和相对论效应在不同能区对光电离截面的影响，并研究了光电离截面随光子能量、壳层、电离度变化的规律。     

Excitation and photoionization processes involving the bound ns electrons

We have considered the processes of excitation and ionization of light multicharged ions by impact of high-energy particles, which proceed with participation of the ns electrons. The screening corrections to the energy levels and photoionization cross sections are evaluated analytically within the framework of the non-relativistic perturbation theory with respect to the electron-electron interaction. The universal scalings for the excitation and ionization cross sections are studied for arbitrary principal quantum numbers n.     

Photoionization of highly stripped atomic ions: Relativistic calculations

Relativistic central-field (Dirac-Slater) calculations of photoionization of atoms and ions have been performed. The results show that the photoionization cross sections for inner-shell njl electrons are largely unaffected by removal of outer shell electrons (with principal quantum number greater than n) except for a shift in threshold, just as in the non-relativistic case. The most dramatic results are obtained for Th(Z=90) compared with Th⁸⁰⁺ where σ(hv) remains almost constant through 80 stages of ionization. The results are explained in terms of the fact that 〈r〉 is primarily a function of principal quantum number.     

Inner-shell ionization of atoms by electron,positron and photon impacts

Plane wave Born approximation with Coulomb, relativistic and exchange corrections is employed to obtain L1-, L2- and L3-subshell ionization cross sections of several atoms due to electron and positron impacts for projectile energy varying from the threshold of ionization to 60 times the threshold energy. Photoionization cross sections for all the three L-subshells of the atoms are also calculated using the hydrogenic approximation for the atomic wave functions. For L3-subshell the present cross sections due to electron impact are in good agreement with a number of experimental data for different atoms over the entire energy range investigated. For L1- and L2-subshells the present calculations yield qualitative agreement with the experimental data. The agreement between the present results and the limited experimental data for positron impact is also satisfactory. The hydrogenic approximation for the L-subshell photoionization is found to be good at small photon energies but it underestimates the cross sections at large photon energies.     

Many-electron effects in atomic processes

The major role of the collectivization of electrons in atoms and quasiatomic formations is demonstrated. The random-phase approximation with exchange, which permits allowance for these effects, is discussed in detail. The need to extend the scope of this approximation when some processes are considered, which is achieved by combining it with perturbation theory, is noted. The role of the collective effects is illustrated by the results of recently performed calculations of the photoionization cross sections of atomic iodine and its positive and negative ions, the single-electron ionization of Xe⁺, resonance-enhanced photon emission in collisions of electrons with atoms and quasiatomic formations, the nondipole corrections to the angular distribution of photoelectrons, and the probabilities of two-electron transitions in which all the energy is released in the form of a single photon. Zh. Tekh. Fiz. 69, 31–35 (September 1999)     

The contribution of the central region of the electron energy spectrum to the total double photoionization cross section of helium in the asymptotic nonrelativistic energy region

The double photoionization of helium at high photon energies is considered using a nonrelativistic approach. The central region of the energy spectrum and its contribution to the total process cross section and to the ratio between the double and single ionization cross sections are studied. Interelectronic interaction in the initial state is included exactly, whereas the interaction between the fast outgoing electrons is calculated by perturbation theory. A detailed derivation of the expression for the cross section ratio between double and single ionizations is given. The corresponding results obtained by other authors are analyzed and corrected.     

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.