Cascade Mi (i = 1–5) subshell X‐ray emission at incident photon energies across the Lj (j = 1–3) subshell absorption edges of 66Dy

The total M shell and the M_k (k = ξ, αβ, γ, m) X‐ray production cross sections for ₆₆Dy have been measured at incident photon energies across its L_j (j = 1–3) subshell absorption edge energies, ranging 7.8–9.2 keV. This study aims to investigate the evolution of the probability for cascade decay of L_j subshell vacancies as the tunable incident energy ionizes progressively different ₆₆Dy L_j subshells. The experimental X‐ray production cross sections have been compared with theoretical ones calculated using the nonrelativistic Hartree–Fock–Slater (HFS) model‐based photoionization cross sections; three sets of the X‐ray emission rates, fluorescence and Coster–Kronig yield based on the nonrelativistic Hartree–Slater (NRHS) model, Dirac–Hartree–Slater (DHS) model and Dirac–Fock (DF) model; the L_j (j = 1–3) subshell to the M_i (i = 1–5) subshell vacancy transfer probabilities evaluated in the present work. Presently measured total M shell and the M_αβ X‐ray production cross sections are found to be significantly lower than the theoretical ones evaluated using physical parameters based on the relativistic Dirac–Fock/Dirac–Hartree–Slater model calculations, whereas a much better agreement is observed with respect to the NRHS model‐based calculations; however, the measured X‐ray production cross sections are still systematically lower than the NRHS values.     

低能质子引起的金LX射线相对产生截面

对于能量为０．５－１ＭｅＶ的入射质子，在计算中采用ＡｕＬ１次壳层荧光产额的实验值代替相应的Ｄｉｒａｃ－Ｈａｒｔｒｅｅ－Ｓｌａｔｅｒ值时，使用ＲＰＷＢＡ－ＢＣ（经结合能和库仑歪曲修正的相对论平面波玻恩近似）电离截面计算得到的金原子ＬＸ射线相对产生截面与测量值相符。以前报道的对ＲＰＷＢＡ－ＢＣ截面的各种修正都是不需要的     

Synchrotron radiation induced X‐ray production cross sections of 66Dy at energies across its Li (i = 1–3) subshell absorption edges

The X‐ray production (XRP) cross sections for the ₆₆Dy L_k (k = l, α, η, β_2,6,7,15, β_1,6, β_1,3,4,6, β_2,7,15, γ_1,5, γ₂,₃) emission lines have been measured by tuning the incident synchrotron radiation at energies over the range 7.8–9.2 keV and ~10–370 eV above the respective L_i (i = 1–3) absorption edges. These measurements aim to check the reliability of the independent particle approximation models used to generate the theoretical data sets of different physical parameters required to calculate the XRP cross sections and also investigate the influence of many body effects on the photoionization process. The measured values have been compared with 4 sets of XRP cross sections calculated using the Dirac–Fock model‐based X‐ray emission rates, 2 sets of the L_i (i = 1–3) subshell photoionization cross sections deduced from the self‐consistent Dirac–Hartree–Fock model‐based values and the nonrelativistic Hartree–Fock–Slater model‐based values, and 2 sets of the fluorescence (ω_i) and Coster–Kronig (f_ij) yields. The present measured Lγ_2,3 (originating from decay of the L₁ subshell vacancies) XRP cross sections are found to be significantly higher than different sets of theoretical values, whereas a good agreement is generally observed for the various other XRP cross sections and relative intensities.     

激光金等离子体的电子离子碰撞电离速率系数

电子离子碰撞电离过程在超组态碰撞辐射(SCROLL)模型中真实模拟非局域热动力学平衡(non-LTE)高Z材料Au激光等离子体M带谱5f-3d跃迁中各种复杂离子的电离态特性,诸如离子的平均电离度和电荷态分布是一个主要过程.基于准相对论扭曲波玻恩交换近似,采用组态平均的方法,从头计算了金M带类铁金离子-类锗金离子的电子离子碰撞电离速率系数,其中电离截面的高能行为由Bethe系数决定.结果表明:在"神光Ⅱ"实验装置诊断的电子温度～2keV,电子密度～6×1021cm-3范围内,这些参数有利于使用超组态碰撞辐射模型拟Au的激光等离子体M带细致谱5f-3d跃迁的平均电离度和电荷态分布.     

Electronic structure of two-electron quantum dot with parabolic potential

In this study, we investigate the parabolic potential effects on the ground and excited energy states of two-electron quantum dot with impurity inside an infinite spherical confining potential well. The wave function and energy eigenvalues were calculated using a modified variational optimization procedure based mainly on quantum genetic algorithm and Hartree–Fock–Roothaan method. The results show that the parabolic potential and impurity charge have a strong effect on the energy states and ionization energies. It is worth pointing out that as impurity charge increases, the ionization energy rises, but the ionization dot radius decreases. On the other hand, as parabolic potential increases, the ionization energy decreases, but the ionization dot radius increases.     

高离化态Au离子光电离过程的理论研究

基于多组态Dirac-Fock方法的程序包GRASP92和RATIP及在此基础上最新发展的RELPHOTO08程序, 系统地研究了高离化态金离子M壳层的光电离截面随入射光子能量、 离化度以及壳层的变化规律。结果表明: 光电离截面随光子能量的增大而单调减小; 电离nl电子时, 如果相关电子的主量子数较大, 则该电子存在与否对其光电离截面几乎没有影响; 在同一离化度下, 角量子数l可引起两种性质不同的效应, 其相互竞争可导致光电离截面随入射光子能量的复杂变化。Based on multiconfiguration Dirac Fock method and the corresponding packages GRASP92 and RATIP, as well as the newly developed RELPHOTO08, the variations of M subshell photoionization cross sections with the photon energy, ionization degree and subshells for highly charged gold ions are studied systemically. The present results show that the cross sections are decreasing monotonously with the photon energy; for the photoionization of nl electrons, if the principal quantum number of removed electron is large enough, the cross sections are essentially unchanged upon the presence or absence of outer electrons; for same ionization degree, the angular quantum number introduces two opposite effects which could exist simultaneously, and the intricate variations of cross sections with the photon energy originate from the competition between these two different effects.     

Understanding of nuclear quadrupole interactions of 35 Cl, 79 Br and 129 I and binding energies of solid halogens at first-principles level

This paper deals with the understanding at a first-principles level of the nuclear quadrupole interaction (NQI) parameters of solid chlorine, bromine and iodine as well as the intermolecular binding of these molecules in the solid. The electronic structure investigations that we have carried out to study these properties of the solid halogens are based on the Hartree–Fock Cluster approach using the Roothaan variational procedure with electron correlation effects included using many-body perturbation theory with the empty orbitals used in the perturbation theory investigations for the excited states. The results of our investigations provide good agreement with the measured NQI parameters primarily from the Hartree–Fock one electron wave-functions with many-body effects making minor contributions. The binding (dissociation) energies for the molecules with the solid state environment on the other hand arises from intermolecular many body effects identified as the Van der Waals attraction with one-electron Hartree–Fock contribution being repulsive in nature.     

原子体系近核区电子波函数振幅(Ⅰ)——离化态原子高能光电离过程

本文具体地阐述近核区波函数和高能光电离截面的关系。根据相对论自洽场理论,计算各种离化态铁原子和铀原子的近核区波函数和光电离截面。计算结果表明:光电离截面比值函数随着光子能量的增加规则平缓变化,在光子能量约大于10¹keV以后,其和相应的近核区波函数振幅平方比的精度在千分之几的范围内。     

Autoionization resonances in the photoabsorption spectra of Fe<Superscript><Emphasis Type="Italic">n</Emphasis>+</Superscript> iron ions

The photoabsorption cross sections of a neutral iron atom, as well as positive Fe⁺ and Fe²⁺ ions, are calculated in the relativistic random-phase approximation with exchange in the energy range 20–160 eV. The wavefunctions of the ground and excited states are calculated in the single-configuration Hartree–Fock–Dirac approximation. The resultant photoabsorption spectra are compared with experimental data and with the results of calculations based on the nonrelativistic spin-polarized version of the random-phase approximation with exchange. Series of autoionization resonance peaks, as well as giant autoionization resonance lines corresponding to discrete transitions 3p → 3d, are clearly observed in the photoabsorption cross sections. The conformity of the positions of calculated peaks of giant autoionization resonances with experimental data is substantially improved by taking into account additionally the correlation electron–electron interaction based on the model of the dynamic polarization potential.     

Electron shake probabilities of heavy elements as a result of M‐shell vacancy production

The electron shakeup‐plus‐shakeoff probabilities accompanying M‐shell vacancy creation have been calculated for elements between Z = 72 and 92. The calculations were performed relativistically in the sudden approximation by the use of the Dirac–Fock–Slater wave functions. The relativistic effects are demonstrated in comparison with the nonrelativistic calculations, and the validity of the approximation method based on the difference in the effective nuclear charge is discussed. The dependence of different initial M‐subshell vacancies on the shake probability is studied. Copyright © 2014 John Wiley & Sons, Ltd.     

A mathematical and computational review of Hartree–Fock SCF methods in quantum chemistry

We present a review of the fundamental topics of Hartree–Fock theory in quantum chemistry. From the molecular Hamiltonian, using and discussing the Born–Oppenheimer approximation, we arrive at the Hartree and Hartree–Fock equations for the electronic problem. Special emphasis is placed on the most relevant mathematical aspects of the theoretical derivation of the final equations, and on the results regarding the existence and uniqueness of their solutions. All Hartree–Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. The discretization of the one-electron orbital space is then reviewed and the Roothaan–Hall formalism introduced. This leads to an exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing on algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (especially those related to the design of linear-scaling methods) are commented on and linked to the issues discussed. The paper is intentionally introductory and rather self-contained, and may be useful for non-experts intending to use quantum chemical methods in interdisciplinary applications. Moreover, much material that can be found scattered in the literature has been put together to facilitate comprehension and to serve as a handy reference.     

Do Dyson Orbitals resemble canonical Hartree–Fock orbitals?

ABSTRACT

Dyson orbitals are overlaps between states with N and N±1 electrons and provide conceptual links between transition probabilities of electron detachment or attachment, density matrices, total energies and general principles of chemical bonding. Canonical, Hartree–Fock orbitals are compared with Dyson orbitals obtained with electron–propagator calculations that retain all elements of the self–energy matrix, wherein all orbital–relaxation and electron–correlation corrections to Koopmans results reside. For valence ionization energies and electron affinities of representative closed–shell molecules, canonical, Hartree–Fock orbitals usually are excellent approximations to Dyson orbitals, although there are some notable cases where the resemblance is not as strong. Numerical relationships between pole strengths and the Koopmans contributions to Dyson orbitals also are inferred from the data.     

Theoretical calculation of the triple differential cross sections of the 2p orbital of argon in a coplanar highly asymmetric（e,2e） reaction

The triple differential cross sections of the 2p electron of argon in a coplanar highly asymmetric geometry have been calculated with the modified distorted wave Born approximation (DWBA) and the target Hartree－Fock approximation methods. The damping polarization of the semi-classical short-range potentials and the M_ee factor are included in the distorting potentials of the modified DWBA. Theoretical results are compared with a recent experiment. The dynamic mechanism of inner shell ionization in a coplanar highly asymmetric geometry (e, 2e) reaction are also discussed.     

Lifetimes and transition probabilities in Kr V

Weighted oscillator strengths (gf), weighted transition probabilities (gA) and lifetimes are presented for all experimentally known dipole transitions and levels of Kr V. Values were determined by four methods. Three of them are based on the Hartree–Fock method, including relativistic corrections and core-polarization effects, with electrostatic parameters optimized by a least-squares procedure in order to obtain energy levels adjusted to the corresponding experimental values. The fourth method is based on a relativistic multiconfigurational Dirac–Fock approach. In addition, 47 new classified lines belonging to the Kr V spectrum are presented.     

相对论Hartree-Fock研究奇特核的性质

采用相对论Hartree-Fock(RHF)理论来描述奇特核的性质.为了研究Fock项和矢量介子对奇特核性质的贡献和避免有效相互作用的不惟一性,本文推广应用没有自由参数的密度有关的相对论Hartree(RDH)和Hartree-Fock(RDHF)理论来描述奇特核的性质.在RDH和RDHF近似下,计算了钙同位素链的性质,特别研究了Fock交换项和矢量介子的贡献.研究表明交换项和矢量介子对非常丰中子核的性质,如结合能,中子均方根半径,中子密度分布的影响是非常不同于对稳定线附近核性质的影响.同时,对研究滴线奇特核性质的重要性及其理论模型做了简单的讨论.     

Electron-induced scattering dynamics of Boron,Aluminium and Gallium trihalides in the intermediate energy domain

This article is focused on the calculation of electron-induced ionisation and total scattering cross sections by Boron, Aluminium and Gallium trihalide molecules in the intermediate energy domain. The computational formalism, spherical complex optical potential has been employed for the study of these two scattering cross sections. The ionisation cross section has been derived from the inelastic cross section using a semi-empirical method called complex scattering potential-ionisation contribution (CSP-ic) method. We have also calculated the ionisation cross section using the BEB theory with Hartree–Fock and density functional theory (DFT- ωB97XD) orbitals so that a comparison can be made with the cross sections predicted by CSP-ic method. For this theoretical study, we have also calculated polarisability and bond length of some targets which were not found in literature using DFT/B3LYP in Gaussian 09 software.     

相对论和非相对论理论模型研究奇异核的性质

采用相对论和非相对论理论模型可描述奇异核的性质 .相对论平均场理论预言了2 6,2 7,2 8P存在一个质子晕 ,而27,28,29S存在两个质子晕 .最近 ,MSU的最新的实验发现了2 6,2 7,2 8P核存在一个质子晕.采用相对论 Hartree- Fock理论研究了 Fock项和矢量介子对奇异核性质的贡献,研究表明交换项和矢量介子对非常丰中子核性质的影响非常不同于对稳定线附近核性质的影响.同时,采用形变的Hartree- Fock- Bogoliubov理论研究了某些轻核同位素链的性质和形变.     

M X‐ray production cross sections for heavy elements by proton impact

We present in this paper, M‐shell ionization cross sections and M X‐ray production cross sections calculated within the Energy loss, Coulomb deflection, Perturbed Stationary State and Relativistic effects (ECPSSR) theory for elements with 72 ≤ Z ≤ 90 for protons with 0.1–4.0 MeV energy. Our results are compared to the plane wave Born approximation (PWBA) predictions, the relativistic plane‐wave Born approximation including corrections for binding and Coulomb deflection effect (RPWBA‐BC) results and the ECPSSR calculations from earlier works. On the other hand, semiempirical and empirical M X‐ray production cross sections are deduced from the polynomial fitting of the available experimental data collected from different sources. A comparison is made between the different sets of results. The differences between the above calculations and the experimental results are pointed out and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Random-phase approximation correlation methods for molecules and solids

Random-phase approximation (RPA) correlation methods based on Kohn–Sham density-functional theory and Hartree–Fock are derived using the adiabatic-connection fluctuation dissipation theorem. It is shown that the correlation energy within the adiabatic-connection fluctuation-dissipation theorem is exact in a Kohn–Sham framework while for Hartree–Fock reference states this is not the case. This shows that Kohn–Sham reference states are probably better suited to describe electron correlation for use in RPA methods than Hartree–Fock reference states. Both, Kohn–Sham and Hartree–Fock RPA methods are related to each other both by comparing the underlying correlation functionals and numerically through the comparison of total energies and reaction energies for a set of small organic molecules.     

Convergence acceleration for the multilevel Hartree–Fock model

In the previously introduced multilevel Hartree–Fock (HF) model, the electronic density is optimised in a given region of the molecular system. The approach is based on generating an active occupied and active virtual space by decomposing a start guess density for the entire system. In this work, a diagonalisation based implementation for Roothaan–Hall (RH) with direct inversion in iterative subspace (DIIS) and a quasi-Newton minimisation procedure using the augmented RH (ARH) approach are described for accelerating convergence for the multilevel HF model. The equations are derived to be consistent with convergence acceleration for traditional atomic orbital based HF calculations. The main idea is to formulate all quantities in the molecular orbital basis to exploit that the active molecular orbital basis is significantly smaller than the atomic orbital basis, and thus enable the application of wave function approaches that are well-studied for small molecular systems to large molecular systems. Thus, all equations are formulated such that no atomic orbital density or Fock matrices are needed for the DIIS and ARH algorithms. Results show that the acceleration schemes yield efficient optimisation of the multilevel HF wave function.