Virial relations for the Dirac equation in a central field and their applications to calculations of H-like atoms are considered. It is demonstrated that using these relations allows one to evaluate various average values for a hydrogenlike atom. The corresponding relations for non-diagonal matrix elements provide an effective method for analytical evaluations of infinite sums that occur in calculations based on using the reduced Coulomb-Green function. In particular, this method can be used for calculations of higher-order corrections to the hyperfine splitting and to the g factor in hydrogenlike atoms.
Closed-form expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
给出了处于任意离散能量本征态的狄拉克单电子原子的偶极磁屏蔽常数的解析表达式。假设扰动原子态的外部磁场是弱的、均匀的、与时间无关的。关于原子核，我们假定它是点状的、无自旋的、不动的，并且带有电荷Ze。计算是基于广义狄拉克-库仑格林函数的Sturmian展开[R. Szmytkowski，J. Phys. B 30，825（1997）; erratum 30，2747（1997）]，结合超几何函数理论。最后的结果是一个初等形式，并同意相应的公式，以前得到的其他作者对某些特定的状态的原子。
Applicability of the Dirac-Fock method combined with Core Polarization in calculations of alkali atoms
St. Petersburg State University（圣彼得堡国立大学）；Petersburg Nuclear Physics Institute named by B.P. Konstantinov of NRC “Kurchatov Institute”（核物理研究所（以B.P.康斯坦丁诺夫命名，隶属于国家研究中心“库尔恰托夫研究所”））
Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
Atomic Kapitza-Dirac Bragg regime scattering is a multiphoton process in which a neutral atom undergoes a change of momentum through an interaction with a coherent light source. When the Bragg conditions are met, the outgoing atom beams are spatially quantized. Counterpropagating lasers act as pump and probe scattering from far-off-resonant excited intermediate electronic states, leaving the atoms in the electronic ground state with quantized transverse momentum. Each nontrivial scattering event imparts transverse velocity and therefore kinetic energy to the deflected atoms through recoil. In …
Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
广义Dirac-Coulomb Green函数[R. Szmytkowski，J.物理学\ B \textbf{30}，825（1997）; \textbf{30}，2747（E）（1997）]导出了相对论性单电子原子在任意离散态下的磁化率的封闭表达式，原子核为点状、无自旋、静止的荷电核$Ze$ .结果具有涉及单位辐角的广义超几何函数${}_3F_2$的双重有限和的形式。我们的一般表达式与其他作者对原子某些特殊状态用解析方法得到的公式一致。我们还提出了一些选定的类氢离子与$1 \leqslant Z \leqslant 137$激发态的磁化率的数值，并与文献中的数据进行比较。
The $K$-shell level radiative, non-radiative, and total widths, $K$-shell fluorescence yields and $K$-shell hole state lifetimes for atoms with 20$\le$Z$\le$30 have been calculated in fully-relativistic way using the extensive multiconfiguration Dirac-Fock calculations with the inclusion of the Breit interaction and QED corrections and also using multiconfiguration Dirac-Hartree-Slater calculations.
Magnetic field-induced electric quadrupole moment in the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
Static electric multipole susceptibilities of the relativistic hydrogen-like atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
Addendum to "The Dirac-Coulomb Sturmians and the series expansion of the Dirac-Coulomb Green function: application to the relativistic polarizability of the hydrogen-like atom" [J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 825-61, (E) 30 (1997) 2747]
Relativistic strong-field ionization of hydrogen-like atoms or ions in a constant crossed electromagnetic field is studied. The transition amplitude is formulated within the strong-field approximation in Göppert-Mayer gauge, with initial and final electron states being described by the corresponding Dirac-Coulomb and Dirac-Volkov wave functions, respectively. Coulomb corrections to the electron motion during tunneling are taken into account by adjusting an established method to the present situation. Total and energy-differential ionization rates are calculated and compared with predictions fr…
We present tabulated data for the nuclear magnetic shielding constants ($σ$) of the Dirac one-electron atoms with a pointlike, motionless and spinless nucleus of charge $Ze$. Utilizing the exact general analytical formula for $σ$ derived by us \mbox{[P. Stefa{ń}ska, Phys. Rev. A. 94 (2016) 012508/1-15],} valid for an arbitrary discrete energy eigenstate, we have computed the numerical values of the magnetic shielding factors for the ground state and for the first and the second set of excited states, i.e.: 2s$_{1/2}$, 2p$_{1/2}$, 2p$_{3/2}$, 3s$_{1/2}$, 3p$_{1/2}$, 3p$_{3/2}$, 3d$_{3/2}$, and …
In this paper, we consider the Dirac-Hartree-Fock equations for system has many-particles. The difficulties associated with Gaussians model are likely to be more complex in relativistic Dirac-Hartree-Fock calculations. To processing these problem, we use accurate techniques. The four-component spinors will be expanded into a finite basis-set, using Gaussian basis-set type dyall.2zp to describe 4-component wave functions, in order to describe the upper and lower two components of the 4-spinors, respectively. The small component Gaussian basis functions have been generated from large component G…
Bohr's model of the hydrogen atom can be extended to account for the observed spin-orbit interaction, either with the introduction of the Thomas precession, or with the stipulation that, during a spin-flip transition, the orbital radius remains intact. In other words, if there is a desire to extend Bohr's model to accommodate the spin of the electron, then experimental observations mandate the existence of the Thomas precession, which is a questionable hypothesis, or the existence of artificially robust orbits during spin-flip transitions. This is tantamount to admitting that Bohr's model, whi…
Electric and magnetic dipole shielding constants for the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
Neutral tungsten is the primary candidate as a wall material in the divertor region of the International Thermonuclear Experimental Reactor (ITER). The efficient operation of ITER depends heavily on precise atomic physics calculations for the determination of reliable erosion diagnostics, helping to characterise the influx of tungsten impurities into the core plasma. The following paper presents detailed calculations of the atomic structure of neutral tungsten using the multiconfigurational Dirac-Fock method, drawing comparisons with experimental measurements where available, and includes a cr…
