A state-of-the-art approach for calculating the finite nuclear size correction to atomic energy levels and the bound-electron $g$ factor is introduced and demonstrated for a series of highly charged hydrogen-like ions. Firstly, self-consistent mean-field calculations based on the Skyrme-type nuclear interaction are employed in order to produce a realistic nuclear proton distribution. In the second step, the obtained nuclear charge density is used to construct the potential of an extended nucleus, and the Dirac equation is solved numerically. The ambiguity in the choice of a Skyrme parametrization is supressed by fine-tuning of only one parameter of the Skyrme force in order to accurately reproduce the experimental values of nuclear radii in each particular case. The homogeneously charged sphere approximation, the two-parameter Fermi distribution and experimental nuclear charge distributions are used for comparison with our approach, and the uncertainties of the presented calculations are estimated. In addition, suppression of the finite nuclear size effect for the specific differences of $g$ factors is demonstrated.
This library (collection of subroutines) is presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. These quantities include the coefficients of fractional parentage, the reduced coefficients of fractional parentage as well as reduced and completely reduced matrix elements for several operators. So the library is assigned for any computational scheme. The software is an implementation of a methodology based on the second quantization in coupled tensorial form, the angular momentum theory in 3 spaces (orbital, spin and quas…
An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm allows the use of the same piece of computer code to evaluate any particular diagram in any specific order of the perturbation theory or to calculate similar terms in other areas of the many-body theory, like e.g. terms in the coupled-cluster equations. The use of the algorithm is illustrated by calculating the second and third order correlation corrections to the removal energies of electrons from the ground state of sodium, copper and gallium and by cal…
The hyperfine interaction as a probe of the microscopic structure of the atomic nucleus
Center for Quantum Nanoscience, Institute for Basic Science（量子纳米科学中心，基础科学研究院）；Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg（斯特拉斯堡大学，法国国家科学研究中心，斯特拉斯堡材料物理与化学研究所）；Ewha Womans University（梨花女子大学）；Université de Strasbourg, CNRS, Institut de Chimie（斯特拉斯堡大学，法国国家科学研究中心，化学研究所）；Université de Strasbourg, CNRS, Institut pluridisciplinaire Hubert Curien（斯特拉斯堡大学，法国国家科学研究中心，于贝尔·居里跨学科研究所）
Energy levels, radiative rates and lifetimes are reported for four S-like ions, namely Sc~VI, V VIII, Cr IX, and Mn~X. Two independent atomic structure codes, namely the general-purpose relativistic atomic structure package ({\sc grasp}) and the flexible atomic code ({\sc fac}), have been adopted for calculating the energy levels, with differing amounts of configuration interaction. This is mainly to make some assessment of accuracy. However, the {\sc grasp} alone is used for calculating the remaining parameters. Results are reported for varying number of levels of these ions, and for calculat…
Using a new result on the integral involving the product of Bessel functions and associated Laguerre polynomials, published in the mathematical literature some time ago, we present an alternative method for calculating discrete-discrete transition form factors for hydrogen-like atoms. For comparison, an overview is also given of two other commonly used methods.
In this work, atomic calculations were performed within the local-density and generalized-gradient approximations of exchange and correlation density functionals within density-functional theory to provide accurate periodic trends of first ionization energies and electron affinities of the atomic series from hydrogen to xenon. Electronegativities were determined directly from Mulliken's formula and were shown to be equivalently calculated rather by using Slater-Janak's transition state or by calculating the electrostatic self-energies of the orbitals involved in the transition to ions. Finally…
The ac Stark shift of hyperfine levels of neutral atoms can be calculated using the third order perturbation theory(TOPT), where the third order corrections are quadratic in the atom-photon interaction and linear in the hyperfine interaction. In this paper, we use Green's function to derive the $E^{[2+ε]}$ method which can give close values to those of TOPT for the differential light shift between two hyperfine levels. It comes with a simple form and easy incorporation of theoretical and experimental atomic structure data. Furthermore, we analyze the order of approximation and give the conditi…
We present a theoretical study of three-photon electromagnetically induced absorption for a ladder-type three-level atomic system. A probe beam was tuned to the lower line and two counter-propagating, linearly polarized coupling beams were tuned to the upper line. The system can be modeled with a three- (or five-) level scheme when the polarization directions of the coupling beams are parallel (or perpendicular). By calculating the absorption coefficients analytically for the two schemes, we found that the corresponding absorption coefficients were identical except for different transition str…
In this article we report the release of a new program for calculating the emissivity of atomic transitions. The program, which can be obtained with its documentation from our website www.scienceware.net, passed various rigorous tests and was used by the author to generate theoretical data and analyze observational data. It is particularly useful for investigating atomic transition lines in astronomical context as the program is capable of generating a huge amount of theoretical data and comparing it to observational list of lines. A number of atomic transition algorithms and analytical techni…
In order to study 4-body atomic collisions such as excitation-ionization, transfer with target excitation, and double electron capture, the calculation of a nine-dimensional numerical integral is often required. This calculation can become computationally expensive, especially when calculating fully differential cross sections (FDCS), where the positions and momenta of all the particles are known. We have developed a new technique for calculating FDCS using fewer computing hours, but more memory. This new technique allows for much more efficient calculations and the use of many fewer resources…
We outline a non-perturbative procedure for calculating the total photoionization cross-section of two-electron atomic systems. The procedure is based on the Floquet-Fourie representation of the solution of the time-dependent Schrodinger equation. The Floquet-Fourie ansatz produces a set of equations which is recast into a generalized eigenvalue problem by means of the complex rotation procedure. With the use of the Hylleraas-type basis functions, the total photoionization cross-sections are obtained within the accuracy of a fraction of a percent. The total photoionization cross-sections for n…
The contribution of the CP violating three-gluon Weinberg operator, $\frac{1}{3!} w f^{abc} ε^{νραβ} G^a_{μν} G^b_{αβ} G^{c μ}_ρ$, to the atomic and nuclear EDMs is estimated using QCD sum rules. After calculating the transition matrix element between the pion and the vacuum through the Weinberg operator, we obtain the long-range CP-odd nuclear force by determining the isovector CP-odd pion-nucleon vertex, using chiral perturbation theory at NLO. The EDMs of $^{199}$Hg, $^{129}$Xe, $^{225}$Ra, $^2$H, and $^3$He are finally given including comprehensive uncertainty analysis. While the leading c…
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 …
ARC 3.0 is a modular, object-oriented Python library combining data and algorithms to enable the calculation of a range of properties of alkali and divalent atoms. Building on the initial version of the ARC library [N. Šibalić et al, Comput. Phys. Commun. 220, 319 (2017)], which focused on Rydberg states of alkali atoms, this major upgrade introduces support for divalent atoms. It also adds new methods for working with atom-surface interactions, for modelling ultracold atoms in optical lattices and for calculating valence electron wave functions and dynamic polarisabilities. Such calculations …
Background: Atomic spectral lines from different isotopes display a small shift in energy, commonly referred to as the line isotope shift. One of the components of the isotope shift is the field shift, which depends on the extent and the shape of the nuclear charge density distribution. Purpose: To investigate how sensitive field shifts are with respect to variations in the nuclear size and shape and what information of nuclear charge distributions that can be extracted from measured field shifts. Methods: Nuclear properties are obtained from nuclear density functional theory calculations base…
