We demonstrate that $V^{N-M}$ approximation is a good starting point for the configuration interaction calculations for many-electron atoms and ions. $N$ is the total number of electrons in the neutral atom, $M$ is the number of valence electrons. $V^{N-M}$ is the self-consistent Hartree Fock potential for a closed-shell ion with all valence electrons removed. Using of the $V^{N-M}$ approximation considerably simplifies the many-body perturbation theory for the core-valence correlations. It makes it easier to include higher-order correlations which often significantly improves the accuracy of the calculations. Calculations for krypton and barium and their positive ions are presented for illustration.
It is demonstrated, how the theoretical analysis preceding the numerical calculations helps to calculate the energy of the ground state of helium atom, and enables to avoid qualitative errors in the calculations of the characteristics of the double photoionization.
We present the AMBiT software package for general atomic structure calculations. This software implements particle-hole configuration interaction with many-body perturbation theory (CI+MBPT) for fully relativistic calculations of atomic energy levels, electric- and magnetic-multipole transition matrix elements, g-factors and isotope shifts. New numerical methods and modern high-performance computing techniques employed by this software allow for the calculation of open-shell systems with many valence-electrons ($N > 5$) to a high degree of accuracy and in a highly computationally efficient man…
The FAC, GRASP2K, and MCDFGME codes are compared in three case study of radiative transitions occurring in tungsten ions: (i) Ni1 and Ni2 lines in Ni-like tungsten, (ii) $3p_{3/2}{-}3p_{1/2}$ fine splitting in Cl-like tungsten, and (iii) $Kα_{1}$ and $Kα_{2}$ lines in W VIII. Various approaches to including the Breit interaction term and QED corrections in atomic calculations are examined. Electron correlation effects are also investigated and compared to the Breit and QED contributions. The data presented here may be used to estimate theoretical uncertainties relevant to interpretation of hig…
A brief review of the search for variation of the fine structure constant in quasar absorption spectra is presented. Special consideration is given to the role of atomic calculations in the analysis of the observed data. A range of methods which allow to perform calculations for atoms or ions with different electron structure and which cover practically all periodic table of elements is discussed. Critical compilation of the results of the calculations as well as a review of the most recent results of the analysis are presented.
We use all-order relativistic many-body perturbation theory to study 5s^2 nl configurations of In I and Sn II. Energies, E1-amplitudes, and hyperfine constants are calculated using all-order method, which accounts for single and double excitations of the Dirac-Fock wave functions.
We calculate the spectra, electric dipole transition rates and isotope shifts of the super heavy elements Ds (Z=110), Rg (Z=111) and Cn (Z=112) and their ions. These calculations were performed using a recently developed, efficient version of the ab initio configuration interaction combined with perturbation theory to treat distant effects. The successive ionization potentials of the three elements are also calculated and compared to lighter elements.
We calculate the spectrum and allowed E1 transitions of the superheavy element Og (Z=118). A combination of configuration interaction (CI) and perturbation theory (PT) is used (Dzuba \textit{et at.} Phys. Rev. A, \textbf{95}, 012503 (2017)). The spectrum of lighter analog Rn I is also calculated and compared to experiment with good agreement.
We develop a theoretical method within the framework of relativistic many-body theory to accurately treat correlation corrections in atoms with few valence electrons. This method combines the all-order approach currently used in precision calculations of properties of monovalent atoms with the configuration-interaction approach that is applicable for many-electron systems. The method is applied to Mg, Ca, Sr, Zn, Cd, Ba, and Hg to evaluate ionization energies and low-lying energy levels.
We review the progress in atomic structure theory with a focus on superheavy elements and the aim to predict their ground state configuration and element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is important to correctly solve the Dirac equation in strong Coulomb fields, and also to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-elect…
This contribution reviews a selection of findings on atomic density functions and discusses ways for reading chemical information from them. First an expression for the density function for atoms in the multi-configuration Hartree--Fock scheme is established. The spherical harmonic content of the density function and ways to restore the spherical symmetry in a general open-shell case are treated. The evaluation of the density function is illustrated in a few examples. In the second part of the paper, atomic density functions are analyzed using quantum similarity measures. The comparison of ato…
High precision atomic data is indispensable for experiments involving studies of fundamental interactions, astrophysics, atomic clocks, plasma science, and others. We develop new parallel atomic structure codes and explore the difficulties of load-balancing in these codes. Efficient load-balancing of matrix elements for many-electron systems is very difficult due to the intrinsic nature of the computational methods used to compute them. By arithmetically selecting determinants for each core, we achieve very even workload distribution, and attain near-perfect linear scalability and efficiency w…
We employ a technique that combines the configuration interaction method with the singles-doubles coupled-cluster method to perform calculation of the energy levels, transition amplitudes, lifetimes, g-factors, and magnetic dipole and electric quadrupole hyperfine structure constants for many low-lying states of neutral actinium. We find very good agreement with existing experimental energy levels and make accurate predictions for missing levels. It has been noted that some of the levels have been previously misidentified; our analysis supports this claim. If spectroscopy is performed with act…
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 elastic scattering of twisted electrons by neutral atoms is studied within the fully relativistic framework. The electron-atom interaction is taken into account in all orders, thus allowing us to explore high-order effects beyond the first Born approximation. In order to illustrate these effects, detailed calculations of the total and differential cross sections as well as the degree of polarization of scattered electrons are performed. Together with the analysis of the effects beyond the first Born approximation, we discuss the influence of the kinematic parameters of the incident twisted…
The Rabi frequency (coupling strength) of an electric-dipole transition is an important experimental parameter in laser-cooling and other atomic physics experiments. Though the relationship between Rabi frequency and atomic wavefunctions and/or atomic lifetimes is discussed in many references, there is a need for a concise, self-contained, accessible introduction to such calculations suitable for use by the typical student of laser cooling (experimental or theoretical). In this paper, I outline calculations of the Rabi frequencies for atoms with sub-structure due to orbital, spin and nuclear a…
We present a detailed study of the effect of the double core polarization (the polarization of the core electrons due to the simultaneous action of the electric dipole and parity-violating weak fields) for amplitudes of the s-s and s-d parity non-conserving transitions in Rb, Cs, Ba +, La 2+, Tl, Fr, Ra +, Ac 2+ and Th 3+ as well as electron EDM enhancement factors for the ground states of the above neutral atoms and Au. This effect is quite large and has the potential to resolve some disagreement between calculations in the literature. It also has significant consequences for the use of exper…
The existence of a finite electric dipole moment (EDM) d_a of the closed-shell atom Yb implies parity and time reversal violations involving the nuclear sector. An important effect which can contribute to the Yb EDM is the tensor-pseudotensor electron-nucleus interaction characterized by the coupling constant C_T. Within the Standard Model (SM) of particle physics C_T=0, as this form of interaction is not allowed. If a finite d_a of Yb is observed in experiments, then an estimate of C_T can be obtained by combining with the theoretical calculations. A non-zero C_T implies physics beyond the st…
The three-body dynamics of the ionization of the atomic hydrogen by 30 keV antiproton impact has been investigated by calculation of fully differential cross sections (FDCS) using the classical trajectory Monte Carlo (CTMC) method. The results of the calculations are compared with the predictions of quantum mechanical descriptions: The semi-classical time-dependent close-coupling theory, the fully quantal, time-independent close-coupling theory, and the continuum-distorted-wave-eikonal-initial-state model. In the analysis particular emphasis was put on the role of the nucleus-nucleus (NN) inte…
Recently, S. Aggarwal [Chin. Phys. B 23 (2014) 093203] reported energy levels, radiative rates and lifetimes for the lowest 60 levels belonging to the 2s$^2$2p$^5$, 2s2p$^6$ and 2s$^2$2p$^4$3$\ell$ configurations of F-like tungsten. There is no discrepancy for his calculated energies for the levels and the radiative rates for the limited number of E1 transitions, but the reported results for lifetimes are highly inaccurate. According to our calculations, errors in his reported lifetimes are up to 6 orders of magnitude for several levels. Here we report the correct lifetimes for future comparis…
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine-structure constant $α$. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, $r_1$, $r_2$ and $r = |\vec{r}_1-\vec{r}_2|$. The choice of the exponential basis functions of the form $\exp(-αr_1 -βr_2 -γr)$ allows us to construct an accurate and c…
We study a wide range of neutral atoms and ions suitable for ultra-precise atomic optical clocks with naturally suppressed black body radiation shift of clock transition frequency. Calculations show that scalar polarizabilities of clock states cancel each other for at least one order of magnitude for considered systems. Results for calculations of frequencies, quadrupole moments of the states, clock transition amplitudes and natural widths of upper clock states are presented.
The combination of the configuration interaction method and all-order single-double coupled-cluster technique is used to calculate excitation energies, ionization potentials and static dipole polarizabilities of superheavy elements nobelium, lawrencium and rutherfordium. Breit and quantum electrodynamic corrections are also included. The results for the superheavy elements are compared with earlier calculations where available. Similar calculations for lighter analogs, ytterbium, lutetium, and hafnium are used to study the accuracy of the calculations. The estimated uncertainties of the final …
We report on deviations beyond the Born-Oppenheimer approximation in the potassium inter-atomic potentials. Identifying three up-to-now unknown $d$-wave Feshbach resonances, we significantly improve the understanding of the $^{39}$K inter-atomic potentials. Combining these observations with the most recent data on known inter- and intra-isotope Feshbach resonances, we show that Born-Oppenheimer corrections can be determined from atomic collisional properties alone and that significant differences between the homo- and heteronuclear case appear.
Petaflop architectures are currently being utilized efficiently to perform large scale computations in Atomic, Molecular and Optical Collisions. We solve the Schrödinger or Dirac equation for the appropriate collision problem using the R-matrix or R-matrix with pseudo-states approach. We briefly outline the parallel methodology used and implemented for the current suite of Breit-Pauli and DARC codes. In this report, various examples are shown from our theoretical results compared with experimental results obtained from Synchrotron Radiation facilities where the Cray architecture at HLRS is pla…
We have developed an efficient tabulation scheme to evaluate $6j$ symbol for atomic calculations. The scheme is appropriate for coupled-cluster based calculations. In particular, for perturbed coupled-clusters calculations, which has another perturbation in addition to the residual Coulomb interaction. The scheme relies on the symmetry of the $6j$ symbol and the triangular conditions.
The multiconfiguration Dirac-Hartree-Fock (MCDHF) method has been employed to calculate atomic electric dipole moments (EDM) of 225^Ra, 199^Hg, and 171^Yb. For the calculations of the matrix elements we extended the relativistic atomic structure package GRASP2K. The extension includes programs to evaluate matrix elements of (P, T)-odd e-N tensor-pseudotensor and pseudoscalar-scalar interactions, the atomic electric dipole interaction, the nuclear Schiff moment, and the interaction of the electron electric dipole moment with nuclear magnetic moments. The interelectronic interactions were accoun…
Atomic spectra and other properties of superheavy element dubnium (Db, Z=105) are calculated using recently developed method combining configuration interaction with perturbation theory (the CIPT method, Dzuba et al, Phys. Rev. A, {\bf 95}, 012503 (2017)). These include energy levels for low-lying states of Db and Db~II, electric dipole transition amplitudes from the ground state of Db, isotope shift for these transitions and ionisation potential of Db. Similar calculations for Ta, which is lighter analog of Db, are performed to control the accuracy of the calculations.
Today, relativistic calculations are known to provide a very successful means in the study of open-shell atoms and ions. But although accurate atomic data are obtained from these computations, they are traditionally carried out in jj-coupling and, hence, do often not allow for a simple LSJ classification of the atomic levels as needed by experiment. In fact, this lack of providing a proper spectroscopic notation from relativistic structure calculations has recently hampered not only the spectroscopy of medium and heavy elements, but also the interpretation and analysis of inner-shell processes…
We have designed a Euler approximation Monte-Carlo code for the calculation of the ionization of atomic hydrogen by protons with energies between 0.05 and 1.0 MeV. This code is used to calculate the total ionization cross sections s(E), the angular distribution double differential cross sections d2s/ (dW - dE) for electrons with energies of 150 eV ionized by 300 keV protons and the energy distribution d2s/ (dW - dE) for the ionized electrons emitted at 10o by protons of energy 300 keV. Our calculations are compared to experimental values of these quantities as well as independent calculations.…
The magnetic hyperfine structure constants have been calculated for low-lying levels in neutral gold atom and gold-like ion of mercury taking into account Bohr--Weisskopf (BW) effect. BW effect is represented as a product of atomic and nuclear ($d_\mathrm{nuc}$) factors. We have calculated the atomic factors, which enable one to extract BW-correction values for far from stability gold nuclei from the experimental data. The possible uncertainty of our atomic calculations have been estimated by the comparison with the available experimental data. It has been shown that the standard single-partic…
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…
We derive the expression for spontaneous emission rate in finite one-dimensional photonic crystal with arbitrary defects using the effective resonator model to describe electromagnetic field distributions in the structure. We obtain explicit formulas for contributions of different types of modes, i.e. radiation, substrate and guided modes. Formal calculations are illustrated with a few numerical examples, which demonstrate that the application of effective resonator model simplifies interpretation of results.
A review of a renewed effort to recalculate astrophysical opacities using the R-Matrix method is presented. The computational methods and new extensions are described. Resulting enhancements found in test calculations under stellar interior conditions compared to the Opacity Project could potentially lead to the resolution of the solar abundances problem, as well as discrepancies between recent experimental measurements at the Sandia Z-pinch inertial confinement fusion device and theoretical opacity models. Outstanding issues also discussed are: (i) accuracy, convergence, and completeness of a…
Constrained molecular dynamics(CoMD) model, previously introduced for nuclear dynamics, has been extended to the atomic structure and collision calculations. Quantum effects corresponding to the Pauli and Heisenberg principle are enforced by constraints, in a parameter-free way. Our calculations for small atomic system, H, He, Li, Be, F reproduce the ground-state binding energies within 3%, compared with the results of quantum mechanical Hartree-Fock calculations.
We propose a new type of gauge-invariant expansion of the ionization probability amplitudes of atoms by short pulses of electromagnetic radiation. Contrary to previous gauge-invariant approaches to this problem it does not require different partitions of the total Hamiltonian depending on the choice of gauge. In a natural way the atomic potential is treated as perturbation acting on an electron interacting with strong pulse. Whereas this is a standard assumption of strong field approximation (SFA), we show that grouping consequently together \textit{all} terms of the same order in the atomic p…
A methodology is developed to compute photoionization cross-sections beyond the electric dipole (BED) approximation from response theory, using Gaussian type orbitals and plane waves for the initial and final states, respectively. The methodology is applied to compute photoionization cross-sections of atoms and ions from the first four rows of the Periodic Table. Analysing the error due to the plane wave description of the photoelectron, we find kinetic energy and concomitant photon energy thresholds above which the plane wave approximation becomes applicable. The correction introduced by goin…
A model of dense plasmas relying on the superconfiguration approximation is presented. In each superconfiguration the nucleus is totally screened by the electrons in a Wigner-Seitz sphere (ion-sphere model). Superconfigurations of the same charge are grouped into ions. It is shown that boundary values of the wavefunctions play a crucial role in the form of the Virial theorem from which the pressure formula is derived. Finally, a condition is presented and discussed, which makes the ion-sphere model variational when bound electrons are treated quantum-mechanically and free electrons quasi-class…
In this article we study the effects of higher body excitations in the relativistic CC calculations for atoms and ions with one valence electron using Fock-space CCSD, CCSD(T) and its unitary variants. The present study demonstrates that CCSD(T) estimates the ionization potentials (IPs) and the valence electron removal energies quite accurately for alkali atoms and singly ionized alkaline earth ions, but yields unphysical energy levels for atoms and/or ions with partially filled sub-shell like C II. We further demonstrate that the higher body excitation effects can be incorporated more effecti…
Basing on the relation between the Coulomb Green function and the Green function of harmonic oscillator, the algebraic representation of the many-particle Coulomb Green function in the form of annihilation and creation operators is established. These results allow us to construct purely algebraic method for atomic calculations and thus to reduce rather complicated calculations of matrix elements to algebraic procedures of transforming the products of annihilation and creation operators to a normal form. Effectiveness of the constructed method is demonstrated through the example problem: the gr…
The superposition of atomic potentials (SAP) approach has recently been shown to be a simple and efficient way to initialize electronic structure calculations [S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019)]. Here, we study the differences between effective potentials from fully numerical density functional and optimized effective potential calculations for fixed configurations. We find that the differences are small, overall, and choose exchange-only potentials at the local density approximation level of theory computed on top of Hartree-Fock densities as a good compromise. The differenc…
We prove some trigonometric identities involving Chebyshev polynomials of second kind. The identities were inspired by atomic form factor calculations. Generalizations of these identities, if found, will help to increase the numerical stability of atomic form factors calculations for highly excited states.
The accuracy of atomic theory calculations limits the extraction of nuclear charge radii from isotope shift measurements of odd-proton nuclei. For Na isotopes, though precise spectroscopic measurements have existed since more than half a century, calculations by different methods offer a wide range of values. Here, we present accurate atomic calculations to reliably extract the Na charge radii. By combining experimental matter radii with nuclear coupled-cluster calculations based on nucleon-nucleon and three-nucleon forces, we constrain the parameters obtained from the atomic calculations. The…
The photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environ…
The millicharged particle has become an attractive topic to probe physics beyond the Standard Model. In direct detection experiments, the parameter space of millicharged particles can be constrained from the atomic ionization process. In this work, we develop the relativistic impulse approximation (RIA) approach, which can duel with atomic many-body effects effectively, in the atomic ionization process induced by millicharged particles. The formulation of RIA in the atomic ionization induced by millicharged particles is derived, and the numerical calculations are obtained and compared with tho…
We benchmark three standard approximations for the many-body problem -- the Hartree-Fock, projected Hartree-Fock, and random phase approximations -- against full numerical configuration-interaction calculations of the electronic structure of atoms, from Li through to Ne. These configuration-interaction calculations used up to $2 \times 10^8$ uncoupled basis states, equivalent to $ 10^7$ coupled basis states (configuration state functions.) Each method uses exactly the same input, i.e., the same single-particle basis and Coulomb matrix elements, so any differences are strictly due to the approx…
We calculate the relative permittivity of a cold atomic gas under weak probe illumination, up to second order in the density. Within the framework of a diagrammatic representation method, we identify all the second order diagrams that enter into the description of the relative permittivity for coherent light transmission. These diagrams originate from pairwise position correlation and recurrent scattering. Using coupled dipole equations, we numerically simulate the coherent transmission with scalar and vector waves, and find good agreement with the perturbative calculations. We applied this pe…
Current-density-functional theory is used to calculate ionization energies of current-carrying atomic states. A perturbative approximation to full current-density-functional theory is implemented for the first time, and found to be numerically feasible. Different parametrizations for the current-dependence of the density functional are critically compared. Orbital currents in open-shell atoms turn out to produce a small shift in the ionization energies. We find that modern density functionals have reached an accuracy at which small current-related terms appearing in open-shell configurations a…
We report the implementation of a general-order relativistic coupled-cluster method for performing high-precision calculations of atomic and molecular properties. As a first application, the static dipole polarizabilities of the ground and first excited states of Al+ have been determined to precisely estimate the uncertainty associated with the BBR shift of its clock frequency measurement. The obtained relative BBR shift is -3.66+-0.44 for the 3s^2 ^1S_0^0 --> 3s3p ^3P_0^0 transition in Al+ in contrast to the value obtained in the latest clock frequency measurement, -9+-3 [Phys. Rev. Lett. 104…
It is demonstrated that Breit and negative-energy state contributions reduce the 2.5 sigma deviation [S.C. Bennett and C.E. Wieman, Phys. Rev. Lett. 82, 2484 (1999)] in the value of the weak charge of 133Cs from the Standard Model prediction to 1.7sigma. The corrections are obtained in the relativistic many-body perturbation theory by combining all-order Coulomb and second-order Breit contributions. The corrections to parity-nonconserving amplitudes amount to 0.6% in 133Cs and 1.1% in 223Fr. The relevant magnetic-dipole hyperfine structure constants are modified at the level of 0.3% in Cs, and…
Singly ionised Lutetium has recently been suggested as a potential clock candidate. Here we report a joint experimental and theoretical investigation of \ce{Lu^+}. Measurements relevant to practical clock operation are made and compared to atomic structure calculations. Calculations of scalar and tensor polarizabilities for clock states over a range of wavelengths are also given. These results will be useful for future work with this clock candidate.
The wavelengths and radiative transition probabilities for transitions 2lnl'-1snl", 2lnl'-1s2l", 1s2lnl'-1s^2.nl", 1s2lnl'-1s^2.2l", and the autoionization decay probabilities for doubly excited states 2lnl', 1s2lnl' were calculated in ions with atomic numbers Z=6-36 for n=2-10, l'=0-3. The calculations were carried out by means of the MZ code based on the Z-expansion method. Relativistic corrections were taken into account within the framework of the Breit operator. The main difference with previous calculations by MZ code consists in accounting for the first order corrections in powers of 1/…
