scholarly journals Numerical Procedures for Relativistic Atomic Structure Calculations

Atoms ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 85
Author(s):  
Charlotte Froese Fischer ◽  
Andrew Senchuk
Keyword(s):  
Variational Methods ◽  
Atomic Structure ◽  
Finite Differences ◽  
Heavy Elements ◽  
Transition Rates ◽  
Numerical Accuracy ◽  
Hartree Fock ◽  
Atomic Structure Calculations ◽  
Structure Calculations

Variational methods are used extensively in the calculation of transition rates for numerous lines in a spectrum. In the GRASP code, solutions of the multiconfiguration Dirac–Hartree–Fock (MCDHF) equations that optimize the orbitals are represented by numerical values on a grid using finite differences for integration and differentiation. The numerical accuracy and efficiency of existing procedures are evaluated and some modifications proposed with heavy elements in mind.

scholarly journals Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

Atoms ◽  
2018 ◽  
Vol 6 (2) ◽  
pp. 22 ◽  
Author(s):  
Thomas Gomez ◽  
Taisuke Nagayama ◽  
Chris Fontes ◽  
Dave Kilcrease ◽  
Stephanie Hansen ◽  
...  
Keyword(s):  
Atomic Structure ◽  
Line Broadening ◽  
Matrix Methods ◽  
Hartree Fock ◽  
Atomic Structure Calculations ◽  
Structure Calculations

scholarly journals Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

2018 ◽  
Author(s):  
Thomas Gomez ◽  
Taisuke Nagayama ◽  
Dave Kilcrease ◽  
Stephanie Hansen ◽  
Mike Montgomery ◽  
...  
Keyword(s):  
Differential Equation ◽  
Atomic Structure ◽  
Shooting Method ◽  
Local Density ◽  
Line Broadening ◽  
Matrix Methods ◽  
Hartree Fock ◽  
Spectral Line Broadening ◽  
Atomic Structure Calculations ◽  
Structure Calculations

Atomic structure of N-electron atoms is often determined using the Hartree-Fock method, which is an integro-differential equation. The exchange term of the Hartree-Fock equations is usually treated as an inhomogeneous term of a differential equation, or with a local density approximation. This work uses matrix methods to solve for the Hartree-Fock equations, rather than the more commonly-used shooting method to integrate an inhomogeneous differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using computer linear-algebra packages. We extend the same technique to integro-differential equations, where a discretized integral can be written as a sum in matrix form. This method is compared against experiment and standard atomic structure calculations. We also can use this method for free-electron wavefunctions. This technique is important for spectral line broadening in two ways: improving the atomic structure calculations, and improving the motion of the plasma electrons that collide with the atom.

scholarly journals Atomic structure calculations and beam-foil observations of La IV

2009 ◽  
Vol 87 (12) ◽  
pp. 1275-1282 ◽  
Author(s):  
Émile Biémont ◽  
Mathieu Clar ◽  
Saturnin Yoca Enzonga ◽  
Vanessa Fivet ◽  
Pascal Quinet ◽  
...  
Keyword(s):  
Atomic Structure ◽  
Extreme Ultraviolet ◽  
Complex Situation ◽  
Time Resolved ◽  
Hartree Fock ◽  
Spark Discharges ◽  
Ion Energies ◽  
Atomic Structure Calculations ◽  
Structure Calculations ◽  
Beam Foil

Relativistic Hartree–Fock and multiconfigurational Dirac–Fock calculations of atomic structure and transition rates have been carried out in trebly ionized lanthanum (La3+, Z = 57). The calculations have to cope with configuration interaction effects but also with the very complex situation of the collapse of the 4f wave function. The calculations are compared to experimental data obtained with beam-foil spectroscopy in the extreme ultraviolet, at ion energies that favour the production of the spectrum La IV. Besides lines known from sliding spark discharges, many more lines are observed that have not yet been identified. Time-resolved measurements yield three level lifetimes in La IV that agree roughly with the results of our own calculations.

A study of 5p excitation in atomic barium. I. The 5p absorption spectra of Ba 1, Cs 1 and related elements

1979 ◽  
Vol 290 (1371) ◽  
pp. 327-352 ◽  
Keyword(s):  
Absorption Spectra ◽  
Atomic Structure ◽  
Double Ionization ◽  
Hartree Fock ◽  
Atomic Structure Calculations ◽  
Structure Calculations ◽  
Limit Structure

New observations of the 5p spectra of Cs i and Ba i are reported. The extreme complexity of the structure does not permit precise configuration labels to be attached to all the excited levels. Nevertheless, more than 160 transitions in Ba i have been ordered into 14 series converging on experimentally known levels of the parent ion. An attempt has been made to analyse the limit structure by comparison with the data for Cs I and Hartree-Fock atomic structure calculations. The results obtained are consistent with previous interpretations of the double ionization anomaly in Ba I. Further comments are made on the comparison between experiment and the predictions of the r.p.a.e. theory for 5p excitation in Ba i. It is shown that the 5p 6 6s 2 S 1/2 -> 5p 5 6s 2 2 P 1/2 and 2 P 3/2 transitions of Cs i have been incorrectly identified and new assignments are proposed.

scholarly journals Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

Sign in / Sign up

Export Citation Format

Share Document