Relativistic many-body calculations of excitation energies and transition rates from core-excited states in silverlike ions

2009 ◽  
Vol 87 (1) ◽  
pp. 83-94 ◽  
Author(s):  
U I Safronova ◽  
A S Safronova
Keyword(s):  
Energy Levels ◽  
Second Order ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Transition Rates ◽  
Matrix Elements ◽  
Coupling Coefficients ◽  
Many Body ◽  
Excitation Energies ◽  
Radiation Spectra

Energies of [Kr]4d94f2, [Kr]4d94f5l, and [Kr]4d95l5l′ states (with l = s, p, d, f) for Ag-like ions with Z = 50–100 are evaluated to second order in relativistic many-body perturbation theory (RMBPT) starting from a Pd-like Dirac–Fock potential ([Kr]4d10). Second-order Coulomb and Breit–Coulomb interactions are included. Correction for the frequency dependence of the Breit interaction is taken into account in lowest order. The Lamb-shift correction to energies is also included in lowest order. Intrinsic particle–particle–hole contributions to energies are found to be 20–30% of the sum of the one- and two-body contributions. Transition rates and line strengths are calculated for the 4d–4f and 4d–5l electric-dipole (E1) transitions in Ag-like ions with nuclear charge Z = 50–100. RMBPT including the Breit interaction is used to evaluate retarded E1 matrix elements in length and velocity forms. First-order RMBPT is used to obtain intermediate coupling coefficients and second-order RMBPT is used to calculate transition matrix elements. A detailed discussion of the various contributions to the dipole matrix elements and energy levels is given for silverlike tungsten (Z = 74). The transition energies included in the calculation of oscillator strengths and transition rates are from second-order RMBPT. Trends of the transition rates as functions of Z are illustrated graphically for selected transitions. Additionally, we perform calculations of energies and transition rates for Ag-like W by the Hartree–Fock relativistic method (Cowan code) and the Multiconfiguration Relativistic Hebrew University Lawrence Atomic Code (HULLAC code) to compare with results from the RMBPT code. These atomic data are important in modeling of N-shell radiation spectra of heavy ions generated in various collision as well as plasma experiments. The tungsten data are particularly important for fusion application.PACS Nos.: 31.15.A–, 31.15.ag, 31.15.am, 31.15.aj

Relativistic many-body calculations of excitation energies, line strengths, transition rates, and oscillator strengths in Pd-like ions

2005 ◽  
Vol 83 (8) ◽  
pp. 813-828 ◽  
Author(s):  
U I Safronova ◽  
T E Cowan ◽  
W R Johnson
Keyword(s):  
Perturbation Theory ◽  
Transition Probabilities ◽  
Second Order ◽  
Oscillator Strengths ◽  
Transition Rates ◽  
Matrix Elements ◽  
Coupling Coefficients ◽  
Many Body ◽  
Excitation Energies ◽  
Line Strengths

Excitation energies, line strengths, oscillator strengths, and transition probabilities are calculated for 4d–14f, 4d–15p, 4d–15f, and 4d–16p hole–particle states in Pd-like ions with nuclear charges Z ranging from 49 to 100. Relativistic many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start from a [Kr] 4d10 closed-shell Dirac–Hartree–Fock (DHF) potential and include second- and third-order Coulomb corrections and second-order Breit–Coulomb corrections. First-order perturbation theory is used to obtain intermediate-coupling coefficients and second-order MBPT is used to determine matrix elements. Contributions from negative-energy states are included in the second-order electric-dipole matrix elements. The resulting transition energies, line strengths, and transition rates are compared with experimental values and with other recent calculations. Trends of oscillator strengths as functions of nuclear charge Z are shown graphically for all transitions from the 4d–14f, 4d–15p, 4d–15f, and 4d–16p states to the ground state. PACS Nos.: 31.15.Ar, 31.15.Md, 32.70.Cs, 32.30.Rj, 31.25.Jf

E1, E2, M1, and M2 transitions in the nickel isoelectronicsequence

2004 ◽  
Vol 82 (5) ◽  
pp. 331-356 ◽  
Author(s):  
S M Hamasha ◽  
A S Shlyaptseva ◽  
U I Safronova
Keyword(s):  
Perturbation Theory ◽  
Negative Energy ◽  
Second Order ◽  
Oscillator Strengths ◽  
Transition Rates ◽  
Matrix Elements ◽  
Coupling Coefficients ◽  
Many Body ◽  
Negative Energy States ◽  
Energy States

A relativistic many-body method is developed to calculate energy and transition rates for multipole transitions in many-electron ions. This method is based on relativistic many-body perturbation theory (RMBPT), agrees with MCDF calculations in lowest order, includes all second-order correlation corrections, and includes corrections from negative-energy states. Reduced matrix elements, oscillator strengths, and transition rates are calculated for electric-dipole (E1) and electric-quadrupole (E2) transitions, and magnetic-dipole (M1) and magnetic-quadrupole (M2) transitions in Ni-like ions with nuclear charges ranging from Z = 30 to 100. The calculations start from a 1s22s22p63s23p63d10 Dirac–Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order E1, M1, E2, and M2 matrix elements. The resulting transition energies and transition rates are compared with experimental values and withresults from other recent calculations.PACS Nos.: 32.30.Rj, 32.70.Cs, 32.80.Rm, 34.70.+e

Excitation energies, E1, M1, and E2 transition rates, and lifetimes in Ca+, Sr+, Cd+, Ba+, and Hg+ 1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

2011 ◽  
Vol 89 (4) ◽  
pp. 465-472 ◽  
Author(s):  
U.I. Safronova ◽  
M.S. Safronova
Keyword(s):  
Electric Quadrupole ◽  
Oscillator Strengths ◽  
Transition Rates ◽  
Order Method ◽  
Matrix Elements ◽  
Many Body ◽  
Excitation Energies ◽  
International Colloquium ◽  
The Matrix ◽  
Many Body Perturbation Theory

Excitation energies of ns1/2, npj, and ndj states in Cd+ (n = 5), Hg+ (n = 5) and ns1/2, npj, and (n – 1)dj states in Ca+ (n = 4), Sr+ (n = 5), and Ba+ (n = 6) are evaluated using the linearized coupled-cluster (all-order) method. Reduced matrix elements, oscillator strengths, and transition rates are determined for the ns–npj–ndj (or ns–npj–(n – 1)dj) possible electric dipole transitions in Ca+, Sr+, Ba+, Cd+, and Hg+. Electric quadrupole matrix elements are evaluated to obtain ns1/2–(n – 1)dj transition rates in Ca+ (n = 5), Sr+ (n = 5), and Ba+ (n = 6). The matrix elements are calculated using both relativistic many-body perturbation theory, complete through third order, and the relativistic all-order method restricted to single and double (SD) excitations. The SD lifetime results for the np and nd states in Ca+, Sr+, Ba+, Cd+, and Hg+, are compared with the latest available experimental measurements. The contribution of the magnetic dipole nd3/2–nd5/2 transition to the lifetimes of the lowest nd5/2 level ln Ca+, Sr+, and Ba+ ions is discussed. These calculations provide a theoretical benchmark for comparison with experiment and theory as well as data needed for various applications.

Systematic calculations of energy levels and transitions rates in Mo XXVIII

2020 ◽  
Vol 75 (8) ◽  
pp. 739-747
Author(s):  
Feng Hu ◽  
Yan Sun ◽  
Maofei Mei
Keyword(s):  
Energy Levels ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Data Sets ◽  
Electron Systems ◽  
Excitation Energies ◽  
Experimental Values ◽  
Qed Effects ◽  
Hyperfine Structures ◽  
Good Agreement

AbstractComplete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé gJ-factors and E1, E2, M1, and M2 line strengths, oscillator strengths, transitions rates are reported for the low-lying 41 levels of Mo XXVIII, belonging to the n = 3 states (1s22s22p6)3s23p3, 3s3p4, and 3s23p23d. High-accuracy calculations have been performed as benchmarks in the request for accurate treatments of relativity, electron correlation, and quantum electrodynamic (QED) effects in multi-valence-electron systems. Comparisons are made between the present two data sets, as well as with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology wherever available. The calculated values including core-valence correction are found to be in a good agreement with other theoretical and experimental values. The present results are accurate enough for identification and deblending of emission lines involving the n = 3 levels, and are also useful for modeling and diagnosing plasmas.

Relativistic many-body calculations of atomic properties in Pd-like ions

2008 ◽  
Vol 86 (1) ◽  
pp. 131-149 ◽  
Author(s):  
U I Safronova ◽  
R Bista ◽  
R Bruch ◽  
H Merabet
Keyword(s):  
Perturbation Theory ◽  
Negative Energy ◽  
Second Order ◽  
Energy Splitting ◽  
Transition Rates ◽  
Matrix Elements ◽  
Many Body ◽  
Negative Energy States ◽  
Many Body Perturbation Theory ◽  
Energy States

Wavelengths, transition rates, and line strengths are calculated for the 85 possible multipole transitions between the excited 4p6 4d9 4f, 4p6 4d9 5l, 4p5 4d10 4f, and 4p5 4d10 5l states and the ground 4p6 4d10 state in Pd-like ions with the nuclear charges ranging from Z = 47 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in hole–particle systems. This method is based on the relativistic many-body perturbation theory, agrees with MCDF calculations in lowest order, includes all second-order correlation corrections, and includes corrections from negative energy states. The calculations start from a [Zn]4p64d10 Dirac–Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order multipole matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. Trends of the transitions rates for the selected multipole transitions as function of Z are illustrated graphically. The Z dependence of the energy splitting for all triplet terms of the 4p64d9 4f and 4p64d9 5l configurations are shown for Z = 47–100. PACS Nos.: 31.15.Ar, 31.15.Md, 32.70.Cs, 32.30.Rj, 31.25.Jf

scholarly journals Theoretical investigation of oscillator strengths and lifetimes in Ti II

2020 ◽  
Vol 643 ◽  
pp. A156
Author(s):  
W. Li ◽  
H. Hartman ◽  
K. Wang ◽  
P. Jönsson
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Electric Quadrupole ◽  
General Purpose ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Excitation Energies ◽  
Hartree Fock ◽  
Self Energy ◽  
Theoretical Predictions

Aims. Accurate atomic data for Ti II are essential for abundance analyses in astronomical objects. The aim of this work is to provide accurate and extensive results of oscillator strengths and lifetimes for Ti II. Methods. The multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2018, were used in the present work. In the final RCI calculations, the transverse-photon (Breit) interaction, the vacuum polarisation, and the self-energy corrections were included. Results. Energy levels and transition data were calculated for the 99 lowest states in Ti II. Calculated excitation energies are found to be in good agreement with experimental data from the Atomic Spectra Database of the National Institute of Standards and Technology based on the study by Huldt et al. Lifetimes and transition data, for example, line strengths, weighted oscillator strengths, and transition probabilities for radiative electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) transitions, are given and extensively compared with the results from previous calculations and measurements, when available. The present theoretical results of the oscillator strengths are, overall, in better agreement with values from the experiments than the other theoretical predictions. The computed lifetimes of the odd states are in excellent agreement with the measured lifetimes. Finally, we suggest a relabelling of the 3d2(12D)4p y2 D3/2o and z2 P3/2o levels.

Allowed and forbidden transition rates and corresponding wavelengths for Si-like Au ion (Au65+) by relativistic configuration interaction method

2018 ◽  
Vol 96 (10) ◽  
pp. 1116-1137
Author(s):  
S.M. Hamasha ◽  
A. Almashaqba
Keyword(s):  
Configuration Interaction ◽  
Energy Levels ◽  
Theoretical Data ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Transition Rates ◽  
Interaction Method ◽  
Configuration Interaction Method ◽  
Relativistic Configuration ◽  
Relativistic Configuration Interaction

Large-scale atomic calculations are carried out to produce data of atomic structure and transitions rates for Si-like Au ion (Au65+). Generated atomic data are essential for modeling of M-shell spectra of gold ions in Au plasma, and fusion research. Energy levels are calculated by applying two methods: the relativistic configuration interaction method (RCI) of the flexible atomic code (FAC) and the multi-reference many body perturbation theory method (MR-MBPT). Energy levels, oscillator strengths, and transition rates are calculated for transitions between excited and ground states from n = 3l to n′l′, where n′ = 4, 5, 6, and 7; and l and l′ are the proper angular momenta of shells n and n′, respectively. The electric dipole (E1), electric quadrupole (E2), electric octupole (E3), magnetic dipole (M1), magnetic quadrupole (M2), and magnetic octupole (M3) transitions are all considered in the calculations. Correlation effects, relativistic effects, and QED effects are also included in the calculations. The two methods yield comparable values of energy levels. Data of energy levels of low-lying states and data for inner shell transitions reported in this study demonstrate good agreement with published experimental and theoretical data.

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