Reliable Predictions of Benzophenone Singlet–Triplet Transition Rates: A Second-Order Cumulant Approach

2020 ◽  
Author(s):  
Amalia Velardo ◽  
Alessandro Landi ◽  
Raffaele Borrelli ◽  
Andrea Peluso
Keyword(s):  
Second Order ◽  
Transition Rates ◽  
Triplet Transition

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

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

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

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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