scholarly journals Atomic X-ray Transition Probabilities: A Comparison of the Dipole Length, Velocity and Acceleration Forms

1984 ◽  
Vol 37 (1) ◽  
pp. 45 ◽  
Author(s):  
HM Quiney ◽  
FP Larkins
Keyword(s):  
Transition Probabilities ◽  
Nuclear Charge ◽  
Principal Quantum Number ◽  
Dipole Transition ◽  
Final States ◽  
X Ray ◽  
Hartree Fock ◽  
Isoelectronic Series ◽  
Rydberg Electron ◽  
Dipole Length

The length, velocity and acceleration forms of the dipole transition operator are examined in calculations of diagram and satellite X-ray emission probabilities in the Ne + to Ar 9 + isoelectronic series. All calculations are within the relaxed nonrelativistic Hartree-Fock framework, using separately optimized numerical wavefunctions for the initial and final electronic states. Divergence between the alternative forms of the transition moment, as the principal quantum 'number of the Rydberg electron and nuclear charge are increased, is discussed in the context of electron correlation differences between the initial and final states.

scholarly journals Corrigendum: Atomic X-ray Transition Probabilities: A Comparison of the Dipole Length, Velocity and Acceleration Forms

1984 ◽  
Vol 37 (6) ◽  
pp. 709
Author(s):  
HM Quiney ◽  
FP Larkins
Keyword(s):  
Matrix Element ◽  
Transition Probabilities ◽  
Typographical Error ◽  
X Ray ◽  
The Matrix ◽  
Dipole Length

All the expressions given in Table 1 (p. 47) must be multiplied by -}3/-}2 and the numerical values in Tables 2-4 by 3/2. Due to a typographical error, the coefficient of the matrix element for process C [ls]-[2p2(lS)]3p should be --}2/3 and not --}2/-}3 as printed.

scholarly journals X-ray Emission Spectra of Some Carbon-containing Molecules

1986 ◽  
Vol 39 (5) ◽  
pp. 717 ◽  
Author(s):  
RA Phillips ◽  
FP Larkins
Keyword(s):  
Transition Probabilities ◽  
Emission Spectra ◽  
Fluorescence Yield ◽  
Total Carbon ◽  
Molecular Orbital Calculations ◽  
Electronic Relaxation ◽  
X Ray ◽  
Hartree Fock ◽  
Relaxation Effects ◽  
Absolute Transition

Ab initio molecular orbital calculations for the energy and intensity of X-ray transitions associated with the carbon monoxide, hydrogen cyanide and carbon dioxide molecules have been calculated at the Hartree-Fock level. It is demonstrated that in general the absolute transition probabilities are sensitive to the inclusion of electronic relaxation effects and interatomic transition moment contributions. It is concluded that calculations for molecular X-r!ly emission henomena should be undertaken at least at the multicentre relaxed Hartree-Fock level to achieve a realistic basis for comparison with experiment. Total carbon-K X-ray rates do not show a strong variation with changes in the molecular environment. The total rates are of a similar magnitude to those reported for the atom. The calculated carbon-K fluorescence yield is also similar in both the carbon atom and the CO2 molecule.

Systematic Trends in Atomic Oscillator Strengths: The Helium Isoelectronic Sequence

1972 ◽  
Vol 50 (12) ◽  
pp. 1363-1369 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran
Keyword(s):  
Electric Dipole ◽  
Nuclear Charge ◽  
Principal Quantum Number ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Dipole Oscillator ◽  
Good Agreement ◽  
Comparison Data ◽  
Dipole Length

Electric dipole oscillator strengths (f values) have been calculated for a large number of singlet and triplet S–P, P–D, and D–F transitions in the helium isoelectronic sequence through O+6. The analytical orbital wave functions employed were of frozen-core type, and generally produce very good agreement between length and velocity values of the calculated oscillator strengths. A conspicuous exception occurs in many cases where the principal quantum number remains unchanged in the transition, and the more reliable dipole length values have been adopted for such transitions. The smooth variation of the calculated f values as functions of the inverse of the nuclear charge Z provided a sensitive check on the accuracy of the computations and indicated a considerable number of P–D transitions where the velocity values seemed the more reliable. Wherever comparison data are available, our calculated oscillator strengths are in excellent agreement with the most accurate values; in other cases, the absolute uncertainty in the f values should in no case exceed 5%.

ON THE EVALUATION OF THE RIGOROUS ELECTROSTATIC POTENTIAL/ATOMIC ENERGY RELATIONSHIP

2007 ◽  
Vol 06 (04) ◽  
pp. 761-788
Author(s):  
ABRAHAM F. JALBOUT
Keyword(s):  
Electrostatic Potential ◽  
Ground State ◽  
Density Functional ◽  
Nuclear Charge ◽  
Electrostatic Potentials ◽  
Atomic Energy ◽  
Hartree Fock ◽  
Isoelectronic Series ◽  
Neutral Ground

A series of atomic energy formulas that relate atomic energies to the electrostatic potentials V0 at nuclei are obtained by a series of polynomial and series fits of V0 versus nuclear charge (Z). Density functional and Hartree–Fock V0 are used for a series of fits that involve an isoelectronic series of anions, cations, and neutral ground state atoms to approximate atomic energies. Comparisons to the exact energies were performed in order to demonstrate the efficacy of the rigorous expressions.

EELS white line intensities calculated for the 3d and 4d metals

1989 ◽  
Vol 47 ◽  
pp. 388-389
Author(s):  
C. C. Ahn ◽  
D. H. Pearson ◽  
P. Rez ◽  
B. Fultz
Keyword(s):  
Experimental Data ◽  
Line Intensity ◽  
Transition Probabilities ◽  
Initial Increase ◽  
White Line ◽  
Hartree Fock ◽  
Line Intensities ◽  
Integrated Intensity ◽  
X Ray Absorption ◽  
The Continuum

Previous experimental measurements of the total white line intensities from L2,3 energy loss spectra of 3d transition metals reported a linear dependence of the white line intensity on 3d occupancy. These results are inconsistent, however, with behavior inferred from relativistic one electron Dirac-Fock calculations, which show an initial increase followed by a decrease of total white line intensity across the 3d series. This inconsistency with experimental data is especially puzzling in light of work by Thole, et al., which successfully calculates x-ray absorption spectra of the lanthanide M4,5 white lines by employing a less rigorous Hartree-Fock calculation with relativistic corrections based on the work of Cowan. When restricted to transitions allowed by dipole selection rules, the calculated spectra of the lanthanide M4,5 white lines show a decreasing intensity as a function of Z that was consistent with the available experimental data.Here we report the results of Dirac-Fock calculations of the L2,3 white lines of the 3d and 4d elements, and compare the results to the experimental work of Pearson et al. In a previous study, similar calculations helped to account for the non-statistical behavior of L3/L2 ratios of the 3d metals. We assumed that all metals had a single 4s electron. Because these calculations provide absolute transition probabilities, to compare the calculated white line intensities to the experimental data, we normalized the calculated intensities to the intensity of the continuum above the L3 edges. The continuum intensity was obtained by Hartree-Slater calculations, and the normalization factor for the white line intensities was the integrated intensity in an energy window of fixed width and position above the L3 edge of each element.

scholarly journals New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV)

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 48
Author(s):  
M. Raineri ◽  
M. Gallardo ◽  
J. Reyna Almandos ◽  
A. G. Trigueiros ◽  
C. J. B. Pagan
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Pulsed Discharge ◽  
Core Polarization ◽  
Polarization Effects ◽  
Hartree Fock ◽  
Theta Pinch ◽  
New Energy ◽  
First Time

A capillary pulsed-discharge and a theta-pinch were used to record Kr spectra in the region of 330–4800 Å. A set of 168 transitions of these spectra were classified for the first time. We extended the analysis to twenty-five new energy levels belonging to 3s23p24d, 3s23p25d even configurations. We calculated weighted transition probabilities (gA) for all of the experimentally observed lines and lifetimes for new energy levels using a relativistic Hartree–Fock method, including core-polarization effects.

scholarly journals Hartree–Fock critical nuclear charge in two-electron atoms

2021 ◽  
Vol 154 (11) ◽  
pp. 111103
Author(s):  
Hugh G. A. Burton
Keyword(s):  
Nuclear Charge ◽  
Hartree Fock

scholarly journals Circular Rydberg states of helium atoms or helium-like ions in a high-frequency laser field

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 11-17
Author(s):  
Nikolay Kryukov ◽  
Eugene Oks
Keyword(s):  
High Frequency ◽  
Laser Field ◽  
Nuclear Charge ◽  
Rydberg States ◽  
Orbital Plane ◽  
Precession Frequency ◽  
Nonmonotonic Dependence ◽  
Absolute Value ◽  
Rydberg Electron ◽  
Frequency Laser

Abstract In the literature, there were studies of Rydberg states of hydrogenic atoms/ions in a high-frequency laser field. It was shown that the motion of the Rydberg electron is analogous to the motion of a satellite around an oblate planet (for a linearly polarized laser field) or around a (fictitious) prolate planet (for a circularly polarized laser field): it exhibits two kinds of precession – one of them is the precession within the orbital plane and another one is the precession of the orbital plane. In this study, we study a helium atom or a helium-like ion with one of the two electrons in a Rydberg state, the system being under a high-frequency laser field. For obtaining analytical results, we use the generalized method of the effective potentials. We find two primary effects of the high-frequency laser field on circular Rydberg states. The first effect is the precession of the orbital plane of the Rydberg electron. We calculate analytically the precession frequency and show that it differs from the case of a hydrogenic atom/ion. In the radiation spectrum, this precession would manifest as satellites separated from the spectral line at the Kepler frequency by multiples of the precession frequency. The second effect is a shift of the energy of the Rydberg electron, also calculated analytically. We find that the absolute value of the shift increases monotonically as the unperturbed binding energy of the Rydberg electron increases. We also find that the shift has a nonmonotonic dependence on the nuclear charge Z: as Z increases, the absolute value of the shift first increases, then reaches a maximum, and then decreases. The nonmonotonic dependence of the laser field-caused energy shift on the nuclear charge is a counterintuitive result.

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