Z-dependence of correlation effects and f values in the sodium iso-electronic sequence

1976 ◽  
Vol 54 (14) ◽  
pp. 1465-1481 ◽  
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Theoretical Study ◽  
Ionization Potentials ◽  
Initial Increase ◽  
Correlation Effects ◽  
Core Polarization ◽  
Hartree Fock ◽  
Analytic Expressions ◽  
Beam Foil

An accurate theoretical study of ionization potentials and f values in the sodium iso-electronic sequence has been performed using a frozen core, multi-configuration Hartree-Fock procedure.The Z-dependence of core-polarization and its effect on the transition integral are investigated. The initial increase in both these quantities as Z increases is explained in terms of a relative collapse in the size of the atom. Analytic expressions are derived for 3s–3p, 3s–4p, 3p–4s, and 4s–4p transition integrals.Core-polarization has reduced the f values for the 3s–3p transitions somewhat, but still leaves a discrepancy of up to 25% between theory and recent beam–foil results.

Beam-foil measurements of lifetimes of energy levels belonging to Sn III and Sn IV

1987 ◽  
Vol 65 (1) ◽  
pp. 7-12 ◽  
Author(s):  
E. H. Pinnington ◽  
J. A. Kernahan ◽  
W. Ansbacher
Keyword(s):  
Decay Curve ◽  
Energy Levels ◽  
Resonance Transition ◽  
Isoelectronic Sequence ◽  
Core Polarization ◽  
Hartree Fock ◽  
Intensity Decay ◽  
Polarization Calculation ◽  
Beam Foil ◽  
Good Agreement

Beam-foil intensity decay curves for transitions in the wavelength range 750–5250 Å are used to derive the lifetimes of the 6s1S, 5p1P, 6p1P, 5d1D, 6d1D, 5p21D, 4f1F, 6s3S, 6p3p, 5p23p, 5d3D, 6d3D, and 4f3F levels of Sn III, and of the 6s2S, 5p2P, 6p2P, 5d2D, 6d2D, 4d95 s22D, and 4f2F levels of Sn IV. The arbitrarily normalized decay-curve analyses are used for most levels. Good agreement is found between experiment and a recent (relativistic Hartree–Fock + core-polarization) calculation for the resonance transition in low-Z members of the Cd 1 isoelectronic sequence, but the experimental f values are found to lie systematically about 20% above the theoretical trend obtained from a similar calculation for the Ag I sequence. Configuration interaction is found to produce very different lifetimes for the two 4d95s22D levels of Sn IV, and the energy of the J = 3/2 level is determined to be 177 060 ± 50 cm−1.

Core polarization, relaxation, and relativistic effects in the first ionization potentials for some systems in Cu, Ag, and Au isoelectronic sequences

1982 ◽  
Vol 60 (9) ◽  
pp. 1317-1322 ◽  
Author(s):  
J. Migdalek ◽  
W. E. Baylis
Keyword(s):  
Ionization Potential ◽  
Valence Electron ◽  
Relativistic Effects ◽  
Polarization Potential ◽  
Ionization Potentials ◽  
Dipole Polarizability ◽  
Core Polarization ◽  
Hartree Fock ◽  
The Core ◽  
Single Configuration

Single-configuration relativistic Hartree – Fock values of the first ionization potentials for Cu through Kr7+, Ag through 16+, and Au through Pb3+ are computed in "frozen" and "relaxed core" approximations with and without allowance for core polarization. Effects of the polarization of the atomic core by the valence electron are included by introducing a polarization potential in the one-electron Hamiltonian of the valence electron. The core polarization potential depends on two parameters, the static dipole polarizability of the core α and the cut-off radius r0, which are chosen independently of the ionization potential data. It is demonstrated that by including the core polarization potential with a and r0 parameters which are simply chosen instead of being empirically fitted, it is still possible to account, on the average, for at least 70% of the discrepancy between the single-configuration relativistic Hartree – Fock ionization potentials and the experiment, a discrepancy usually ascribed to the contribution of valence-core electron correlations, and to bring the theoretical ionization potentials to an average agreement with experiment of around 1%. The core polarization contribution to ionization potentials is also compared with the contribution of the relaxation of the core and with relativistic effects. An estimate of 55.0 ± 0.1 eV is suggested as the best value of the ionization potential of Sb4+.

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 Mobility Enhancement in Square Quantum Wells: Symmetric Modulation of the Envelop Wave Function

2010 ◽  
Vol 20 (3) ◽  
pp. 193
Author(s):  
Doan Nhat Quang ◽  
Nguyen Huyen Tung ◽  
Nguyen Trung Hong ◽  
Tran Thi Hai
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Low Temperature ◽  
Quantum Wells ◽  
Quantum Transport ◽  
Variational Approach ◽  
Theoretical Study ◽  
Recent Experimental Data ◽  
Carrier Distribution ◽  
Analytic Expressions

We present a theoretical study of the effects from symmetric modulation of the envelop wave function on quantum transport in square quantum wells (QWs). Within the variational approach we obtain analytic expressions for the carrier distribution and their scattering in symmetric two-side doped square QWs. Roughness-induced scattering are found significantly weaker than those in the asymmetric one-side doped counterpart. Thus, we propose symmetric modulation of the wave function as an efficient method for enhancement of the roughness-limited QW mobility. Our theory is able to well reproduce the recent experimental data about low-temperature transport of electrons and holes in two-side doped square QWs, e.g., the mobility dependence on the channel width, which have not been explained so far.

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