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+.

Influence of relativistic valence-core correlation on p-state fine structure in some univalent systems

1981 ◽  
Vol 59 (6) ◽  
pp. 769-774 ◽  
Author(s):  
J. Migdalek ◽  
W. E. Baylis
Keyword(s):  
Fine Structure ◽  
Valence Electron ◽  
Closed Shell ◽  
Polarization Potential ◽  
Atomic Core ◽  
Hartree Fock ◽  
The Core ◽  
Ab Initio Approach ◽  
The One ◽  
Single Configuration

Single-configuration relativistic Hartree–Fock values of fine-structure separations are calculated for p-levels in systems with a single electron outside a closed-shell core, both with and without allowance for relaxation and polarization of the core. Effects of the polarization of the atomic core by the valence electron are included by the addition of a polarization potential to the one-electron Hamiltonian. The results obtained generally compare well with available experimental data and indicate a significant influence of core polarization on fine-structure splittings. Contributions of the relaxation of the core are considerable only for the heavier systems. The choice of the cut-off parameter r0 in the polarization potential, as well as of the shape of the cut-off function, and the success of the ab initio approach are discussed. It is suggested that for indium and thallium, in contrast to the case for rubidium, silver, and gold, the simplified picture of a core plus a single valence electron is no longer entirely satisfactory.

Hyperfine structure of Eu I

1965 ◽  
Vol 289 (1416) ◽  
pp. 81-96 ◽  
Keyword(s):  
Theoretical Analysis ◽  
Hyperfine Structure ◽  
Relativistic Effects ◽  
Interaction Constant ◽  
Tensor Operator ◽  
Quadrupole Moments ◽  
Core Polarization ◽  
The Core ◽  
Least Squares Fit ◽  
Good Agreement

A theoretical analysis is made of the hyperfine structure of the twelve levels of Eu I 4 f 7 ( 8 S ) 6 s 6 p using intermediate-coupled eigenfunctions obtained from a least-squares fit of the energies of the levels. Relativistic effects for the 6 p electron are calculated throughout by tensor-operator techniques. Good agreement is obtained with the observed A values, treating as parameters the polarization of the core (by the f electrons) and the hyperfine interaction constant of the 6 s electron. The magnitude of the core polarization is related to data on Eu I 4 f 7 ( 8 S ) 6s 2 , Euii 4 f 7 ( 8 s ) 6 s , and Eu III 4 f 7 ( 8 S ). The hyperfine-structure anomalies also fall into a consistent pattern. The observed B values are related to quadrupole moments of 151 Eu and 153 Eu.

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.

scholarly journals Calculation of the hyperfine structure of the superheavy elements E113 and E114+

2019 ◽  
Vol 15 (3) ◽  
pp. 5
Author(s):  
Dinh Thi Hanh
Keyword(s):  
Hyperfine Structure ◽  
Superheavy Elements ◽  
Many Body ◽  
Core Polarization ◽  
Hartree Fock ◽  
The Core ◽  
Many Body Perturbation Theory ◽  
Structure Constants ◽  
The Many ◽  
Qed Effects

The hyperfine-structure constants of the lowest s and p1/2 states of superheavy elements E113 and E114+ are presented in this article. The relativistic Hartree-Fock method with the core polarization being taken into account by means of the many-body perturbation theory. Breit and quantum electrodynamic (QED) effects are also considered. Similar calculations for Tl and Pb+ are used to gauge the accuracy of the calculations.

Relativistic Hartree–Fock and model-potential ionization energies and oscillator strengths for transitions in the principal, sharp, and diffuse series of neutral rubidium and silver with allowance for core polarization

1979 ◽  
Vol 57 (10) ◽  
pp. 1708-1718 ◽  
Author(s):  
J. Migdałek ◽  
W. E. Baylis
Keyword(s):  
Model Potential ◽  
Oscillator Strengths ◽  
Core Polarization ◽  
Ionization Energies ◽  
Hartree Fock ◽  
Dipole Moment Operator ◽  
Exchange Effects ◽  
Moment Operator ◽  
The One ◽  
Single Configuration

Relativistic single-configuration Hartree–Fock computations of ionization energies and oscillator strengths for transitions in principal, sharp, and diffuse series of neutral rubidium and silver spectra have been performed both with and without allowance for core polarization and are compared with several model-potential calculations. The effect of polarization of the atomic core by the valence electron is included by introducing a polarization potential in the one-electron Hamiltonian and by employing the corresponding correction to the dipole-moment operator of the transition. The results obtained compare well with available experimental data and indicate a significant influence of core polarization on both ionization energies and oscillator strengths. The inclusion of polarization and exchange effects in the model-potential approach and the choice of free parameters is discussed.

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 Extended analysis of Xe VII and Xe VIII

2017 ◽  
Vol 95 (9) ◽  
pp. 805-810 ◽  
Author(s):  
M. Raineri ◽  
M. Gallardo ◽  
J. Reyna Almandos ◽  
C.J.B. Pagan ◽  
R. Sarmiento
Keyword(s):  
Light Source ◽  
Energy Levels ◽  
Excited Configuration ◽  
Pulsed Discharge ◽  
Hartree Fock ◽  
The Core ◽  
New Energy ◽  
Extended Analysis ◽  
First Time ◽  
Atomic Parameters

A pulsed discharge light source to study the six and seven times ionized xenon spectra in the 419–4642 Å region was used. A set of 40 transitions of Xe VII and 25 transitions of Xe VIII were classified for the first time. We revised the values for the previously known energy levels and extended the analysis for Xe VII to 10 new energy levels belonging to 5s6d, 5s7s and 5s7p, 4d95s25p even and odd configurations, respectively. Seven new energy levels of the core excited configuration 4d95s5d of Xe VIII are presented. For the prediction of the atomic parameters, energy levels, and transition, relativistic Hartree–Fock calculations were used.

scholarly journals O2 State in 18 O by using Core – Polarization effects

2008 ◽  
pp. 66-72
Keyword(s):  
Perturbation Theory ◽  
Experimental Studies ◽  
Form Factors ◽  
Wave Model ◽  
Collective Model ◽  
Core Polarization ◽  
Polarization Effects ◽  
The Core ◽  
The Subject ◽  
Space Wave

Coulomb form factors for E0 transition in 18O are discussed taking into account core-polarization effects. These effects are taken into account through the collective model of Tassie and also through a microscopic perturbation theory including excitations up to 2p1f shell. Space wave model functions defined for the orbits 1 and 2125O nucleus has been the subject of extensive theoretical and experimental studies, which received much attention in last decade [Alex Brown et.al.2005]. The 18O system contains two neutrons in addition to the16O core distributed in the sd – shell. d1 are obtained from the diagonalization of the interaction Hamilonian of Wildenthal. The calculations include the 0 2state with excitation energies3.6337MeV. The core – polarization effects which incorporate the ollective model of Tassei describe the data very well for this state.

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