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.

Calculation of the Knight Shift in Palladium

1979 ◽  
Vol 34 (4) ◽  
pp. 523-524 ◽  
Author(s):  
R. Krieger ◽  
J. Voitländer
Keyword(s):  
Fermi Surface ◽  
Knight Shift ◽  
Enhancement Factor ◽  
Negative Contribution ◽  
Core Polarization ◽  
Conduction Electrons ◽  
The Core ◽  
Core Electrons ◽  
Palladium Metal ◽  
Good Agreement

The direct and core-polarization contributions to the Knight shift in palladium metal have been calculated taking an enhancement factor of 10 for d- and 1.28 for s-electrons. We found a large negative contribution of - 3.88% for the core electrons and a comparatively small direct contribution of 0.18% for s-electrons on the Fermi surface. Together with an estimated contribution of 0.36% for conduction electrons in s-orbitals, but not on the Fermi surface, the calculated total amount of - 3.34% is in good agreement with the experimental value of - 4% obtained by the Jaccarino plot for palladium at 0 K

Core-polarization-corrected multiconfiguration Dirac–Fock oscillator strengths and excitation energies for the 5s2 1S0 – 5s5p 3P1, 1P1 transitions in Sr I and Y II spectra

1987 ◽  
Vol 65 (12) ◽  
pp. 1612-1619 ◽  
Author(s):  
J. Migdalek ◽  
W. E. Baylis
Keyword(s):  
Electron Correlation ◽  
Oscillator Strengths ◽  
Excitation Energies ◽  
Core Electron ◽  
Polarization Model ◽  
Core Polarization ◽  
The Core ◽  
Relativistic Configuration ◽  
Comparison Of The Results ◽  
Good Agreement

Energies and oscillator strengths for the spin-allowed 5s2 1S0 – 5s5p 1P1 and spin-forbidden 5s2 1S0 – 5s5p 3P1 transitions in neutral strontium and singly ionized yttrium are determined in relativistic multiconfiguration Dirac–Fock computations where modest relativistic configuration mixing to represent intravalence correlation is combined with a polarization model to account for valence–core electron correlation. It is demonstrated, by comparison of the results corrected for electron correlation with those obtained from relativistic intermediate coupling Dirac–Fock calculations, that both intravalence and core–valence correlation are important for achieving good agreement with experiment. However, for neutral strontium it is the intravalence correlation that seems to be more important whereas for the isoelectronic singly ionized yttrium the core-valence correlation, as represented by the core-polarization model, dominates. A delicate balance resulting from the partial collapse of the 4d orbital in Y+ may be a reason for the greater sensitivity to core polarization in this system.

Large scale multi-configuration Hartree-Fock calculation of the hyperfine structure of the ground state of vanadium

Open Physics ◽  
2006 ◽  
Vol 4 (1) ◽  
pp. 42-57
Author(s):  
Oliver Scharf ◽  
Gediminas Gaigalas
Keyword(s):  
Hyperfine Structure ◽  
Ground State ◽  
Large Scale ◽  
Electric Quadrupole ◽  
State Function ◽  
Hartree Fock ◽  
The Core ◽  
Experimental Values ◽  
State Functions ◽  
Good Agreement

AbstractThe hyperfine structure of the ground state of vanadium, 51VI, is calculated in the nonrelativistic framework of the multi-configuration Hartree-Fock approximation. A configuration state function limiting algorithm is used to make the calculations feasible and to study the influence of core, valence and core-valence correlations in detail. The obtained configuration state function space captures the most important orbital correlations within 2%. Further correlations are included through configuration interaction calculation. The atomic state functions are used to evaluate the magnetic dipole hyperfine factor A and the electric quadrupole factor B. It turns out that the ab initio calculation can not capture the core polarization of the 2s shell. It introduces an error that is higher than the Hartree-Fock approximation. However, the detailed correlations being observed suggest the introduction of a wrong correlation orbital due to the algorithm being used. Neglecting this orbital leads to good agreement with 2% deviation from the experimental values for the A factors.

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.

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+.

Relativistic effects in many electron hyperfine structure II. Relativistic quadrupole interaction in manganese

1965 ◽  
Vol 289 (1416) ◽  
pp. 108-113 ◽  
Keyword(s):  
Theoretical Result ◽  
Hyperfine Structure ◽  
Quadrupole Interaction ◽  
Ground State ◽  
Relativistic Effects ◽  
Interaction Constant ◽  
Effective Operator ◽  
Relativistic Limit ◽  
Atomic Beams ◽  
Order Of Magnitude

Theoretical and experimental work has been carried out on the quadrupole interaction constant, B , for the ground state of manganese, whose ground configuration is a half-filled d shell. In the non-relativistic limit B = 0. The theory is based on a new relativistic calculation involving the use of an effective operator acting between non-relativistic states, and a non-vanishing value of B has been obtained. To check the theory, the hyperfine structure of the ground state of manganese has been remeasured by the method of atomic beams and an experimental value of B has been found. The results are B rei . ≈ — 0.019 Mc/s, B expt> = — 0.0183 ± 0.0008 Mc/s. The agreement is satisfactory as to sign and order of magnitude, but high precision is not claimed for the theoretical result

Contributions to the electron affinity of calcium and scandium

1992 ◽  
Vol 70 (12) ◽  
pp. 1283-1290 ◽  
Author(s):  
Charlotte Froese Fischer ◽  
Tomas Brage
Keyword(s):  
Ab Initio ◽  
Electron Affinity ◽  
Polarization Effect ◽  
Core Polarization ◽  
The Core ◽  
Theoretical Predictions ◽  
Good Agreement

Theoretical predictions of the electron affinity of Ca vary from 0 to 130 meV. Not all calculations have included the same effects. In this paper, the different approaches are reviewed, the effect of assumptions estimated whenever possible, and some new ab initio results reported that estimate the effect of core polarization on electron affinity for both Ca and Sc. For the latter our predicted electron affinity is in good agreement with the experimental value for the lowest 4s23d4p1D state and underestimates the electron affinity for 4s23d4p3D, where the calculation of outer correlation is more demanding and the core-polarization effect is small.

Relativistic effects in many electron hyperfine structure III. Relativistic dipole and quadrupole interaction in europium and remeasurement of the nuclear magnetic dipole moments of 151 Eu and 153 Eu

1965 ◽  
Vol 289 (1416) ◽  
pp. 114-121 ◽  
Keyword(s):  
Hyperfine Structure ◽  
Magnetic Dipole ◽  
Quadrupole Interaction ◽  
Dipole Moments ◽  
Relativistic Effects ◽  
Dipole Interaction ◽  
Triple Resonance ◽  
Limits Of Error ◽  
Good Agreement ◽  
Nuclear Magnetic

The nuclear magnetic dipole moments of 151 Eu and 153 Eu have been re-measured. The revised values (corrected for diamagnetic shielding) are: μ( 151 Eu) = 3.4630 ± 0-0006 n.m., μ( 153 Eu) = 1.5292 ± 0-0008 n.m. The ratio of the moments is μ( 151 Eu)/μ( 153 Eu) = 2.26505 ±0.00042. These results were obtained by the method of triple resonance in an atomic beam. The hyperfine structure anomaly in the ground state of the europium atom is zero within limits of error. In this special circumstance it is shown that part of the nuclear magnetic dipole interaction is explained by relativistic effects. The quadrupole interaction is treated by the same theory, and good agreement with experiment is obtained, but high precision is not claimed for the theoretical result. This theory is based on a new relativistic calculation involving the use of an effective operator acting between non-relativistic states.

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