Hyperfine structure operator in the tensorial form of second quantization

Open Physics ◽  
2004 ◽  
Vol 2 (4) ◽  
Author(s):  
Gediminas Gaigalas ◽  
Zenonas Rudzikas ◽  
Oliver Scharf
Keyword(s):  
Hyperfine Structure ◽  
Large Scale ◽  
Hyperfine Interactions ◽  
Matrix Elements ◽  
Correlation Effects ◽  
Second Quantization ◽  
Interaction Operator ◽  
Momentum Theory ◽  
Graphical Technique ◽  
Efficient Program

AbstractThe general tensorial form of the hyperfine interaction operator in the formalism of second quantization is presented. Both diagonal and off-diagnonal matrix elements of the above-mentioned operator are found using an approach based on a combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin) and a generalised graphical technique. This methodology allows us to account for correlation effects efficiently and, therefore, to study the hyperfine interactions in complex many-electron atoms, those with openf-shells included, in a practical manner. All this will lead us to design an efficient program for large scale calculations of hyperfine structure and isotope shift.

Nuclear-mass dependent spin-orbit interaction

1991 ◽  
Vol 69 (2) ◽  
pp. 161-163
Author(s):  
T. L. Sordo ◽  
J. A. Sordo ◽  
S. Fraga
Keyword(s):  
Hyperfine Structure ◽  
Ground States ◽  
Orbit Interaction ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Nuclear Mass ◽  
Tensor Form ◽  
Interaction Operator ◽  
Spin Orbit Interaction ◽  
Mass Dependent

The nuclear-mass dependent spin-orbit interaction is discussed. The corresponding interaction operator is given in tensor form and the expression for its matrix elements in a basis of SL functions is presented. Monoconfigurational calculations have been performed for the ground states of carbon and oxygen. The results for the J-level splittings show that the contribution from this interaction is comparable with, or even greater than, the contribution from the hyperfine-structure interactions.

scholarly journals Large Scale Shell Model Calculations of the Negative-Parity States Structure in 24Mg Nucleus

2021 ◽  
Vol 66 (4) ◽  
pp. 293
Author(s):  
A.A. Al-Sammarraie ◽  
F.A. Ahmed ◽  
A.A. Okhunov
Keyword(s):  
Shell Model ◽  
Large Scale ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Energy Levels ◽  
Form Factors ◽  
Model Space ◽  
Negative Parity ◽  
Matrix Elements ◽  
Model Calculations

The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.

Electron Correlation Effects on the Lattice Dynamics of Sodium and Potassium

1975 ◽  
Vol 53 (16) ◽  
pp. 1507-1512 ◽  
Author(s):  
V. K. Jindal
Keyword(s):  
Dielectric Function ◽  
Lattice Dynamics ◽  
Phonon Dispersion ◽  
Matrix Elements ◽  
Correlation Effects ◽  
Phonon Dispersion Curves ◽  
Electron Correlation Effects ◽  
Experimental Values ◽  
The One ◽  
Sodium And Potassium

The phonon dispersion curves for sodium and potassium have been calculated using the one OPW (orthogonalized plane wave) bare electron matrix elements and the dielectric function of Vashishta and Singwi. Results are compared with experimental results as well as with similar calculations using the dielectric function of Geldart and Taylor. It is found that the screening function of Vashishta and Singwi gives at least as good an agreement with experimental values as obtained from the screening function of Geldart and Taylor. The interionic potentials for these metals have also been calculated and compared with similar calculations done previously. The reason for the appreciable difference between the potentials is discussed.

scholarly journals Irreducible tensor form of three-particle operator for open-shell atoms

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Rytis Juršėnas ◽  
Gintaras Merkelis
Keyword(s):  
Angular Momentum ◽  
Symmetric Group ◽  
Open Shell ◽  
Matrix Elements ◽  
Irreducible Tensor ◽  
Tensor Form ◽  
Momentum Theory ◽  
Recoupling Coefficients ◽  
Particle Operator

AbstractA three-particle operator in a second quantized form is studied systematically and comprehensively. The operator is transformed into irreducible tensor form. Possible coupling schemes, identified by the classes of symmetric group S6, are presented. Recoupling coefficients that make it possible to transform a given scheme into another are produced by using the angular momentum theory combined with quasispin formalism. The classification of the three-particle operator which acts on n = 1, 2,..., 6 open shells of equivalent electrons of atom is considered. The procedure to construct three-particle matrix elements are examined.

scholarly journals ββ DECAY AND NUCLEAR STRUCTURE

2007 ◽  
Vol 16 (02) ◽  
pp. 552-560 ◽  
Author(s):  
E. CAURIER ◽  
F. NOWACKI ◽  
A. POVES
Keyword(s):  
Shell Model ◽  
Nuclear Matrix ◽  
Large Scale ◽  
Predictive Power ◽  
Strong Impact ◽  
Matrix Elements ◽  
Model Calculations ◽  
Mode Stability ◽  
Recent Developments

The determination of accurate nuclear matrix elements for ββ decay processes is a challenge for nuclear theory and can have a strong impact in neutrino physics. Large Scale Shell Model (LSSM) calculations are among the best tools for such determination and recent developments have allowed to extend its application domains. In particular, systematic studies of nuclear matrix elements calculations have been now undertaken in this framework for most of the ββ emitters. These calculations are crucial in the determination of the most favorable emitters in the forthcoming generation of ββ experiments. The present paper focuses on the recent advances and remaining difficulties of shell model calculations for the neutrinoless mode. Stability and predictive power of the results will be discussed.

Comparison of 200 Liter and 40 Milliliter Leach Tests

1982 ◽  
Vol 15 ◽  
Author(s):  
J. H. Westsik ◽  
C. O. Harvey ◽  
F. P. Roberts ◽  
W. A. Ross ◽  
R. E. Thornhill
Keyword(s):  
Large Scale ◽  
Deionized Water ◽  
Waste Form ◽  
Small Scale ◽  
Matrix Elements ◽  
Elemental Concentrations ◽  
The Past ◽  
Leach Test ◽  
The Matrix ◽  
Scale Test

ABSTRACTDuring the past year we have conducted a modified MCC-1 leach test on a 145 kg block of a cast cement waste form. The leach vessel was a 200 liter Teflon®-lined drum and contained 97.5 liters of deionized water. The results of this large-scale leach test were compared with the results of standard MCC-1 tests (40 ml) on smaller samples of the same waste form. The ratio of leachate volumes between the large and small scale tests was 2500 and the ratio of sample masses was 150,000. The cast cement samples for both tests contained plutonium-doped incinerator ash.The leachates from these tests were analyzed for both plutonium and the matrix elements. Evaluation of plutonium plateout in the large-scale test indicated that the majority of the plutonium leached from the samples deposits onto vessel walls and little (<3 × 10−12M) remains in solution. Comparison of elemental concentrations in the leachates indicates some differences up to 5X in the concentration in the large- and small-scale tests. The differences are attributed to differences in the solubilities of Ca, Si, and Fe at pH ˜11.5 and at pH ˜12.5. The higher pH observed for the large-scale test is a result of the larger quantities of sodium in the large block of cement.

Inclusive and Exclusive Decay of B- Meson

1997 ◽  
Vol 12 (37) ◽  
pp. 2873-2882 ◽  
Author(s):  
H. Routh ◽  
V. P. Gautam
Keyword(s):  
Large Scale ◽  
B Meson ◽  
Effective Hamiltonian ◽  
Matrix Elements ◽  
Long Distance ◽  
Logarithmic Approximation ◽  
Fermion Operator ◽  
Color Dipole ◽  
The Matrix ◽  
Exclusive Decay

In our letter we deal with the inclusive and exclusive decay of B- meson. The inclusive b→dγ decay has been considered here including the QCD corrections to the Wilson coefficients and the matrix elements of the operators in the effective Hamiltonian. We calculate the O(αs) virtual corrections to the matrix element for b→dγ, taking into account the contributions of the four-fermion operator O2 and the electromagnetic and color dipole type operators. It drastically reduces the large scale dependence of the leading logarithmic approximation. Moreover, while we are considering the exclusive B-→ρ-γ decay, we have taken into consideration both the short distance as well as long distance contributions. Therefore, we have obtained better result for the partial decay width of B-→ρ-γ.

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