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Research in Atomic Structure : Lecture Notes in Chemistry - S. Fraga

Research in Atomic Structure

Lecture Notes in Chemistry

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This work offers the first comprehensive formulation for the prediction of the energy levels of many-electron atomic systems within the framework of a configuration interaction treatment, with consideration of the most important relativistic corrections as well as the interaction with external electric and magnetic fields. The formulation is developed using tensor-algebra techniques, which are discussed in detail and illustrated in the transformation of operators to tensor form and the formulation of the corresponding matrix elements. In addition to its didactic value, this work has practical applications. The reader will be able to proceed to the study, both theoretical and computational, of additional corrections. The discussion of computational details (on the selection of configurations and the determination of the radial functions) and of representative calculations illustrates both the practical difficulties and the quality of the results.

Theoretical Foundation.- 1 Hamiltonian Operator and Eigenvalue Equations.- 1.1 Hamiltonian operator.- 1.1.1 Extended Breit Hamiltonian operator.- 1.1.2 Generalized Hamiltonian operator.- 1.2 Eigenvalue equations.- Basic Theoretical Formulation.- 2 Angular Functions: Coupling of Angular Momenta.- 2.1 One-electron functions.- 2.2 SL-functions.- 2.3 JMJ- and FMF-functions.- 2.4 Selection of functions.- 3 Tensor-Operator Formulation.- 3.1 Tensor operators.- 3.2 Wigner-Eckart theorem.- 3.3 Reduced matrix elements.- 3.4 Matrix elements.- Application of the Basic Formulation.- 4 Transformation of Operators to Tensor Form.- 4.1 Basic operators.- 4.1.1 Operators s(1), ?(1) and C(k).- 4.1.2 Other common operators.- 4.2 Transformation rules.- 4.3 Application.- 4.4 Summary.- 5 Matrix Elements.- 5.1 General formulation.- 5.2 General expressions.- 5.2.1. SMSLML-coupling.- 5.2.2. JMJ-coupling.- 5.2.3. FMF-coupling.- 5.3 Examples for specific interactions.- 6 Summary of Theoretical Results.- 6.1 Electronic energy.- 6.2 Mass variation.- 6.3 Specific mass effect.- 6.4 One-electron Darwin correction.- 6.5 Two-electron Darwin correction.- 6.6 Electron spin-spin contact interaction.- 6.7 Orbit-orbit interaction.- 6.8 Spin-orbit coupling.- 6.9 Spin-spin dipole interaction.- 6.10 Magnetic dipole and Fermi contact interactions.- 6.11 Electric quadrupole coupling.- 6.12 Magnetic octupole coupling.- 6.13 Zeeman effect (low field).- 6.14 Zeeman effect (high field).- 6.15 Zeeman effect (very high field).- 6.16 Stark effect.- 6.17 Nuclear-mass dependent orbit-orbit interaction.- 6.18 Nuclear-mass dependent spin-orbit coupling (electron spin).- 6.19 Nuclear-mass dependent spin-orbit coupling (nuclear spin).- Implementation.- 7 Practical Details.- 7.1 Selection of configurations.- 7.2 Determination of radial functions.- 7.3 Selection rules.- 7.4 Mass corrections.- 8 Numerical Examples.- 8.1 Accurate energies.- 8.2 SLJ energy levels.- 8.3 Hyperfine-structure splittings.- 8.4 Nuclear-mass dependent corrections.- References.- Reference texts.- Data sources.- Units and Constants.- Constants.- Units.- Notation and Symbols.

ISBN: 9783540562375
ISBN-10: 3540562370
Series: Lecture Notes in Chemistry
Audience: General
Format: Paperback
Language: English
Number Of Pages: 143
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.89
Weight (kg): 0.24