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Screening Constant by Unit Nuclear Charge Method: Description and Application to the Photoionization of Atomic Systems

Screening Constant by Unit Nuclear Charge Method: Description and Application to the Photoionization of Atomic Systems

Ibrahima Sakho

ISBN: 978-1-786-30273-1

Mar 2018, Wiley-ISTE

402 pages

In Stock

$165.00

Description

The reader will find in this collection a clear exposition of the method of the Screen Constant by Nuclear Charge Unit which can be applied in a simple and immediate way to many fields of Physics in relation to atomic spectroscopy.

Foreword xi

Preface xv

Introduction xix

Part 1 1

Chapter 1. Different Photoionization Processes, Rydberg Series 3

1.1. Photoionization processes 3

1.2. Rydberg Series 10

Chapter 2. Experimental and Theoretical Methods of Photoionization 21

2.1. Experimental methods 21

2.2. Theoretical methods 22

2.3. Absolute photoionization cross-section 24

2.4. Analysis of resonance energies and quantum defect 28

Chapter 3. General Formalism of the Screening Constant by Unit Nuclear Charge Method Applied to Photoionization 33

3.1. Genesis of the screening constant by unit nuclear charge method 33

3.2. Expression of the total energy of three-electron atomic systems 43

3.3. General expressions of the resonance energies and widths of Rydberg series of multi-electron atomic systems 48

Part 2. Applications in the Calculations of Energies and Natural Widths of the Resonance States of
Multi-Electron Atomic Systems 55

Introduction to Part 2 57

Chapter 4. Application to the Calculation of Energies of Two-electron Atomic Systems (Helium-like Systems) 59

4.1. Energy of the ground state of helium-like systems 59

4.2. Energy of the excited states, 1sns 1,3Se, of helium-like systems 61

4.3. Energy of the doubly excited symmetric states, ns2 and np2, of helium-like systems 65

4.4. Calculation of the resonance energies and natural widths of the Rydberg series, 2 (1,0)n1Se, of the helium atom 67

4.5. Effect of the nucleus on the accuracy of semi-empirical calculations 71

4.6. Resonance energy of the Rydberg series, 2 (1,0)n1,3P°and 2 (1,0)n−P°, of the Li+ helium-like ion 72

4.7. Resonance energies of the Rydberg series,1,3Se, of the Li+ helium-like ion converging toward the excitation threshold, n = 2 78

4.8. Calculation of the energies of the Rydberg states,3 (1,1)n 1P0, of helium-like systems 80

4.9. Physical interpretation of the angular-correlation quantum number, K 82

Chapter 5. Calculating the energies of Three-electron Atomic Systems (Lithium-like Systems) 117

5.1. Energy of the ground state of lithium-like systems 117

5.2. Energy of the doubly excited states, ls2snl 2L, of lithium-like systems 119

5.3. Energy of the doubly excited states, ls2sns 2S, of lithium-like systems 123

5.4. Energy of the single excitation states, 1s2nl 2L„Ãn(1 ≤ƒnl ≤ƒn3), of lithium-like systems 132

Chapter 6. Application in the Resonant Photoionization of Atomic Systems of Atomic Numbers Z = 4–12 149

6.1. Resonance energies of the Rydberg series, (2pns 1P°) and (2pnd 1P°), of beryllium 149

6.2. Resonance energies of the excited states, 1s2p4 2,4L, of five-electron atomic systems (boron-like systems) 153

6.3. Energies and widths of the Rydberg series, 2pns 1,3P°and 2pnd 1.3P°, of the beryllium-like B+ ion 164

6.4. Energies and widths of the Rydberg series, 2pnl 1,3P°, of beryllium-like ions C2+, N3+. ….. and Ar14+  181

6.5. Resonance energies of the Rydberg series, 2s22p4 (1D2)ns, nd, 2s22p4 (1S0)ns, nd and 2s2p5 (3P2)np, of the Ne+ ion 206

6.6. Energies of the Rydberg series, 2s22p2 (1D)nd (2L), 2s22p2 (1S)nd (2L), 2s2p3(5S0)np (4P) and 2s22p3 (3D)np, of the F2+ ion 222

6.7. Energies and widths of the Rydberg series, 3pns 1.3P, 3pnd 1.3P and 3pnd 3D, of magnesium (Mg) 230

6.8. Energies and widths of several resonance states resulting from the photoexcitation 1s →2p of the N3+ and N4+ ions 245

Chapter 7. Resonant Photoionization of Sulfur (S) and Ar+, Se+, Se2+ and Kr+ Ions 255

7.1. Photoionization of sulfur 255

7.2. Photoionization of the krypton ion (Kr+) 264

7.3. Photoionization of the Argon ion (Ar+) 270

7.4. Resonant photoionization of the selenium ions, Se+, Se2+ and Se3+  283

Conclusion 319

Appendices 325

Appendix 1. Detailed Calculation of the Screening Constant by Unit Nuclear Charge Relative to the Ground State of Two-electron Atomic Systems 327

Appendix 2. Formalism of Slater’s Atomic Orbital Theory 335

Appendix 3. Modified Formalism of the Atomic Orbital Theory 341

Bibliography 353

Index 371