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This work is dedicated to Professor Ahmadou Wagué for guiding me as I embarked on my first steps in research.

For supervising both my PhD Thesis (2007) and my National PhD Thesis in Physical Sciences (2013).

May he find expressed in these few lines, my entire recognition as well as my full congratulations in his being the first African to be elected to the council of the American Physical Society (APS) in August 2017.

First published 2018 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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The rights of Ibrahima Sakho to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2017962533

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-78630-273-1

Table of Contents

Cover

Dedication

Title

Foreword

Preface

Introduction

Part 1

1 Different Photoionization Processes, Rydberg Series
1. 1.1. Photoionization processes
2. 1.2. Rydberg Series
2 Experimental and Theoretical Methods of Photoionization
1. 2.1. Experimental methods
2. 2.2. Theoretical methods
3. 2.3. Absolute photoionization cross-section
4. 2.4. Analysis of resonance energies and quantum defect
3 General Formalism of the Screening Constant by Unit Nuclear Charge Method Applied to Photoionization
1. 3.1. Genesis of the screening constant by unit nuclear charge method
2. 3.2. Expression of the total energy of three-electron atomic systems
3. 3.3. General expressions of the resonance energies and widths of Rydberg series of multi-electron atomic systems

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

Introduction to Part 2
4 Application to the Calculation of Energies of Two-electron Atomic Systems (Helium-like Systems)
1. 4.1. Energy of the ground state of helium-like systems
2. 4.2. Energy of the excited states, 1sns ^1,3S^e, of helium-like systems
3. 4.3. Energy of the doubly excited symmetric states, ns² and np², of helium-like systems
4. 4.4. Calculation of the resonance energies and natural widths of the Rydberg series, ₂(1,0)_n^{+ 1}S^e, of the helium atom
5. 4.5. Effect of the nucleus on the accuracy of semi-empirical calculations
6. 4.6. Resonance energy of the Rydberg series, ₂(1,0)_n^{± 1,3}P^° and ₂(1,0)_n^{− 1}P^°, of the Li⁺ helium-like ion
7. 4.7. Resonance energies of the Rydberg series, ^1,3S^e, of the Li⁺ helium-like ion converging toward the excitation threshold, n = 2
8. 4.8. Calculation of the energies of the Rydberg states,
9. 4.9. Physical interpretation of the angular-correlation quantum number, K
5 Calculating the energies of Three-electron Atomic Systems (Lithium-like Systems)
1. 5.1. Energy of the ground state of lithium-like systems
2. 5.2. Energy of the doubly excited states, ls2snl ²L, of lithium-like systems
3. 5.3. Energy of the doubly excited states, ls²sns ²S, of lithium-like systems
4. 5.4. Energy of the single excitation states, 1s²nl ²L^π (1 ≤ l ≤ 3), of lithium-like systems
6 Application in the Resonant Photoionization of Atomic Systems of Atomic Numbers Z = 4–12
1. 6.1. Resonance energies of the Rydberg series, (2pns ¹P^°) and (2pnd ¹P^°), of beryllium
2. 6.2. Resonance energies of the excited states, 1s2p^{4 2,4}L, of five-electron atomic systems (boron-like systems)
3. 6.3. Energies and widths of the Rydberg series, 2pns ^1,3P^° and 2pnd ^1.3P^°, of the beryllium-like B⁺ ion
4. 6.4. Energies and widths of the Rydberg series, 2pnl ^1,3P^°, of beryllium-like ions C²⁺, N³⁺. … and Ar¹⁴⁺
5. 6.5. Resonance energies of the Rydberg series, 2s²2p⁴ (¹D₂) ns, nd, 2s²2p⁴ (¹S₀)ns, nd and 2s2p⁵ (³P₂)np, of the Ne⁺ ion
6. 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
7. 6.7. Energies and widths of the Rydberg series, 3pns ^1.3P, 3pnd ^1.3P and 3pnd ³D, of magnesium (Mg)
8. 6.8. Energies and widths of several resonance states resulting from the photoexcitation 1s → 2p of the N³⁺ and N⁴⁺ ions
7 Resonant Photoionization of Sulfur (S) and Ar⁺, Se⁺, Se²⁺ and Kr⁺ Ions
1. 7.1. Photoionization of sulfur
2. 7.2. Photoionization of the krypton ion (Kr⁺)
3. 7.3. Photoionization of the Argon ion (Ar⁺)
4. 7.4. Resonant photoionization of the selenium ions, Se⁺, Se²⁺ and Se³⁺

Conclusion: Advantages and Limits of the SCUNC Formalism

Appendices

Appendix 1: Detailed Calculation of the Screening Constant by Unit Nuclear Charge Relative to the Ground State of Two-electron Atomic Systems
Appendix 2: Formalism of Slater’s Atomic Orbital Theory
Appendix 3: Modified Formalism of the Atomic Orbital Theory

Bibliography

Index

End User License Agreement

Description and Application to the Photoionization of Atomic Systems