Computational Atomic Structure: An MCHF Approach

by Froese-Fischer; Charlotte

• ISBN13: 9780750303743
• ISBN10: 0750303743
• Format: Hardcover
• Copyright: 1997-01-01
• Publisher: CRC Press

Summary

Computational Atomic Structure: An MCHF Approach deals with the field of computational atomic structure, specifically with the multiconfiguration Hartree-Fock (MCHF) approach and the manner in which this approach is used in modern physics. Beginning with an introduction to computational algorithms and procedures for atomic physics, the book describes the theory underlying nonrelativistic atomic structure calculations (making use of Brett-Pauli corrections for relativistic effects) and details how the MCHF atomic structure software package can be used to this end. The book concludes with a treatment of atomic properties, such as energy levels, electron affinities, transition probabilities, specific mass shift, fine structure, hyperfine-structure, and autoionization. This modern, reliable exposition of atomic structure theory proves invaluable to anyone looking to make use of the authors' MCHF atomic structure software package, which is available publicly via the Internet.

Table of Contents

Preface	ix	(2)
Acknowledgments	xi
1 Introduction	1	(21)
1.1 Introduction	1	(1)
1.2 Properties of the wave function	2	(2)
1.3 One-electron systems	4	(4)
1.4 Many-electron systems	8	(6)
1.5 The variational method	14	(4)
1.6 Summary	18	(2)
1.7 Exercises	20	(2)
2 Configuration State Functions and Matrix Elements of the Hamiltonian	22	(13)
2.1 Configuration state functions	22	(5)
2.2 Matrix elements of the Hamiltonian	27	(7)
2.3 Exercises	34	(1)
3 Hartree-Fock Calculations	35	(32)
3.1 The Hartree-Fock approximation	35	(1)
3.2 The Hartree-Fock equation for 1s 2p (3)P	36	(2)
3.3 The self-consistent field procedure	38	(5)
3.4 Hartree-Fock solutions for the ground state of lithium	43	(5)
3.5 The Hartree-Fock solutions for 1s2s (3)S and (1)S states in He	48	(3)
3.6 The general Hartree-Fock equations	51	(2)
3.7 Brillouin's theorem	53	(2)
3.8 Term dependence	55	(1)
3.9 Iso-electronic sequences and orbital collapse	56	(1)
3.10 Quantum defects and Rydberg series	56	(1)
3.11 Computational aspects	57	(7)
3.12 Exercises	64	(3)
4 Multiconfiguration Hartree-Fock Wave Functions	67	(21)
4.1 Correlation in many-electron atoms	67	(1)
4.2 Z-dependent perturbation theory	67	(4)
4.3 Pair-correlation expansions	71	(2)
4.4 Complete and restricted active spaces	73	(1)
4.5 The MCHF approximation	73	(3)
4.6 A non-orthogonal extension	76	(2)
4.7 MCHF calculation for 3s(2) 3p (2)P in Al	78	(6)
4.8 Properties of MCHF wave functions	84	(2)
4.9 Computational aspects	86	(1)
4.10 Exercises	87	(1)
5 Two-Electron Systems	88	(17)
5.1 Non-uniqueness of the wave function	88	(1)
5.2 The reduced form	88	(10)
5.3 Rydberg series	98	(1)
5.4 Rydberg series with perturber	99	(3)
5.5 The GBT method	102	(2)
5.6 Exercises	104	(1)
6 Correlation in Many-Electron Systems	105	(24)
6.1 Zero-order wave functions	105	(7)
6.2 First-order wave functions	112	(15)
6.3 Z-dependence of atomic properties	127	(1)
6.4 Exercises	128	(1)
7 Relativistic Effects	129	(22)
7.1 Introduction	129	(1)
7.2 The Breit-Pauli Hamiltonian	130	(1)
7.3 Breit-Pauli wave functions	131	(1)
7.4 Fine-structure levels	132	(2)
7.5 Computational aspects	134	(1)
7.6 Fine structure in helium	135	(4)
7.7 The Blume-Watson approach	139	(1)
7.8 Systems with two valence electrons	140	(1)
7.9 A limited model for core-valence correlation	141	(4)
7.10 Exploring complex spectra	145	(3)
7.11 Z-dependence of relativistic effects	148	(2)
7.12 Exercises	150	(1)
8 Isotope and Hyperfine Effects	151	(28)
8.1 The effects of the nucleus	151	(1)
8.2 Mass shift	151	(6)
8.3 Field shift	157	(2)
8.4 Level isotope shift	159	(1)
8.5 Transition isotope shift	160	(3)
8.6 Field shift correction for 3d(8)(3/F)4p (4)D(5/2) in Ni II	163	(2)
8.7 Hyperfine structure	165	(1)
8.8 Hyperfine interaction	165	(1)
8.9 Angular properties of the hyperfine states	166	(1)
8.10 First-order hyperfine energies	167	(1)
8.11 First-order wave functions	168	(2)
8.12 Computational aspects	170	(1)
8.13 Configuration expansions for hyperfine structure	171	(1)
8.14 Polarization effects	171	(6)
8.15 Exercises	177	(2)
9 Allowed and Forbidden Transitions	179	(38)
9.1 Introduction	179	(3)
9.2 Matrix elements for transition operators	182	(1)
9.3 Selection rules for radiative transitions	183	(4)
9.4 Computational aspects	187	(2)
9.5 Allowed transitions	189	(2)
9.6 LS calculations for allowed transitions	191	(3)
9.7 Cancellations in the transition integral	194	(2)
9.8 Core-valence effects on line strength	196	(4)
9.9 Spin-forbidden transitions	200	(8)
9.10 Branching ratios in complex spectra	208	(1)
9.11 Forbidden lines	209	(3)
9.12 Hyperfine-induced transition	212	(2)
9.13 Z-dependence of transition properties	214	(1)
9.14 Exercises	215	(2)
10 MCHF Continuum Wave Functions	217	(23)
10.1 Continuum processes	217	(1)
10.2 Continuum functions	218	(7)
10.3 Photoionization or photodetachment	225	(5)
10.4 Autoionization	230	(7)
10.5 Computational aspects	237	(2)
10.6 Exercises	239	(1)
Appendices	240	(33)
A Angular Momentum Theory	240	(11)
A.1 Angular momentum operators	240	(3)
A.2 Coupling of two angular momenta	243	(1)
A.3 Coupling of three and four angular momenta	244	(2)
A.4 Spherical tensor operators	246	(2)
A.5 The Wigner-Eckart theorem	248	(1)
A.6 Matrix elements of tensor operators between coupled functions	249	(2)
B The Dirac and Breit-Pauli Theory	251	(9)
B.1 Introduction	251	(1)
B.2 Dirac theory of one-electron systems	251	(8)
B.3 The relativistic wave equation for many-electron systems	259	(1)
C Fundamental Constants	260	(3)
C.1 Atomic units	260	(1)
C.2 Additional units	261	(2)
D Program Input Parameters	263	(10)
References	273	(4)
Index	277