1．INTRODUCTION 1
1．1．SEVEN STEPS IN THE DEVELOPMENT OF ATOMIC THEORY 1
1．2．WHY CALCULATE ATOMIC STRUCTURES? 2
1．3．ATOM AND SOLAR SYSTEM 3
1．4．ATOMIC UNITS 5
1．5．SCHRODINGER＇S EQUATION FOR AN ELECTRON 6
1．6．CENTRAL-FIELD WAVE FUNCTIONS 8
1．7．ELECTRON SPIN 11
1．8．MANY-PARTICLE SYSTEMS IN WAVE MECHANICS 13
1．8．1．The necessity for approximation in calculations of atomic structure 16
1．9．THE SEPARABLE WAVE FUNCTION APPROXIMATION 17
2．THE VARIATION PRINCIPLE 22
2．1．STATIONARY STATES OF A PARTICLE IN ONE DIMENSION 22
2．1．1．E＇ as a Lagrange multiplier 26
2．2．PARTICLE IN THREE DIMENSIONS 27
2．3．MANY-PARTICLE SYSTEMS,IN COORDINATE SPACE 29
2．4．TWO WAYS OF USING THE VARIATION PRINCIPLE TO DERIVE APPROXIMATE WAVE FUNCTIONS 30
2．5．THE SEPARABLE WAVE FUNCTION APPROXIMATION FOR THE NORMAL STATE OF HELIUM 31
2．6．THE VARIATION PRINCIPLE FOR EXCITED STATES 36
2．7．ANALYTIC WAVE FUNCTIONS 37
3．CONFIGURATIONS OF COMPLETE GROUPS 39
3．1．THREE STAGES IN THE CALCULATION OF ATOMIC STRUCTURES 39
3．2．ALGEBRAICAL PRELIMINARIES TO THE MANIPULATION OF DETERMINANT WAVE FUNCTIONS 39
3．3．FIRST STAGE;DERIVATION OF THE EXPRESSION FOR E＇ 42
3．4．USE OF CENTRAL-FIELD WAVE FUNCTIONS 45
3．5．THE Yk AND Zk FUNCTIONS 50
3．6．SECOND STAGE:APPLICATION OF THE VARIATION PRINCIPLE 52
3．6．1．Equations for the normal configuration of a ten-electron system 55
3．7．FOCK＇S EQUATIONS AS INTEGRODIFFERENTIAL EQUATIONS 57
3．8．THE NONDIAGONAL ε PARAMETERS 58
3．9．EQUATIONS WITHOUT EXCHANGE 59
3．9．1．Slater＇s simplified form of the equations with exchange 60
4．NUMERICAL PROCEDURES 63
4．1．FINITE DIFFERENCES 63
4．2．THE MAIN FORMULAE IN FINITE DIFFERENCES 64
4．3．QUADRATURE 65
4．4．SECOND-0ORDER DIFFERENTIAL EQUATION WITH FIRST DERIVATIVE ABSENT 68
4．5．NUMEROV＇S PROCESS FOR A LINEAR SECOND-ORDER EQUATION 71
4．6．FIRST-ORDER EQUATIONS 72
4．7．FOX-GOODWIN PROCESS FOR LINEAR FIRST-ORDER EQUATIONS 73
5．APPLICATION OF THE NUMERICAL PROCEDURES 77
5．1．EQUATIONS WITHOUT EXCHANGE 77
5．1．1．Calculation of Y(γ) and contributions to it 79
5．2．SOLUTION OF THE RADIAL WAVE EQUATION 80
5．2．1．Starting the outward integrations 81
5．2．2．Starting the inward integrations 82
5．3．VARIATION EQUATIONS 84
5．3．1．Matching the inward and outward equations 85
5．3．2．Normalization 87
5．3．3．Revision of the estimates of contributions to Z(γ) 87
5．4．TORRANCE＇S METHOD 88
5．5．EQUATIONS WITH EXCHANGE 90
5．6．CALCULATION OF THE Yk FUNCTIONS 91
5．7．RADIAL WAVE EQUATION WITH EXCHANGE 93
5．7．1．Starting the integrations 95
5．8．REVISION OF THE ESTIMATES OF THE RADIAL WAVE FUNCTIONS 96
5．9．OTHER FORMS OF THE RADIAL WAVE EQUATION 97
6．CONFIGURATIONS COMPRISING INCOMPLETE GROUPS 101
6．1．RUSSELL-SAUNDERS COUPLING 101
6．2．(LS) TERMS FROM A GIVEN CONFIGURATION 103
6．3．DERIVATION OF THE FORMULA FOR E＇ 106
6．4．STRUCTURE OF THE FORMULA FOR E＇ 110
6．5．EQUATIONS FOR THE RADIAL WAVE FUNCTIONS 111
6．6．ONE WAVE FUNCTION IN ADDITION TO COMPLETE GROUPS 113
6．7．DIFFERENT RADIAL WAVE FUNCTIONS WITHIN A SINGLE GROUP 113
7．THE VARIATION OF ATOMIC WAVE FUNCTIONS AND FIELDS WITH ATOMIC NUMBER 115
7．1．THE NEED FOR A PROCEDURE FOR INTERPOLATION WITH RESPECT TO ATOMIC NUMBER 115
7．2．PURE SCALING 116
7．3．LIMITING BEHAVIOR OF THE EQUATIONS AND THEIR SOLUTIONS AS N ？ 118
7．4．VARIATION OF THE REDUCED WAVE FUNCTION WITH R FOR FIXED s 119
7．4．1．The (1s) wave function 123
7．5．VARIATION OF THE SCREENING NUMBERS WITH ATOMIC NUMBER 124
7．6．FURTHER EXAMINATION OF THE BEHAVIOR OF THE RADIAL WAVE FUNCTIONS AS N ？ 128
7．7．INTERPOLATION OF CONTRIBUTIONS TO Z 132
7．8．THOMAS-FERMI APPROXIMATION 134
8．ENERGY RELATIONS 136
8．1．THE TOTAL ENERGY AND CONTRIBUTIONS TO IT 136
8．2．SUBSTITUTION IN THE I INTEGRALS 137
8．3．ONE INCOMPLETE GROUP 139
8．4．ENERGY DIFFERENCES BETWEEN THE (LS) TERMS OF A SINGLE INCOMPLETE GROUP 139
8．5．ONE WAVE FUNCTION IN ADDITION TO COMPLETE GROUPS 140
8．6．TWO INCOMPLETE GROUPS 145
9．RELATIVISTIC EXTENSION 146
9．1．DIRAC＇S RELATIVISTIC WAVE EQUATION 146
9．2．FORM OF SOLUTION OF DIRAC＇S EQUATIONS FOR STATIONARY STATES OF AN ELECTRON IN A CENTRAL FIELD 147
9．3．MANY-ELECTRON ATOM 149
9．4．SOLUTION OF THE RADIAL WAVE EQUATIONS 151
10．BETTER APPROXIMATIONS 153
10．1．TWO KINDS OF IMPROVEMENTS IN THE APPROXIMATION 153
10．2．APPROXIMATE WAVE FUNCTIONS INVOLVING γij OR ？ij EXPLICITLY 155
10．3．SUPERPOSITION OF CONFIGURATIONS 159
10．4．POLARIZATION 162
APPENDIX 1．RESULTS OF CALCULATIONS OF ATOMIC STRUCTURES 164
APPENDIX 2．TABLES OF γ,SCREENING NUMBERS FOR γ,AND REDUCED WAVE FUNCTIONS 166
APPENDIX 3．ADDENDA 174
NAME INDEX 177
SUBJECT INDEX 179