The Calculation of Atomic StructuresPDF|Epub|txt|kindle电子书版本网盘下载

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1．INTRODUCTION1

1．1．SEVEN STEPS IN THE DEVELOPMENT OF ATOMIC THEORY1

1．2．WHY CALCULATE ATOMIC STRUCTURES?2

1．3．ATOM AND SOLAR SYSTEM3

1．4．ATOMIC UNITS5

1．5．SCHRODINGER＇S EQUATION FOR AN ELECTRON6

1．6．CENTRAL-FIELD WAVE FUNCTIONS8

1．7．ELECTRON SPIN11

1．8．MANY-PARTICLE SYSTEMS IN WAVE MECHANICS13

1．8．1．The necessity for approximation in calculations of atomic structure16

1．9．THE SEPARABLE WAVE FUNCTION APPROXIMATION17

2．THE VARIATION PRINCIPLE22

2．1．STATIONARY STATES OF A PARTICLE IN ONE DIMENSION22

2．1．1．E＇ as a Lagrange multiplier26

2．2．PARTICLE IN THREE DIMENSIONS27

2．3．MANY-PARTICLE SYSTEMS,IN COORDINATE SPACE29

2．4．TWO WAYS OF USING THE VARIATION PRINCIPLE TO DERIVE APPROXIMATE WAVE FUNCTIONS30

2．5．THE SEPARABLE WAVE FUNCTION APPROXIMATION FOR THE NORMAL STATE OF HELIUM31

2．6．THE VARIATION PRINCIPLE FOR EXCITED STATES36

2．7．ANALYTIC WAVE FUNCTIONS37

3．CONFIGURATIONS OF COMPLETE GROUPS39

3．1．THREE STAGES IN THE CALCULATION OF ATOMIC STRUCTURES39

3．2．ALGEBRAICAL PRELIMINARIES TO THE MANIPULATION OF DETERMINANT WAVE FUNCTIONS39

3．3．FIRST STAGE;DERIVATION OF THE EXPRESSION FOR E＇42

3．4．USE OF CENTRAL-FIELD WAVE FUNCTIONS45

3．5．THE Yk AND Zk FUNCTIONS50

3．6．SECOND STAGE:APPLICATION OF THE VARIATION PRINCIPLE52

3．6．1．Equations for the normal configuration of a ten-electron system55

3．7．FOCK＇S EQUATIONS AS INTEGRODIFFERENTIAL EQUATIONS57

3．8．THE NONDIAGONAL ε PARAMETERS58

3．9．EQUATIONS WITHOUT EXCHANGE59

3．9．1．Slater＇s simplified form of the equations with exchange60

4．NUMERICAL PROCEDURES63

4．1．FINITE DIFFERENCES63

4．2．THE MAIN FORMULAE IN FINITE DIFFERENCES64

4．3．QUADRATURE65

4．4．SECOND-0ORDER DIFFERENTIAL EQUATION WITH FIRST DERIVATIVE ABSENT68

4．5．NUMEROV＇S PROCESS FOR A LINEAR SECOND-ORDER EQUATION71

4．6．FIRST-ORDER EQUATIONS72

4．7．FOX-GOODWIN PROCESS FOR LINEAR FIRST-ORDER EQUATIONS73

5．APPLICATION OF THE NUMERICAL PROCEDURES77

5．1．EQUATIONS WITHOUT EXCHANGE77

5．1．1．Calculation of Y(γ) and contributions to it79

5．2．SOLUTION OF THE RADIAL WAVE EQUATION80

5．2．1．Starting the outward integrations81

5．2．2．Starting the inward integrations82

5．3．VARIATION EQUATIONS84

5．3．1．Matching the inward and outward equations85

5．3．2．Normalization87

5．3．3．Revision of the estimates of contributions to Z(γ)87

5．4．TORRANCE＇S METHOD88

5．5．EQUATIONS WITH EXCHANGE90

5．6．CALCULATION OF THE Yk FUNCTIONS91

5．7．RADIAL WAVE EQUATION WITH EXCHANGE93

5．7．1．Starting the integrations95

5．8．REVISION OF THE ESTIMATES OF THE RADIAL WAVE FUNCTIONS96

5．9．OTHER FORMS OF THE RADIAL WAVE EQUATION97

6．CONFIGURATIONS COMPRISING INCOMPLETE GROUPS101

6．1．RUSSELL-SAUNDERS COUPLING101

6．2．(LS) TERMS FROM A GIVEN CONFIGURATION103

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 FUNCTIONS111

6．6．ONE WAVE FUNCTION IN ADDITION TO COMPLETE GROUPS113

6．7．DIFFERENT RADIAL WAVE FUNCTIONS WITHIN A SINGLE GROUP113

7．THE VARIATION OF ATOMIC WAVE FUNCTIONS AND FIELDS WITH ATOMIC NUMBER115

7．1．THE NEED FOR A PROCEDURE FOR INTERPOLATION WITH RESPECT TO ATOMIC NUMBER115

7．2．PURE SCALING116

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 s119

7．4．1．The (1s) wave function123

7．5．VARIATION OF THE SCREENING NUMBERS WITH ATOMIC NUMBER124

7．6．FURTHER EXAMINATION OF THE BEHAVIOR OF THE RADIAL WAVE FUNCTIONS AS N ？128

7．7．INTERPOLATION OF CONTRIBUTIONS TO Z132

7．8．THOMAS-FERMI APPROXIMATION134

8．ENERGY RELATIONS136

8．1．THE TOTAL ENERGY AND CONTRIBUTIONS TO IT136

8．2．SUBSTITUTION IN THE I INTEGRALS137

8．3．ONE INCOMPLETE GROUP139

8．4．ENERGY DIFFERENCES BETWEEN THE (LS) TERMS OF A SINGLE INCOMPLETE GROUP139

8．5．ONE WAVE FUNCTION IN ADDITION TO COMPLETE GROUPS140

8．6．TWO INCOMPLETE GROUPS145

9．RELATIVISTIC EXTENSION146

9．1．DIRAC＇S RELATIVISTIC WAVE EQUATION146

9．2．FORM OF SOLUTION OF DIRAC＇S EQUATIONS FOR STATIONARY STATES OF AN ELECTRON IN A CENTRAL FIELD147

9．3．MANY-ELECTRON ATOM149

9．4．SOLUTION OF THE RADIAL WAVE EQUATIONS151

10．BETTER APPROXIMATIONS153

10．1．TWO KINDS OF IMPROVEMENTS IN THE APPROXIMATION153

10．2．APPROXIMATE WAVE FUNCTIONS INVOLVING γij OR ？ij EXPLICITLY155

10．3．SUPERPOSITION OF CONFIGURATIONS159

10．4．POLARIZATION162

APPENDIX 1．RESULTS OF CALCULATIONS OF ATOMIC STRUCTURES164

APPENDIX 2．TABLES OF γ,SCREENING NUMBERS FOR γ,AND REDUCED WAVE FUNCTIONS166

APPENDIX 3．ADDENDA174

NAME INDEX177

SUBJECT INDEX179