Relativistic Effects and QED Effects

l    Diracs Paper

l    Binding Energies of Hg (Z=80) (in eV)

 

Relativistic HF

Nonrelativistic HF

Experiment

1s

83655

75613

83102.3

4f1/2

117.3 (104.8)

136.4

107.1

5s

138.9 (131.7)

113.8

134

6s

8.93

7.10

10.43

 

l    <r> of Hg (in a0)

 

RHF

NRHF

R/NR (%)

4s

0.399

0.439

91

4p3/2

0.434

0.443

98

4d5/2

0.453

0.450

101

4f7/2

0.483

0.469

103

6s

2.84

3.33

85

l    Numerical Example

Mg-like Ions (12 electrons)

Wavelengths for the 3s2 (1S0) 3s3p (3P1) transition

 

Mg

Ca8+

Cu17+

Mo30+

Experiment (Å)

4572.5

691.37

345.54

190.47

Hartree-Fock (%)

68.2

88.1

87.2

82.3

Dirac-Fock (%)

68.6

90.3

93.3

95.7

Multiconfig. Dirac-Fock (%)

96.2

99.3

99.7

99.99

 

 

l    Contribution to Total Energy (eV)

 

U (Z=92)

Zn (Z=30)

Dirac+Coul

-763364

-48834.8

Breit

994

20.6

Lamb Shift

690

13.8

Lamb (bare Z)

779

15.5

 

l    Importance of QED corrections (in eV)

U89+, 2s 2p1/2 transition

Dirac-Fock, without Breit

286.54

DF, Breit interaction

36.44

Correlation (RMBPT – DF)

-0.73

QED corrections, hydrogenic self energy

-43.96

Screening of the self energy (charge density ratio)

2.38

Screened QED corrections

-41.57

Total, DF + RMBPT

280.68

Experiment (Schweppe et al.)

280.590.10

Blundell (honest QED theory)

280.83

l    The Most Important QED corrections

             curly line : photon propagator

             double line : bound electron propagator

(a)    self energy

(b)   vacuum polarization

 

l    For a H-atom