Contents
I Theory and methodology 1
1 Background and motivation 3
1.1 Polarizabilities . . . 3
1.2 Two-photon decay rates . . . 6
1.3 Electronic isotope-shift factors . . . 7
1.4 Thesis outline . . . 8
2 Dirac equation 9 2.1 Relativistic context . . . 9
2.2 Hydrogenic ions . . . 12
2.2.1 Radial Dirac equations . . . 15
3 Dirac-Hartree-Fock method 19 3.1 Relativistic context . . . 19
3.2 DHF equations . . . 20
3.3 grasp2k package . . . 24
4 Beyond the DHF method 25 4.1 Corrections to the DC Hamiltonian . . . 25
4.2 Electron correlation . . . 26
4.2.1 MCDHF method . . . 26
4.2.2 Semi-empirical approach . . . 29
5 Lagrange-mesh method 31 5.1 Principle . . . 31
5.2 Lagrange functions . . . 31
5.2.1 Gauss-quadrature rule . . . 31
5.2.2 Lagrange conditions . . . 32
5.3 Meshes based on orthogonal polynomials . . . 33
5.4 Regularized Lagrange functions . . . 34
5.4.1 Regularized Laguerre mesh . . . 35
6 Static dipole polarizabilities 39 6.1 Definition . . . 39
6.2 Hydrogenic ions . . . 39
6.2.1 Scalar polarizability . . . 41 xv
Table of contents
6.2.2 Tensor polarizability . . . 44
6.3 Alkali-like ions . . . 44
7 Radiative multipole transitions 45 7.1 Interaction Hamiltonian . . . 45
7.2 Multipole expansion of the radiation field . . . 46
7.2.1 Gauge transformation . . . 47
7.2.2 One-electron transition amplitudes . . . 47
7.3 One- and two-photon decay rates . . . 48
7.3.1 Hydrogenic ions . . . 48
7.3.2 Alkali-like ions . . . 51
8 Electronic isotope-shift factors 53 8.1 Isotope shift theory . . . 53
8.2 Relativistic recoil Hamiltonian . . . 55
8.2.1 Normal mass-shift factors . . . 55
8.2.2 Specific mass-shift factors . . . 55
8.3 Relativistic field-shift factors . . . 56
8.4 Direct diagonalization of the Hamiltonian matrix . . . 58
9 Conclusions and perspectives 59
Bibliography 61
II Papers 71
Paper AI 73
Paper AII 85
Paper AIII 99
Paper AIV 115
Paper BI 133
Paper BII 143
Paper BIII 155
Corrigendum of the papers 167
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