Abstract
This chapter summarizes the traditional theory of one- and many-electron systems, which has been developed and successfully applied to many atomic problems for almost a century. The presentation is deliberately brief. A more detailed introduction to atomic physics can be found in the textbook by Bransden and Joachain [BJ83]. At a much more formal level there is “Atomic Many-Body Theory” by Lindgren and Morrison [LM85]. Finally we mention “Atomic Structure” by Condon and Odabasi [CO80], where a comprehensive account of conventional atomic structure calculations can be found.
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- 1.
The constant κ is related to the factor F(j, l) in front of the spin-orbit contribution in the radial Schrödinger equation (1.362) by κ = −1 − F(j, l A ).
- 2.
The fact that the energy of the H− ion in the first column of Table 2.1 lies above the energy − 0. 5 of the H atom shows a weakness of the restricted Hartree-Fock method, which was used here and in which both electrons were restricted to having the same spatial part of the single-particle wave function. In an unrestricted Hartree-Fock calculation the Hartree-Fock energy can at least come arbitrarily close to the value − 0. 5. To see this construct a two-electron Slater determinant in which one occupied single-particle state is the ground state of atomic hydrogen and the other is a very distant almost plane wave with (almost) vanishing wave number.
- 3.
Vectors a, b with complex components are orthogonal when a x ∗ b x + a y ∗ b y + a z ∗ b z = 0.
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Friedrich, H. (2017). Atoms and Ions. In: Theoretical Atomic Physics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-47769-5_2
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