Review Questions

1. Why is it not possible to obtain a closed analytical solution for the wave functions and transition energies for multi-electron atoms and ions?

2. Perturbation theory applied to different physical interactions is carried out to compute the energy states of multi-electron atoms/ions. The Hamiltonian is thus written in parts from stronger to weak interactions.  Qualitatively, describe the three strongest terms of the Hamiltonian, H1, H2, and H3, given in Equation 22.2.

3. Briefly describe the Hartree-Fock method.

4. What is parity?

5. Briefly describe the essence of the Russell-Saunders vector model. Describe the basic rules of quantized vector addition.

6. There are four quantities appearing in the Russell-Saunders state term (see Equation 22.11).  Write down the state term and define each of these four quantities. Write down the mathematical expressions for computing each.

7. What is the difference between a "shell" and "subshell"?

8. A common misconception is the L-S coupling is spin-orbit coupling, but in fact L-S coupling results from the Hamiltonian term H2, which describes the Coulomb interaction between bound electrons.  Provide a qualitative description of L-S coupling and how this governs the binding energies of electrons in a given subshell. (HINT: the bound electrons want to be as far apart from one another as possible!).

9. What is the Lande' interval and what rule does it provide when determining the relative energies of fine structure states? What are the conditions for a "normal" interval and for an "inverted" interval.

10. For what type of atoms/ions does L-S coupling scheme best describe the energy structure and for what type does j-j coupling best describe the energy structure.  What is the essence of the physics modeled in j-j coupling? 

11. What is the utility, or practical usefulness, of quantifying the three atomic constants of term averaged transitions.

12. What is an "allowed transition" versus a "forbidden transition". Compare and contrast them in terms of the dipole selection rules and the timescales for spontaneous emission.

Problems

1. Under construction