Università Roma Tre

1- Bohr model for hydrogen-like atoms. Absorption and emission spectroscopic series. Quantum theory for the hydrogen-like atoms. The Schroedinger equation of an electron in Coulomb field. Eigenfunctions and energy levels. Classification of states. Some properties of the radial atomic functions.

2- Interaction of hydrogen-like atoms with the e.m. field. Time dependent perturbation theory for the interaction of electron with the e.m. field. Absorption and emission terms. Transition probability for the absorption and stimulated emission. Cross section for the absorption. Spontaneous emission. Dipole approximation. Selection rules.

3- Grotrian diagram. Polarization of radiation and helicity of the photons. Einstein coefficients.
Form of the lines due to the lifetime of the levels.

4- Relativistic corrections. Spin-orbit interaction. Darwin correction. Fine structure corrections for the hydrogenic atoms.

5- Effects of electric and magnetic static fields. Stark effect. Normal Zeeman effect. Paschen-Back effect. Anomalous Zeeman effect.

6- Definition of atomic units. Atoms with two electrons. Approximation of independent electrons. Interaction
electron-electron as a perturbation. Variational method. Excited states. Coulomb energy and exchange energy
for states with two electrons. Energy levels in the continuum .

7- Many-electron atoms. Approximation of central field. Diagram of levels. Many-particle wave function, Slater determinant. Hartree-Fock equations and exchange term.

8- Diagram of levels and Hund's rules. LS coupling. Hund's rule in the presence of the spin-orbit term. Examples of energy levels for
not equivalent and equivalent electrons. J-j coupling.

9- Selection rules for atoms with many electrons in the dipole approximation.
Spectra of alkali atoms, the quantum defect. Atomic spectra of He and alkaline earths.

10- Molecular Physics. Born-Oppenheimer approximation. Schroedinger problem
for electrons. Equation for the nuclei.

11- The hydrogen molecular ion. Applications of the LCAO method. Symmetry properties of
diatomic molecules. Hydrogen molecule with the molecular orbital method. LCAO method in general.
Bonding and antibonding states. Covalent and ionic bonding.

12. Dynamics of nuclei. Rotational and vibrational levels. Total angular momentum of the nuclei and the electrons.

13- Morse potential. Anharmonic corrections. centrifugal corrections to the Morse potential.

14. Transitions between vibrational and rotational levels. Selection rules. Examples of eteronuclear and diatomic molecules.
Raman effect. Electronic transitions.

15- Franck-Condon principle.

B. H. Bransden and C. J. Joachain "Physics of Atoms and Molecules" (I-st or II-nd edition)