Line shapes of diatomic systems

When spectra of binary systems are considered, it is useful to introduce a normalized pair absorption coefficient, A, and a pair line shape function, G, according to 

A(y) = A(v)/v. Whereas A describes the absorption of spectral intensity or energy, A is proportional to the probability of absorbing a photon per unit path length. We will not make great use of the quantity A, because the spectral density G defined above is more closely related to the squared dipole transition matrix elements, even at low frequency G is the preferred quantity. 

The simplest systems of interest consist of two interacting, non-reactive atoms, such as He-Ar. In such cases (if electronic transitions are ignored), there is only the translational band to be considered. Line shape computations are straightforward but will in general require the use of digital computers if realistic intermolecular potentials are employed. 

The dipole operator is expressed in terms of spherical vector components, Eqs. 4.6 and 4.14, according to 

The factor C k of B(R) is often called the /th component of the Racah spherical tensor of rank k the three tensor components of rank 1 may be considered unit basis vectors spanning the (spherical) space. 

---

Kong s periodic systems of diatomic and triatomic molecules (Kong 1982, 1989) are truly beautiM. They are the silver lining of the dark cloud of his long-term house arrest related to the Cultural Revolution in the People s Republic of China. His systems place molecules in the compartments of a flat chart with approximately the same shape as the chart of the elements. The period and group numbers are the sums of the atoms period and group numbers. 

Schematic potential energy diagraim for ground and excited electronic singlet states of a diatomic molecule, A-B and A-B, respectively. The horizontal lines represent vibrational energy levels. The wavy lines represent the arrival or departure of light quanta. It is important to recognize that the curves shown here are schematic and, for actual systems, the positions and shapes of the curves may be quite different from those shown.

---