Emission and absorption of radiation Infrared

Two ingredients are needed to compute the intensities of transitions the wave functions of the initial and final states and the form of the transition operator (Ogilvie and Tipping, 1983). For infrared transitions the appropriate operator is the dipole operator, M(r, 0, (j ). This operator is a vector (tensor of rank 1) and thus can be written as 

These matrix elements can be separated into a radial and an angular part 

The angular part depends only on properties of the angular momentum. Using the Wigner-Eckart theorem, one has 

The reduced matrix elements of the spherical harmonics can be written in terms of a Wigner 3 - j symbol 

The first term in Eq. (1.41) is the dipole moment, while the second is the electric anharmonicity. The expansion (1.40) diverges for large r. More appropriate forms of expansions are 

---