Homogeneous line-broadening

Equation (2.27) illustrates what is called the natural line broadening. Since each atom or molecule behaves identically in this respect it is an example of homogeneous line broadening, which results in a characteristic lorentzian line shape. 

Studying moderately thin samples, the molecular time constants can be directly obtained from the experimental data without the need of computer simulations. This situation is termed nearly-free induction decay (NFID) which is related to the case of free induction decay in very thin samples. Some numerical results are depicted in Fig. 1. A specific experimental situation is considered with resonant, weak input pulses of Gaussian shape and duration tp (FWHM) and two values of the normalized propagation length, ai 0.2 and aJl 1. Here a denotes the conventional absorption coefficient at the maximum of the absorption band. The intensity of the transmitted pulse is evaluated from Maxwell-Bloch equations for homogeneous line broadening. 

In crystalline solids the electric field E(R) at the location R of the excited molecule A has a symmetry depending on that of the host lattice. Because the lattice atoms perform vibrations with amplitudes depending on the tem-peratur T, the electric field will vary in time and the time average E(T, t, R)) will depend on temperature and crystal structure [3.41-3.43]. Since the oscillation period is short compared with the mean lifetime of A ( /), these vibrations cause homogeneous line broadening for the emission or absorption of the atom A. If all atoms are placed at completely equivalent lattice points of an ideal lattice, the total emission or absorption of all atoms on a transition Ei Ek would be homogeneously broadened. 

C. Szantay Jr, NMR and the Uncertainty Principle How to and how not to Interpret Homogeneous Line Broadening and Pulse Nonselectivity. I. The Fundamentals , Concepts Magn. Reson., A, 2007, 30A, 309. 

Fig. 10 2H spectra of C12E5, selectively deuterated in the a, P or y position, respectively, and adsorbed to colloidal silica, displayed together with Lorentzian fits, demonstrating a homogeneous line broadening. 

Macfarlane RM and Shelby RM. Homogeneous line broadening of optical transitions of ions and molecules in glasses. J. Lumin. 1987 36 179-207. 

---