Line homogeneous

Even if the homogeneous line shape can be extracted, many other processes can contribute. Every decay process contributes to the finite lifetime of an excited species. A, with an individual decay constant k ... 

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. 

Saturation as described above can be observed either when all the molecules in the initial state have the same absorption probability, or when some of the state population is preferentially absorbed, depending on the spatial orientation of the molecules or on their transition frequency, selected from a certain frequency interval. The first case is called homogeneous line saturation, the second is due to inhomogeneous saturation or hole-burning. This different cases will be explained in more detail by discussing some relevant experiments. 

Fig. 11 a Comparison of the observed field cooled (FC red line) and zero field cooled (ZFC black line) NMR line shape in a PMN single crystal and the homogeneous line shape (yellow dots) extracted from T2 measurements, and the dipolar... 

Composite - A homogeneous lining created by the assembly of two or more rubber stocks with other materials like fabrics. 

Equation (7.22) is at the heart of spectroscopy. The positions of the absorption lines reflect the energy levels of the excited complex and the widths provide information about the lifetime and therefore about the coupling to the continuum states. The latter requires, however, that the measured widths are the true homogeneous line widths, i.e., unadulterated by poor resolution and/or thermal broadening, for example. Each resonance has a characteristic width. In Chapters 9 and 10 we will discuss how the final fragment distributions reflect the initial state in the complex and details of the fragmentation mechanism. 

The data from Table 3.7 make it possible to make a few estimates. Let us consider a concrete example. If the length of the resonator is L = 2 m, the Doppler contour, say of a K2 molecule in the BlTlu state, contains about 11 axial modes, the distance between them being Au>i = ttc/L m 4 108 s-1. If we assume that the width of the Bennet dip is equal to the homogeneous line width, rBen T = 0.86 108s 1 (see... 

The crudest way of estimating the particle size (D) as an average number from the breadth of a diffraction line is the widely used Scherrer approximation. It may be applied when the instrumental broadening is much smaller than the line profile (20 > 0.5°) and when a monomodal size distribution results in a homogeneous line profile. An explicit version of the equation determined by using the breadth of the diffraction line at half height (FWHM, pi 72) is given as follows ... 

The Hooke s law problem described in Section 2.5 can be revisited. Consider longitudinal waves in a homogeneous line described by x, the position of a particular point on that line, and u, the longitudinal displacement of that point from its equilibrium position. It can be shown (see Problem 5.7.1) that the displacement u obeys a one-dimensional mechanical wave equation ... 

To optimize local enhancement of the electric field we need to minimize all damping as much as possible and the suitability of certain nanoparticle morphologies for MEF by increased excitation of fluorophores can be estimated from measurements of the homogeneous line width of individual nanoparticles. For example, a series of expoiments comparing nanospheres and nanorods (see Figure 11.14) has shown that nanorods typically display dramatically reduced plasmon damping compared to spheres, i.e. narrower line vridths [34], and therefore produce a stronger field enhancement. 

---