Homogeneous width

Homogeneous (a) and inhomogeneous (b) band shapes having inhomogeneous width V, and homogeneous width Av. ... 

Figure 20. Energy levels of neutral sodium atom mostly involved in the resonant incoherent 2-photon excitation for the polychromatic LGS. Wavelengths (nm), lifetimes (ns) and homogeneous widths (MHz).

It is useful to view optical absorption and emission processes in such a system in terms of transitions between distinct vibrational levels of the ground and excited electronic states of a metal atom-rare gas complex or quasi-molecule. Since the vibrational motions of the complex are coupled with the bulk lattice vibrations, a complicated pattern of closely spaced vibrational levels is involved and this results in the appearance of a smooth, structureless absorption profile (25). Thus the homogeneous width of the absorption band arises from a coupling between the electronic states of the metal atom and the host lattice vibrations, which is induced by the differences between the guest-host... 

The temperature dependence of the homogeneous width of zero-phonon lines (ZPLs) in the optical spectra of the impurity centers in crystals is determined by... 

Fig. 1. Temperature dependence of the homogeneous width y (a) and position 8 (b) (in u>d units) of a zero-phonon line in the Debye model for different values of the interaction parameter wcx/w indicated in the right-side boxes. The instability limit corresponds to wcr/w = 1.

Fig. 2. Temperature dependence of the homogeneous width (a) and the peak shift (b) of the 637 nm zero-phonon line in luminescence spectrum of N-V centers in diamond films points experiment the line theoretical approximations according to the laws y — y0 + aT3 + bT1 and 8 = fiT2 - vT4.

The dissociation rate T for each quasi-bound level can be extracted from the homogeneous widths of the absorption lines. It depends on j, J, Q as well as the parity of the considered state. Figure 12.6 depicts experimental and theoretical linewidths for rotational state j — 1 and... 

Here /, is the 13C nuclear spin, S is the unpaired electronic spin, and A j- is the Fermi contact hyperfine coupling tensor. This coupling is identical for all 13C nuclei as long as the C60 ion is spherical, but becomes different for different nuclei after the Jahn-Teller distortion leading to an inhomogeneous frequency distribution. The homogeneous width of the 13C NMR lines is, on the other hand, mainly determined by the electron-nuclear dipolar interaction... 

Figure 4.3. Schematic transition to coherence (Fig. 4.2) for a square distribution of domains as the disorder from A = T to < nr. The extended disorder is opposed by retarded interactions ( R,(z) ->) For A T all the domains have transferred their oscillator strength ( Im z - 00) to the coherent state at = 0, while the strong homogeneous width dominates the emission line.

The role played by y above (homogeneous width) is now played by y . The reflection (and transmission) amplitude is given by the Green s function G at the energy z of the exciting source.126 When the transition dipole lies in the lattice plane, we have for the reflection (rK) and transmission (tK) amplitudes... 

Our first steps toward the single-molecule regime arose from work at IBM Research in the early 1980s on persistent spectral hole-burning effects in the optical transitions of impurities in solids (for a review, see [20]). Briefly, if a molecule with a strong zero-phonon transition and minimal Franck-Condon distortion is doped into a solid and cooled to liquid helium temperatures, the optical absorption becomes inhomogeneously broadened (Fig. 2.2A). The width of the lowest electronic transition for any one molecule (homogeneous width, Yjj) becomes very small because few phonons are present, while at the... 

Fig. 18.11 Upperpanel Diagramofaninhomogeneously broadened absorption band ofwidth Finh, consisting of a superposition of individual transitions of homogeneous width r, Q,y. Bottom Laser induced hole burnt at low temperature and absorption of the photoproduct. (Fig. 1 from S. Volker, Ann. Rev Phys. Chem. 40, 499-530 (1989).)...

To derive an absorption spectrum, several additional assumptions are made the chains are sufficiently long to avoid end effects defects Isolate the electronic states of the segment adjacent defects do not interfere and each component has an intrinsic homogeneous width. The agreement shown between the calculated and observed spectra is surprisingly good considering the simplicity of the model. 

When the distribution being averaged over is dynamic [29] but classical with Gaussian fluctuations x(f), the gammas representing the homogeneous widths of different components should be omitted from the formulas and the average in Eq. (44) must be replaced by... 

Let us consider now the conditions under which the dependencies of the type displayed in Figs. 9.4 and 9.5 can be realized. Note, first of all, that in layered crystals which we discuss now, the width of an exciton band A for wavevectors directed along the normal to the (a, b) plane is rather small and in this consideration can be neglected. For this reason Figs. 9.4 and 9.5 determine the minimum energy of an exciton in a monolayer of a crystal as a function of its distance to the surface.54 However, the large homogeneous width 7 of the lowest exciton transition can destroy this picture of spectra. The picture will survive only for such layered crystals like the anthracene crystal in which the inequalities... 

Assuming that the mean distance between CTEs p 10 a, e.g. that the concentration of CTEs is of the order of 10 2 we obtain that Ae 150 cm-1, which is significant on the scale of the homogeneous width of a CTE transition. 

The theoretical value of Rc has to be compared to the mean minimal distance between resonant chromophores in the compound. In fact, it is not very probable that the condition of resonance within the homogeneous width of a given [Cr(ox)3]3 chromophore is fulfilled by any of the nearest... 

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