Linewidths, electronic transition

The natural linewidth is the smallest contribution to the line profile of a transition and is only rarely seen as limiting within the laboratory. For an electronic transition with a lifetime of 10000 ps the linewidth is of order 0.00053 cm-1 but for a rotational transition the lifetime linewidth 5.3 x 10-15 cm-1. The best microwave spectra recorded in the laboratory have a linewidth of a few Hz or 10-12 cm-1, which is close (but not very) to the natural linewidth limit. 

Medium effects on the linewidths of electronic transitions are quite pronounced in certain instances. For example, it is quite general that the 0-0 band of an electronic transition will be the sharpest line in the vibronic spectrum of that state. The additional line broadening over that of the 0-0 band usually amounts to 1-5 cm-1, and increases in certain progressions with increasing vibrational separation from the origin. These line broadenings must gauge the vibrational relaxation rates, which are clearly much smaller than the usual rates of electronic relaxation. The assistance... 

One is therefore led to look for essential differences between the varying electronic transitions, which may be reflected in the varying linewidths. As the respective transitions are all spin and orbitally (electric dipole) allowed, this aspect of the transition is not a contributory factor, although transition intensities may be important. There are two clear-cut differences, and they concern... 

Fig. 5. Energy level diagram for Pd(2-thpy)2 dissolved in n-octane. The Tj state at 18,418 cm is zero-field split on the order of 0.2 cm. The emission decay times refer to the individual triplet suhstates I, II, and III, respectively, at T = 1.3 K. (Compare Fig. 6.) These suhstates are radiatively deactivated as purely electronic transitions, as well as by Franck-Condon (FC) and Herzberg-Teller (HT) vibrational activity, respectively. This leads the different vibrational satellites. (Compare also Sects. 4.2.2 and 4.2.3.) The lifetime of the S, state is determined from the homogeneous linewidth of the spectrally resolved Sq —> S, electronic origin. (Sect. 3.2) The electronic state at 24.7 x 10 cm is not yet assigned...

It is well known, however, that the width of a spectral line, at least in principle, yields information on the dephasing dynamics of the optical transition. Spectral lineshapes of purely electronic transitions in solids unfortunately are seldom determined by dynamic interactions, but, at least at low temperature, quite often by the effects of strain. The observed, named inhomogeneous linewidth is therefore of little interest. In case of vibronic transitions, however, the effect of vibrational relaxation on the lineshape may exceed the inhomogeneous linebroadening. Even so, classical spectroscopy quite often fails to elucidate the nature and strength of the perturbing forces on the optical (homogeneous) lineshape. 

To understand what controls the value of Up, we recall that for molecules with weak electron-phonon coupling with appreciable oscillator strength in the lowest purely electronic transition, the optical homogeneous linewidth yn becomes very small at low temperatures. The key point to remember is that due to well-known sum rules on optical transitions, the peak cross section depends inversely or yu, so that the narrow finewidth of a ZPL translates into a very large peak absorption cross section. For allowed transitions of rigid molecules, the value of Up becomes extremely large, approaching the ultimate limit of... 

Tn denotes the dephasing time of the optical transition, T the lifetime of the excited state (fluorescence hfetime) and the pure dephasing time. At low temperatures T is essentially independent on temperature while shows a strong dependence on temperature. The actual value of at a given temperature depends on the excitation of low frequency modes (phonons, librations) that couple to the electronic transition of the chromophore. In crystalline matrices at low temperatures (T <2 K) Tl approaches infinity as host phonons and local modes are essentially quenched and the linewidth is solely determined by the lifetime contribution. 

The luminescence of lanthanide ions in solids is characterized by several types of electronic transition, which differ markedly in spectral intensity and linewidth. Some of these are now illustrated. 

Even in the visible or ultraviolet range, atomic or molecular electronic transitions with very small transition probabilities exist. In a dipole approximation these are forbidden transitions. One example is the 2s -o-Is transition for the hydrogen atom. The upper level 2s cannot decay by electric dipole transition, but a two-photon transition to the Is ground state is possible. The natural lifetime is t = 0.12 s and the natural linewidth of such a two-photon line is therefore 8v = 1.3 Hz. 

SWCNTs have been produced by carbon arc discharge and laser ablation of graphite rods. In each case, a small amount of transition metals is added to the carbon target as a catalyst. Therefore the ferromagnetic catalysts resided in the sample. The residual catalyst particles are responsible for a very broad ESR line near g=2 with a linewidth about 400 G, which obscures the expected conduction electron response from SWCNTs. 

The second two terms in (5) are called T-terms or two-photon terms , which have (Qe g — 2hco) in the denominator corresponding to the excitation of an electron into the higher-lying excited state e. If we consider a resonance condition where hco = hcoeig/2 and assume that the transition linewidth is narrow, rt>s, < < h coeg imaginary part of the T-term can then be expressed in SI units as ... 

The width of the spectral line equals the sum of the widths of initial and final levels. Due to the short lifetime of highly excited states with an inner vacancy, their widths, conditioned by spontaneous transitions, are very broad. The other reasons for broadening of X-ray and electronic lines (apparatus distortions, Doppler and collisional broadenings) usually lead to small corrections to natural linewidth. 

---