Power spectrum linewidth

An important consequence of the lineshape theory discussed above concerns the effect of the bath dynamics on the linewidths of spectral lines. We have already seen this in the discussion of Section 7.5.4, where a Gaussian power spectrum has evolved into a Lorentzian when the timescale associated with random frequency modulations became fast. Let us see how this effect appears in the context of our present discussion based on the Bloch-Redfield theory. 

Figure 6. The first single-molecule optical spectra, showing use of the FM/Stark technique for pentacene in />-terphenyl. (a) Simulation of absorption line with (power-broadened) linewidth of 65 MHz. (b) Simulation of FM spectrum for (a), com = 75 MHz. (c) Simulation of FM/Stark line-shape, (d) single-molecule spectra at 592.423 nm, 512 averages, 8 traces overlaid, bar shows value of 2o)m = 150 MHz. (e) Average of traces in (d) with fit to the in-focus molecule (smooth curve), (f) Signal far off line at 597.514 nm. (g) Traces of SFSatthe O2 line center, 592.186 nm. After Ref. 1.

In a typical laser, it is the rate of the phase fluctuations that determines the laser linewidth. In this case, the field power spectrum is Lorentzian with a FWHM linewidth given in terms of SL experimental parameters by... 

Linewidth Analysis From the power spectrum, we can obtain the linewidth F = Acoi/2 = q D (Chu and Nose, 1980). If the measurement is carried out for a polymer in a semidilute solution, we can relate asymptotically F to D and c (concentration) following the scaling law... 

A high-resolution spectrum of the clock transition is shown in Fig. 2. The clock-laser power was reduced to 30 nW to avoid saturation broadening. The fit with a lorentzian curve results in a linewidth of 170 Hz (FWHM), corresponding to a fractional resolution bv/v of 1.3 10-13. A spectral window of 200 Hz width contains 50% of all excitations. According to our present experimental control of the ion temperature, electromagnetic fields and vacuum conditions, no significant Doppler, Zeeman, Stark or collisional broadening of the absorption spectrum of the ion is expected beyond the level of 1 Hz. The linewidth is determined by the frequency instability of the laser and the lineshape is not exactly lorentzian... 

Figure 1 Experimental and simulated EPR spectra of oxidized CooA at pH 7.4. Experimental conditions temperature, 2 K microwave frequency, 35.106GHz microwave power, 20p,W 100 kHz field modulation amplitude, 0.4 mT time constant, 128 ms scan time, 4 min. Lower traces, in absorption line-shape (due to rapid-passage conditions), are the experimental spectrum (blue) and a digital integration of the simulated spectrum (red). Upper traces in first-derivative lineshape are a digital derivative of the experimental spectrum (blue) and the simulated spectrum (red). Simulation parameters component (a) g = [2.60, 2.268, 1.85], (b) g = [2.47, 2.268, 1.90] Gaussian single-crystal linewidths (half-width at half-maximum) W = [500, 200, 400] MHz. Simulated spectra for (a) and (b) are added in the ratio 2 1 to give the summed spectrum shown...

The ESR spectrum of the Ph anion radical has been shown to have a g = 2.0025 and a linewidth of 12.5 G [57,81]. When PSII-RC were illuminated at 220 °K and ESR spectra taken at 6°K, a split signal was observed at high microwave power (50 mW), but not at low power (0.1 mW) [82]. Similar observations, made in bacterial RC, were interpreted as due to an exchange interaction between BPh and the A2peA3 complex [23]. A similar situation and geometry may therefore exist also in PSII-RC. 

Two especially important variants of REMPI (Johnson, et al., 1975) spectroscopy are ionization-dip (Cooper, et al., 1981) and Zero Electron Kinetic Energy (ZEKE) (Miiller-Dethlefs and Schlag, 1991 Merkt, 1997 Signorell and Merkt, 1999) photoelectron spectroscopy. Ionization-dip REMPI spectroscopy is especially useful when one wants to record free<—bound spectra from a single, selectable v, J level. Without such v, J selection, most of the oscillatory structure in a free<—bound spectrum will be washed out. One potential problem with some ionization-dip schemes is that, if the ionization transition originates from the initial level of the free<—bound transition being studied, there is a possibility that the observed linewidths will be distorted by power broadening (especially when the free final state is a weakly predissociated state with linewidth < lcm-1). 

If one had two species in the sample with different chemical shifts and significantly different T2S, the spikelet echo sequence could demonstrate the existence of both species, independent of the pulse repetition rate. The resulting spectrum would be a composite of the spikelet spectra of the two individual species with different breadths (widths or extents of the power spectra) and different linewidths for each of the spikes or lines. This capability of distinguishing species based upon their T2S proved to be important in the identification of disordered phases or components of adsorbate material on the surface. 

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