Energy-resolved spectra

The surface electronic states are typically probed with PES and I-PES (photoemission measures occupied states inverse photoemission, unoccupied states) described in Section 7.3.1, or for more accuracy with two-photon photoemission (2PPE), which is particularly suitable for analyzing the image potential states. In the 2PPE technique, a first laser hght pulse (pump) excites an electron from its initial state below the Fermi level Ep into an unoccupied intermediate state (of Shockley or image potential type). A second pulse (probe) lifts the electron to the final state above the vacuum level E c. so it can be detected as a photoelectron. One of the possible data acquisition modes is to record energy-resolved spectra at a particular delay between pump and probe pulses [51]. 

Figure 25 Schematic illustration for a system based on energy-dispersive coherent X-ray scatter (CXRS). Observation of the scattered photons is restricted to a fixed angle via a pinhole collimator. The spectrum from a highly energy resolving detector will show peaks at particular energies that are characteristic of the polycrystalline target. Computerized identification techniques can be used to identify the target substance.

The luminescence spectrum of the Canada apatite contains the yellow band, which is similar to Mn + emission in the Ca(II) site (Fig. 5.71). Nevertheless, this band has short decay time, which is not suitable for strictly forbidden d-d transitions in Mn +. It dominates in the time-resolved spectrum with a delay of 10 ps and gate of 100 ps when the shorter-lived centers are quenched, while the longer-Hved ones are not detected. A change in the lifetime may be indicative of the energy transfer from Mn + by a radiationless mechanism. A condition necessary for this mechanism is coincidence or a close distance between energy level pairs of the ion sensitizer and the ion activator. Here, the process of luminescence is of an additive nature and a longer duration and greater quantum yield of the activator luminescence accompany a reduced... 

The lowest-energy-resolved features in the absorption spectrum of M0S2-type semiconductors are the A and B excitons, shown in Fig. 3 for the case of M0S2 [30]. The dissociation limit of peaks built off of the A exciton correspond to the direct band edge. Calculations indicate that these transitions are at K and that the A and B excitons correspond to K4 K5 and K1 K5, respectively [25,26]. The lowest-energy direct-transition excited states have considerably different orbital character than the band-edge state. K1 and K4 correspond to 84% and 82% dyy, respectively corresponds to 77%... 

M. Shapiro If the resonances overlap to such an extent that we can no longer break the frequency resolved spectrum to a sum of Fano lines in a unique way, then my analysis would not be unique. However this is an extreme situation and even in this case one can try to fit the spectrum (admittedly in a non-unique way) to a sum of Fano lines (or complex energy poles). 

French, R.H., Miillejans, H., Jones, D.J., Duscher, G., Cannon, R.M. and Ruhle, M. (1998), Dispersion forces and Hamaker constants for intergranular films in silicon nitride from spatially resolved-valence electron energy loss spectrum imaging , Acta Mater., 46 (7), 2271-2287. 

Fig. 13.7. Angle-resolved spectrum of an ultrashort pulse propagating in water (left panel). The dashed lines represent the loci of spectral energy concentration predicted from an effective three-wave mixing argument. The right panel compares these loci to the manifold that supports the spectrum of 2-invariant X-wave solutions that propagate without distortions...

Mossbauer spectroscopy [14-17] involves the use of y-rays as probes. The resonant re-absorption by atomic nuclei of a highly monochromatic beam of y-rays, whose energy can be varied by use of the Doppler effect on a moving source, is monitored as a fimction of energy. The spectrum obtained [10] (Figure 6.4.) is usually a series of poorly-resolved peaks from which information on oxidation... 

Spectroscopic observables can be categorized in several ways. We can follow a temporal profile or a frequency resolved spectrum we may distinguish between observables that reflect linear or nonlinear response to the probe beam we can study different energy domains and different timescales and we can look at resonant and nonresonant response. This chapter discusses some concepts, issues, and methodologies that pertain to the effect of a condensed phase environment on these observables. For an in-depth look at these issues the reader may consult many texts that focus on particular spectroscopies. ... 

The essential point is the complementary nature of the descriptions in the time and frequency domains, a complementarity most familiar to us in the form of the time energy uncertainty principle. For our purpose we want a somewhat more detailed statement, a statement whose physical content can be loosely stated as the overall shape of the spectrum is determined by very short time dynamics, higher resolution corresponds to longer time evolution. A fully resolved spectrum is equivalent to a complete knowledge of the dynamics. We now proceed to make this into a technical statement by an appeal to the convolution theorem for the Fourier transform (51). A preliminary requirement for this development is the definition of the operation of smoothing. To erase details in a function (in our case, the spectrum) we convolute it with a localized window function. A convolution operation is defined by... 

Figure 7 The time auto correlation function and the corresponding spectrum for a Gaussian wave packet propagating on an excited harmonic potential energy surface, (a) The short time decay of C(/) (cf. Eq. (17)) and the broad spectrum (= the Franck Condon envelope (cf. (18)). (b)The longer time dependence of C(r) and the corresponding, vibrationally resolved, spectrum.

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