Photon distribution, characterization

Figure 2 Characterization of the photon distribution in directions and wavelengths.

There is a condition of momentum conservation for photons and electrons which must also be satisfied in the photoemission process. For band electrons, for which the Bloch wavefunctions are characterized by the wavenumber k (proportional to the momentum p of the electron), the momentum conservation condition is important to determine the angular distribution of the photoemitted electrons. Angular J esolved FhotoEmission spectroscopy (ARPES), schematized in Fig. 2, is potentially able to provide, and has been used to obtain, the E(fc) dispersion curves for solids. 

Utilizing ionization efficiency curves to determine relative populations of vibrationally excited states (as in the photoionization experiments) is a quite valid procedure in view of the long radiative lifetime that characterizes vibrational transitions within an electronic state (several milliseconds). However, use of any ionization efficiency curve (electron impact, photon impact, or photoelectron spectroscopic) to obtain relative populations of electronically excited states requires great care. A more direct experimental determination using a procedure such as the attenuation method is to be preferred. If the latter is not feasible, accurate knowledge of the lifetimes of the states is necessary for calculation of the fraction that has decayed within the time scale of the experiment. Accurate Franck -Condon factors for the transitions from these radiating states to the various lower vibronic states are also required for calculation of the modified distribution of internal states relevant to the experiment.991 102... 

Table 1. Basic Quantities in Analyses of CW Laser Scattering for Probability Density Function. In Eq. 1 within the table, F(J) is the photon count distribution obtained over a large number of consecutive short periods. For example, F(3) expresses the fraction of periods during which three photons are detected. The PDF, P(x), characterizes the statistical behavior of a fluctuating concentration. Eq. 1 describes the relationship between Fj and P(x) provided that the effects of dead time and detector imperfections such as multiple pulsing can be neglected. In order to simplify notation, the concentration is expressed in terms of the equivalent average number of counts per period, x. The normalized factorial moments and zero moments of the PDF can be shown to be equal by substitution of Eq.l into Eq.2. The relationship between central and zero moments is established by expansion of (x-a)m in Eq.(4). The trial PDF [Eq.(5)] is composed of a sum of k discrete concentration components of amplitude Ak at density xk. [The functions 5 (x-xk) are delta functions.]...

Photon Correlation Spectroscopy, Transient Electric Birefringence, and Characterization of Particle Size Distributions in Colloidal Suspensions... 

---