Density-dependent emission centers

Figure 3. Density-dependent emission centers of gravity (in nm) for 10 /xM PRODAN in C02, N20, and CF3H.

Neutralino annihilation is enhanced in the spike, because of the dependence of the annihilation rate on square of the density. The Galactic Center then becomes a source of neutrinos, gamma-rays, radio waves, etc. from neutralino annihilation (Figure 26). The intensity of the emission depends on the steepness of the spike. If the spike is shallow, neutralino annihilation is generally undetectable. On the contrary, a steep spike at the Galactic Center produces interesting signals. 

Let N(j,Ni,N2, and Nj, be the equilibrium population densities of the states 0, 1,2, and 3, respectively (reached under continuous wave excitation intensity Iq), and let N = NQ + Ni+N2 + N3he the total density of optical absorbing centers. The up-converted luminescence intensity ho (corresponding to the transition 2 0) depends on both N2 and on the radiative emission probability of level 2, A2. This magnitude, which is dehned below, is proportional to the cross section a20 (called the emission cross section and equal to the absorption cross section ao2, as shown in Chapter 5). Thus we can write... 

The TSC signal strength will be proportional to the appropriate trap density, as seen in Eq. (55). Unfortunately, the lifetime t (or xp for hole emission) also enters the equation, and this quantity will depend on other traps and recombination centers in the sample. If t could be separately determined, then the TSC method could be calibrated for trap density. Essentially the same considerations hold for the transient-current methods (PITS and OTCS), as seen in Eq. (65). A further complication enters if eni and epi are of comparable magnitude, and ejepi is unknown [cf. Eq. (83)]. 

The compounds are luminescent at room temperature with structured emission profiles that suggest aryl ligand-centered emission. Time-dependent density-functional theory calculations support this assignment. Xantphos and related ligands are not spectroscopically innocent the LUMOs of these compounds reside mostly on the connecting pillars and not on gold or the o-aryl ligands. 

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