Transition Probabilities with Broad-Band Excitation

4 Transition Probabilities with Broad-Band Excitation 

In general, thermal radiation sources have a bandwidth 8o), which is much larger than the Fourier limit Arw = jT. Therefore, the finite interaction time imposes no extra limitation. This may change, however, when lasers are considered (Sects. 2.7.5 and 3.4). 

Instead of the field amplitude Eq (which refers to a unit fi equency interval), we introduce the spectral energy density p a ) within the frequency range of the absorption line by the relation, see (2.30), 

We can now generalize (2.71) to inelude the interaction of broadband radiation with our two-level system by integrating (2.71) over all frequencies m of the radiation field. This yields the total transition probability 3 ab t) within the time T. If D b II Eq, we obtain with S2ab = DabEo/h 

For broadband excitation, the transition probability for the time interval between 0 and t 

For thermal light sources or broadband lasers, p (o) is slowly varying over the absorption line profile. It is essentially constant over the frequency range where the 

For thermal light sources or broad-band lasers p(w) is slowly varying over the absorption-line profile. It is essentially constant over the frequency range where the factor [sm (w -w)X/2y[(w -w)/l] is large (Fig.2.18a). We can therefore replace p(w) by its resonance value p w ). The integration can then be performed and gives the value p wy )l K. for the integral. The transition probability for the time interval between 0 and t 

For thermal light sources p((d) is slowly varying compared with the 2 2 

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Selective excitation with a laser tuned to a transition Eq - E. solves the cascade problem [11.19]. In this variant many excited levels of the atoms or ions are populated by broad-band excitation via collisions with target gas atoms in a differentialy pumped gas cell (Fig.11.18c). A few cm behind the exit aperture of the gas cell a laser crosses the ion beam. If the laser frequency is tuned to transition Ej - E. the populations of both levels are changed, due to optical pumping, by an amount AN which depends on the laser intensity, the transition probability A. j, and the initial population of the two levels. The laser intensity can be chopped and the fluorescence intensity Ip- (E -> Ej ) is observed as a function of x alternatively with (I ) or without (I2) laser excitation. The difference... 

Figure 6 shows the emission and excitation spectra of ZnGa204 doped with Mn and Cr. Self-activated luminescence peak is reduced and the fluorescence due to the 3d-3d transition are predominantly observed at 503 nm for Cr and 695 nm for Mnl This implied that the exciting energy was transferred most probably from the self-activated site (broad band... 

Besides a transition to a continuum level of an excited electronic state, dissociation can occur by another mechanism in electronic absorption spectroscopy. If the potential-energy curve of an excited electronic state A that has a minimum in UA(R) happens to be intersected by the U(R) curve of an unstable excited state B with no minimum in U, then a vibrational level of A whose energy lies near the point of intersection of UA and UB has a substantial probability to make a radiationless transition to state B, which then dissociates. This phenomenon is called predissociation. Predissociation shortens the lifetimes of those vibrational levels of A that are involved, and therefore by the uncertainty principle gives broad vibrational bands with rotational fine structure washed out. 

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