Black body induced transitions

As shown in the previous chapter, the spontaneous decay rate of the n state to the lower lying n t state is given by the Einstein A coefficient nf. nf-7 In the presence of thermal radiation the stimulated emission rate Kn,fnt, is simply n times as large as the spontaneous rate. Explicitly, 

The black body photons can also be absorbed as the atoms in the n state make the transition to a higher lying n t state. Both the stimulated emission and absorption rates are given by 

Because of the variation of n with frequency, the frequency dependence of K cnc is quite different from that of An t n(, and these two processes favor different final states. This point is made graphically in Fig. 5.3, which is a plot of An p iss and Kn p lSs vs n for the Na 18s state and T = 300 K. As shown in Fig. 5.3, black body radiation favors transitions to nearby states and spontaneous emission favors transitions to the lowest lying states. 

In addition to driving transitions to discrete states the black body radiation can also photoionize the Rydberg atoms. The photoionization rate, l/r f is given by8 

The matrix elements are the radial matrix elements of r between the initial n state and continuum - 1 and + 1 waves which are normalized per unit energy. 

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Fig. 5.2 shows the dependence of n on v for T = 300 K, again with both frequency (Hz) and wavenumber (cm-1) used as abscissae. It is useful to recall that at 300 K, kTIh 6 x 1012 Hz or kT/hc 200 cm-1. This point is apparent in Fig. 5.2, since n = 1 at A-1 = 200 cm-1. Since the vacuum fluctuations, which lead to spontaneous emission, are given by n = 1/2, black body radiation at frequencies greater than kT/hn, where n 1, does not lead to significant effects. For an atom in its ground state with transitions at 104 cm-1, black body induced transitions are unimportant, since n 1. However, for a Rydberg state with transitions at 10 cm-1, where n 10, the black body induced transition rates can... 

While the representation of black body radiation given in Eq. (5.1) and Fig. 5.1 is the most familiar, it is not the most useful for the most important effect of black body radiation on Rydberg atoms, inducing transitions between neighboring levels. 

We now consider the transition rates for absorption of and stimulated emission induced by the black body radiation and compare these rates to the spontaneous... 

In an analogous experiment in which the initial population was placed in the Na 18s state, the transferred population was found to be in the higher lying p states, as expected for dipole transitions. Furthermore, the fraction of the atoms which had undergone transitions to each of the higher p states after 5 /is was in good agreement with values calculated on the basis of 300 K black body radiation induced transitions, as shown by Table 5.1.2... 

The internal temperature is expected to reach a stationary value due to the competition between the (long-range) collisions between charged particles, interaction with black-body radiation, and collisions with residual gas molecules. The cross-section for collisions between a molecular ion and another charged particle (which in the ensembles discussed here can be another molecular ion or a laser-cooled atomic ion) that induce transitions between the rotational or vibrational states has been discussed in Ref. [102]. The transition probability between two (rovibrational) states n and n is modeled by... 

A second example, mentioned already, is microwave spectroscopy of Rydberg levels that have been exited by resonant two-step absorption of two-dye lasers (Fig. 10.36b). The high accuracy of microwave spectrosopy allows the precise determination of finer details, such as field-induced energy shifts of Rydberg levels, broadening of Rydberg transitions by black-body radiation or other effects, which might not be resolvable with optical spectroscopy. 

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