N-Manifold states

At 2000 K and 1 atm, Hollander s state-specific rate constant becomes k. = 1.46 x 1010 exp(-AE/kT) s-1, where AE is the energy required for ionization. For each n-manifold state the fraction ionized by collisions is determined, as well as the fraction transferred to nearby n-manifold states in steps of An = 1. Then the fractions ionized from these nearby n-manifold states are calculated. In this way a total overall ionization rate is evaluated for each photo-excited d state. The total ionization rate always exceeds the state-specific rate, since some of the Na atoms transferred by collisions to the nearby n-manifold states are subsequently ionized. Table I summarizes the values used for the state-specific cross sections and the derived overall ionization and quenching rate constants for each n-manifold state. The required optical transition, ionization, and quenching rates can now be incorporated in the rate equation model. Figure 2 compares the results of the model calculation with the experimental values. 

Stoneman and Gallagher have used black body radiation to make precise measurements of the avoided crossings between the K ns and n — 2 Stark manifold states in electric fields,36 and these measurements are described in Chapter 6. 

Fig. 6.2 Stark structure and field ionization properties of the m = 1 states of the H atom. The zero field manifolds are characterized by the principal quantum number n. Quasidiscrete states with lifetime r > 10-6 s (solid line), field broadened states 5 x 10 10 s < x < 5 x 10-6 s (bold line), and field ionized states r < 5 x 10 10 s (broken line). Field broadened Stark states appear approximately only for W > ITC. The saddle point limit Wc = -2 /E is shown by a heavy curve (from ref. 3).

Fig. 6.15 Anticrossing signal from the avoided crossing of the K 20s state with the lowest energy n = 18 Stark manifold state. The left-hand peak corresponds to the m = 0 anticrossing, and the right-hand peak to the m = 1 anticrossing (from ref. 29).

Fig. 7.9 Adiabatic and diabatic paths to ionization for n = 15 states in the center and on the edges of the Stark manifold. The diabatic paths are shown by solid bold lines and the adiabatic paths by broken bold lines. In both cases ionization occurs at the large black dots. The diabatic paths are identical to hydrogenic behavior. The adiabatic n = 15 paths are trapped between the adiabatic n = 14 and n = 16 levels. Adiabatic ionization always occurs at lower fields than diabatic ionization.

Fig. 8.1 Squared transformation coefficients from the n = 15 parabolic 15 n m states to spherical 15p states for (a) m = 0 and (b) m = 1. Note that the 15p state is concentrated in the edges of the m = 0 Stark manifold but at the center of the m = 1 manifold.

In Fig. 8.8 we show a graph of the oscillator strengths from the red and blue n — 2 Stark states to the n = 15 Stark states, i.e. /i5 ,o,2 o assuming that a> has its zero field value of 0.123. As shown by Fig. 8.8, from the red n = 2 state predominantly the red n = 15 states are excited, while from the blue n = 2 state predominantly the blue n = 15 states are excited. The result of exciting from the red instead of the blue n = 2 Stark state is simply to reverse the asymmetry of the excitation of the Stark manifold. 

Fig. 10.7 Relevant energy levels of K near the n = 16 Stark manifold. The Stark manifold levels are labeled (n,k), where k is the value of (, to which the stark state adiabatically connects at zero field. Only the lowest two and highest energy manifold states are shown. The laser excitation to the 18s state is shown by the long vertical arrow. The 18s — (16,3) multiphoton rf transitions are represented by the bold arrows. Note that these transitions are evenly spaced in static field, and that transitions requiring more photons occur at progressively lower static fields. For clarity, the rf photon energy shown in the figure is approximately 5 times its actual energy (from ref. 8).

In the experiment of Lovejoy and Nesbitt (1990) the IR photon excites the complex into the (n = 1, j = 1) manifold. There are two pathways for fragmentation within the n — 1 state ... 

For most carbonyl compounds, we expect to have two near-lying excited states in the triplet manifold, which are either n-n or tc-tc in character. The n-7T states frequently show radical-like behavior. Benzophenone is an example of such a molecule which has an n-7t triplet state in which we see occurrences of hydrogen abstraction and very efficient intersystem crossing. When the lowest state is the 71-71 state, largely centered on the aromatic part of the molecule, as in the case of p-methoxyacetophenone, the reactivity decreases significantly (8,9). With the nature of lignin and the nature of the model we have chosen, we are mostly interested in molecules which have this type of behavior. 

The preparation of the Rydberg circular states Is performed by pulsed laser excitation followed by an adiabatic microwave transfer method (A.M.T. M.) already described in ref. [a]. This method requires that the atom interacts with an homogeneous electric field Fj., produced by the stack of equally spaced metallic plates shown on Fig. 1-a. This field removes the degeneracy of the various n-manifolds. 

The laser excitation prepares the atoms in the lowest energy Stark state with m =2 in a chosen n-manifold (n=24 for example) (see Fig. 1-b). This excitation is itself a stepwise process involving three pulsed dye laser beams in resonance with the 2S-2P, 2P-3D and 3D-n, m =2, nx=0 transitions... 

The last conclusion has been confirmed by the experimental study of collision induced transitions between singlet and triplet manifolds of the simplest atomic system—the hehum atom. It has been shown that collision may transfer helium atoms from singlet to triplet states but only by a very specific reaction path collisional relaxation within the singlet manifold populates high n F states—nearly degenerate and significantly mixed with the corresponding n F states the transitions are... 

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