Five-level system

It was shown above that the normal two-level system (ground to excited state) will not produce lasing but that a three-level system (ground to excited state to second excited state) can enable lasing. Some laser systems utilize four- or even five-level systems, but all need at least one of the excited-state energy levels to have a relatively long lifetime to build up an inverted population. 

Shown in Fig. 10 are examples of fitting Z-scan results for a squaraine molecule where triplet states are significantly populated during picosecond excitation. In this case, femtosecond excitation was needed to determine the singlet parameters, shown in Fig. 10a. Picosecond excitation was required to model the full five-level system, shown in Fig. 10b [73], to determine the triplet parameters. To account for the triplet states, it is necessary to consider at a minimum the 5-level system shown Fig. 2 (three singlet and two triplet states). Typically, PDs do not populate triplet states during picosecond excitation [74, 75],... 

Resonant Multiphoton Excitation in a Model Five-Level System... 

Figure 3.3 The model five-level system studied by Etinski, Uiberacker, and Jakubetz. The dipole matrix elements coupling neighboring levels are displayed in the boxes (in a.u.). (From Ref. 51).

Figure 3.5 Total control fields avoided crossing related correction fields and associated population dynamics in the model five-level system, (a) Two Lorentzian pulses centered at r j and (see Figure 3.4). (b) Four Lorentzian pulses centered at (see Figure 3.4). The total...

In their model, Clyne and McDermid [37] assumed a five level system the initially excited state J, a higher energy state J 4- K, and three lower energy states J — K, J — 2K, J — 3K. R—T transitions could occur between consecutive levels with AJ = K, whilst upward transfer from J + K gave a completely unstable (non-fluorescing) state. Rate coefficients for upward and downward R—T transfer (kR) were assumed to be the same and not to vary with J over the range modelled. On the basis of this simple model, the fluorescence intensity, I, is given by... 

For chemical process design the part-whole dimension contains the following five levels system (e.g., process), subsystem (e.g., separation process), functional unit (e.g., distillation column), subassembly (e.g., valve tray), and component (e.g., float valve). 

As an additional example, for nuclei of spin I = 7/2, such as uranium-235, the solution of the Schroedinger equation can be shown to lead to a five-level system of energies given by solutions of the secular equation ... 

We have so far emphasized the nature of the wave function. We now examine the energies of some different arrangements ofthe bases. In Table 15.2 we show energies for five levels of calculation, Kekule-only, Kekule plus Dewar, SCF, SCVB, and full TV structures, where energies are given as the excess energy due to the tv system over that from the core. Cooper eta/. [61] gave the SCVB treatment of benzene. 

The theoretical energy levels of the ground state 4Ig/2 are shown in table 13 together with the results of CF calculations and the experimental values. Among the irreducible representations of S4 symmetry, only I 5. Te, T7, Fg are possible for a three-electron system, where I 5 and 17, or F7 and Tg are degenerate. Comparing with the experimental values, the Stark splittings are somewhat overestimated. However, the order of irreducible representations of these five levels is consistent with both the experimental values and those obtained by CFT. 

The state-symmetry correlation also indicates that electrocyclic radical interconversion favors a conrotatory path from the first excited state and a disrotatory path from the second excited state. Because of the proximity of the energy levels and the violations of the noncrossing rule, it is probable that the excited state process will not be highly stereoselective. The same detailed considerations must be applied to the five-atom five-electron system and yield the results given in Table 1. Differences between the stereochemical predictions of Table 1 and those of others (Woodward and Hoffmann, 1965a Fukui and Fujimoto, 1966b Zimmerman, 1966) tend to be limited to the excited-state reactions of odd-atom radicals. 

An experiment design for one-variable-at-a-time optimization is shown in Table 9.3. The experiment involves five levels for each factor, expressed in coded form which can be linearly transformed back to corresponding true values, so that the arrangement could be applied to other systems. In the coded form, one unit could represent 10 °C difference in reaction temperature,... 

The first level LI corresponds to the electronically excited Cr(CO)6 (fl Tlu) and L5 is the ground state (S0) of Cr(CO)5. Each of these levels produces a different range of ionized fragments following application of the probe pulse. The time-of-flight detector can select ions of a particular mass, and the time-dependent behavior of each fragment ion provides information on the length of time taken for the system to traverse each of the five levels. 

Several excellent works on collaboration have been published (Blount, 1998 Doherty 8c Baird, 1983 Seaburn, Lorenz, Gunn, Ga-winski, 8c Mauksch, 1996). Doherty (1995) developed a model that defines five levels of collaboration. The levels range from minimal collaboration, in which professionals work in different sites and rarely communicate about a case, to close collaboration in a fully integrated system, in which professionals from different disciplines practice in the same site and hold team meetings regularly to discuss collaboration issues. For most physicians and therapists, level 5 is more of a dream than a reality. Because of the structure of health care today, most professionals probably practice at levels 1 or 2. 

Three levels of risk are suggested here (low, medium, and high) although some pharmaceutical and healthcare companies may like to consider five levels of risk to match the system integrity levels defined by lEC/ISO 61508 for safety critical systems. Each system should be rated against a number of weighted risk factors to determine an overall level of risk. Seven example risk factors are considered in Table 14.4 ... 

The ATC Classification System developed by the Nordic coimtries and widely used in Europe meets most classification requirements. Drugs are classified according to their Anatomical, Therapeutic and Chemical characteristics into five levels of specificity, the fifth being that for the single chemical substance. 

The energy-level scheme of the molecular system considered in the experiment is shown in Fig. 20. The five-level molecule consists of two upper levels <7j) and a2), two intermediate levels b) and d), and a single ground level c). The upper levels are separated by the frequency 0012, which is much smaller than the frequencies a>u, and 002b of the a ) —> b) and 2) —> b) transitions and the frequencies o>id and (d2d of the a ) —> d) and ci2) —> d) transitions. As in the sodium dimers used in the experiment, we assume that the frequencies Oj and 0)26 correspond to the visible region, while the frequencies ou and 0)2d... 

Selectivity decreases when the chain length of dinitriles increases from six to ten carbon atoms per molecule, but this relationship levels off at each extreme of the range. We propose to explain this observation by invoking an intramolecular interaction leading to a heterocyclic (n+1) conformation, containing imino- form of the CN, in equilibrium with the linear form. Hence, for example, for the five carbon system ... 

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