Ground-state population

When estimating absorption from the ground state, we totally ignore the depletion of ground state population at finite temperatures, when the system spends some time in an excited state. This is fine because by the relevant temperatures, the excited state absorption dominates anyway (see Fig. 14 and note that an — e < co + e ). This case (i.e., e < 0) is somewhat less straightforward. Let us calculate... 

The experimental results on He2 ICl and He2 Br2 demonstrate that by varying the expansion conditions it is possible to manipulate the relative abundances of the higher order complexes and drive the ground-state population to the more energetically stable configuration. The stabilization of multiple Rg XY conformers suggests that the influence of the multibody interactions... 

In addition to the fourth-order response field Tfourth, the probe light generates two SH fields of the same frequency 211, the pump-free SH field Eq(2 Q), and the pump-induced non-modulated SH field non(td> 211). The ground-state population is reduced by the pump irradiation and the SH field is thereby weakened. The latter term non(td, 211) is a virtual electric field to represent the weakened SH field. Time-resolved second harmonic generation (TRSHG) has been applied to observe E on (td, 211) with a picosecond time resolution [20-25]. The fourth-order field interferes with the two SH fields to be detected in a heterodyned form. 

With the resonance to the electronic transition, the ground-state population is partially depleted by the pump irradiation and restored with the time delay. The raw intensity of SH light was accordingly damped at fa = 0 and recovered in picoseconds, as seen in Figure 6.3a. Intensity modulation due to the vibrational coherence was superimposed on the non-modulated evolution as expected from Eq. (6.3). The coherence continued for picoseconds on this solution surface. The non-modulated component Isecond(fd> 2 ii) was fitted with a multiexponential... 

As the triplet energy of the sensitizer becomes less than that necessary to excite either form of the butadiene (Et < 50 kcal/mole), it is proposed that energy is transferred via nonvertical excitation to lower energy twist forms of the diene triplets.(11> The product distribution again reflects the ground state population of s-cis and s-trans forms ... 

Accelerations (or decelerations) imposed by the cycloamyloses on the rate of an intramolecular reaction may be derived from a conformational effect. The rate of an intramolecular reaction depends not only on the proximity of the reactive groups but also on their relative orientation. For example, Bruice and Bradbury (1965) have shown that the rates of formation of cyclic anhydrides from mono esters of 3-substituted glutaric acids depend on the size of the substituent at the 3-position. This observation was interpreted as a change in the ground state population of reactive and non-reactive conformers as the 3-substituents are varied (Scheme IX). Reason-... 

Figure 8. Li + H2 Ground-state population as a function of time for a representative initial basis function (solid line) and the average over 25 (different) initial basis functions sampled (using a quasi-classical Monte Carlo procedure) from the Lit2/j) + H2(v — 0, j — 0) initial state at an impact parameter of 2 bohr. Individual nonadiabatic events for each basis function are completed in less than a femtosecond (solid line) and due to the sloped nature of the conical intersection (see Fig. 7), there is considerable up-funneling (i.e., back-transfer) of population from the ground to the excited electronic state. (Figure adapted from Ref. 140.)...

One expects the timescale of the nonadiabatic transition to broaden for a stationary initial state, where the nuclear wavepacket will be less localized. To mimic the case of a stationary initial state, we have averaged the results of 25 nonstationary initial conditions and the resulting ground-state population is shown as the dashed line in Fig. 8. The expected broadening is seen, but the nonadiabatic events are still close to the impulsive limit. Additional averaging of the results would further smooth the dashed line. 

It is interesting to note that the latter criterion imphes that the ground-state level density completely dominates the total level density— that is, that No E) N E). Hence the assumption (98) of complete decay into the adiabatic ground state is equivalent to the criterion that the classical and quantum total level densities should be equivalent. Furthermore, it is clear that this criterion determines an upper limit of 7. This is because larger values of the quantum correction would result in ground-state population larger than one (or negative excited-state populations). 

Having determined the appropriate value of the quantum correction from the comparison of classical and quantum level densities, it is interesting to study the accuracy of the simple approximation (99). Extracting from Fig. 19 the longtime limits of the adiabatic ground-state populations as Pq j = 0, oo) = 0.75 and Pq j = 1, oo) = 1.25, the difference of the two populations yields Ky2 Ti) = 0.5, just as predicted by Eq. (99). Furthermore, we may employ the approximation to estimate the optimal quantum correction. Assuming that Pq oo) = 1, we obtain y = 0.5, which is in qualitative agreement with the results obtained above. ... 

Depending on molecular resonances, VOCs with an optical (electronic) absorption at 266 nm absorb a laser photon, while those transparent at 266 nm remain in the ground state. The width of optical absorptions is given by the ground-state population, and broadens with the molecules temperature, which itself depends on the expansion conditions at the inlet system. 

For the purpose of numerical computation, we consider a lattice with M = 10 sites. Our goal is to generate the ground-state population of the harmonic potential for R = M - I, represented by the dashed curve in Figure 3.36, from the ground state for R = 0, represented by the solid curve in Figure 3.36. The ground-state wave function satisfies... 

From Eq. (5) the transition dipoles, the band-shape function, and the population of the ground state components can depend on the applied magnetic field. MCD is caused by the influence of the magnetic field on these three quantities. The three perturbations each correspond to one of the terms in Eq. (1). The perturbation of the transition dipole creates a term, the perturbation of the band-shape function leads to an A term, and the perturbation of the ground state populations provides a C term. 

We see that more than 99.98% of the sodium atoms are in their ground state at 2 600 K. Varying the temperature by 10 K hardly affects the ground-state population and would not noticeably affect the signal in atomic absorption. 

Lifetimes and quenching cross sections of rotational levels in the B3fl (Ou+) state have been measured by Broyer et al. (153) and by Ornstein and Derr (781). The production of iodine atoms 2P1/2, 2P3/2 was observed by absorption in the vacuum ultraviolet following the flash photolysis of l2 above 2000 A (296). While 2P1/21 atoms are produced it is not certain whether the ratio of the metastable to the ground state population is 1 1. 

Dornhofer, Hack, and Langel (180), in a detailed study of the fluorescence that is induced by an ArF laser, have been able to show that an intense ArF laser can distort the observed vibrational distribution by photodissociating CS radicals with v" > 5. The ArF laser absorption by CS will also produce electronically excited CS which, when it emits, will redistribute the vibrational populations. Probing the CS quantum state population under these conditions could distort the CS ground state populations. The LIF measurements will underestimate the amount of CS radicals that are produced, while the direct detection methods will overestimate the amount of S(3p) atoms because of the secondary photolysis of CS. The vibrational distribution of Lu et al. (178) will be less prone to this secondary photolysis because very low laser powers (< 1 mj) were used. Dornhofer, et al. concluded from their results that the S(3p)/S(J-D) ratio was 3, which is in reasonable agreement with the LIF measurements of Lu et al. 

Hydrogen and other one-electron atoms can be made into lasers because the state lifetimes vary so greatly. For example, an X-ray laser can be built by blasting carbon rods with an intense field, stripping off all the electrons. When the first electrons recombine with the nuclei, one-electron C5+ atoms are created in a wide variety of stationary states. Any population in the 2p states rapidly decays to the ground state population in 3s or 3 d decays more slowly. Thus the 3s —> 2p and 3d —> 2p transitions develop an inverted population distribution, and lase at the energy difference between the two states (A, = 13.6 nm). 

In strong light there is an exhaustion of the ground-state population that we ignored in Eq. (3.5) and later on assuming that N Jf = const. Now is the time to admit that the stationary population of the ground state is in fact Ns (c) in the presence of quenchers and Ns (0) in their absence, but at strong illumination either of these quantities is not equal to the total number of donors. 

Figure 3.65. Depletion of the ground-state population of energy acceptor Bs with an increase in the dimensionless light intensity IojVxb/c at different zB equal to 1 ns(A),10ns(B), 100ns(C). jc = 0.1,c = 10 2M,Td = 10ns,ko = 105A3/ns,iD = 6 x 103A3/ns,T(i = 0.25ns. (From Ref. 125.)...

Another most interesting phenomenon has been observed by Mikami et al.31> The ethanol molecules exhibit orientational disorder over three different sites in the high-spin phase, but orient themselves more and more in one of the three sites with decreasing temperature. The variation with temperature of the orientational ground state population seems to be strongly correlated with the temperature dependent spin transition. The authors therefore suggest that the disorder-order transition of the ethanol molecule triggers the spin state transition. 

There is another approach which can be used in suitable circumstances. Developed by Kowalik and Kruger (31), it involves measuring the population of an excited atomic state by LIFS. If the ground state population is known to be uniform in the flow field, then information about temperature can be inferred. They have used the method to measure electron number density in MHD plasma flows. 

Earlier experiments showed a vibrational overpopulation of the first excited vibrational state in desorption that was higher than the vibrational ground-state population by a factor of nine [55]. This result was later questioned on the basis of the quantum calculations which only found an overpopulation by a factor of 2.5 [54]. When the experiments were repeated, the theoretical predictions were confirmed [50], as Fig. 5 demonstrates. This indicates that in the field of surface science theory has reached a level of reliability that makes predictions possible and allows a fruitful and close collaboration with experiment. 

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