Vibrational population transitions

It has been found that the short-range interaction model can be applied to study the vibrational relaxation of molecules in condensed phases. This model is applied to treat vibrational relaxation and pure dephasing in condensed phases. For this purpose, the secular approximation is employed to Eq. (129). This assumption allows one to focus on several important system-heat bath induced processes such as the vibrational population transition processes, the vibrational coherence transfer processes, and the vibronic processes. 

With the same interaction model used in Eq. (130), the vibrational relaxation rate constants associated with the vibrational population transitions bv + 1 -+bv and bv bv— 1 are given by... 

Unless the cavity is tuned to a particular wavelength the vibration-rotation transition with the highest gain is the P-branch transition involving the rotational level which has the highest population in the 3 state. This is P(22), with J" = 22 and J = 21, at normal laser temperatures. The reason why this P-branch line is so dominant is that thermal redistribution of rotational level populations is faster than the population depletion due to emission. 

In the secular approximation [89], we can eliminate the coherence terms [e.g., pr, (x)(u / u")] in Eq. (III.9) such that the only diagonal terms contribute to the vibrational transitions through which the vibrational populations in various states are coupled. By applying the ladder model [89] to the interaction between the vibrational and heat-bath modes, the vibrational population decay constant is expressed as... 

The first term in Eq. (III. 10) is originated from the decay from v to v 1, while the second one, with the Boltzmann factor, is due to the thermally activated transition from v to v + 1. The vibrational population transfer, on the other hand, is only allowed to undergo the v —> v 1 transitions in the ladder model. Thus, the rate constant of the transfer is given by... 

The pattern of intensities in Fig. 4.9 deserves mention. The intensities of absorption lines are proportional to the population of the lower level, and to the square of the dipole-moment matrix element (4.97). It turns out that for vibration-rotation transitions in the same band, the integral (4.97)... 

Pgl and the 584-A/N2 photoionization electron spectra.81 For the three different electronic final states, energetically accessible in the Pgl transition from the single entry channel potential curve, rather narrow unshifted individual distributions and vibrational populations very similar to those for 584-A photoionization are observed. In Fig. 31 the population factors —differently normalized bt v)—for Pgl and photoionization are compared for some systems with well-resolved vibrational lines.48,74... 

Population inversions have been observed in a number of chemical and photochemical reactions. In a few of these cases, laser action has been produced in a suitable cavity. In most cases of molecular laser emission, there is only partial inversion282 in which several vibration-rotation transitions are inverted even though the total population in the upper vibrational state does not exceed that in the lower. In this case there is laser action in P branch transitions only. 

Most known chemical lasers oscillate on vibration-rotation transitions of a hydrogen halide. The first such laser was driven by the flash initiated explosion of H2 + C12 mixtures287. Here the flash dissociates the Cl2 to start the chain decomposition, and the population inversion is due to the subsequent reactions... 

Vibrational Population in Diatomic Molecules. 18 I 4.2 Rotational Population in Diatomic Molecules, 19 I 4.3 Thermal Contribution to Photolysis and Fluorescence. 20 1-5 Electronic Transition in Atoms, 22... 

In eq. (5-2), vt, refers to the frequency of the ith chromophore vibration (populated by the IVR transition), and the proportionality to l/v( is purely phenomenological. This proportionality reflects the expectation that low frequency chromophore modes will couple most efficiently to the (low frequency) vdW modes. Fermi s Golden Rule expression has two important consequences. First, it predicts that... 

The radiation of a vibrational band is directly correlated to the vibrational population in the excited state I(v — v") = n(v ) x Av>v . Av>v is the transition probability. Thus, several vibrational bands which originate from different vibrational levels yield the corresponding vibrational population. In case of hydrogen or deuterium molecules the population of the first four or five vibrational levels, respectively, is accessible. Higher vibrational levels are disturbed by pre-dissociation processes. For further analysis, it is very convenient to use the relative vibrational population n(v )/n(v = 0). 

The vibrational population in the excited state n(v ) is determined by the vibrational population in the ground state n(v), if the electron impact excitation from the ground state is the most dominant excitation mechanism. The application of the Franck-Condon principle for electron impact excitation allows a calculation of n(v ) from n(v) based on the Franck-Condon factors between ground and excited state. Figure 4.2 illustrates this scheme for the three states involved in the Fulcher transition upper and lower state, d3nu and a3A)] respectively, in the triplet system and the ground state... 

In a first step, the vibrational population in the ground state is characterized by a Boltzmann distribution, i.e., n v )/ n v = 0) depends on TVib X). The left column of Fig. 4.3 shows relative vibrational populations in the ground state (X1 ) and in the upper state of the Fulcher transition (d377u) with Tvib(X) as parameter, assigned to the 15 vibrational levels of H2, i.e., v = 0-14. The right column shows the relative vibrational population in the excited state as a function of 7 vib(X) for H2 and D2. Due to the usage of vibrationally resolved excitation rate coefficients a dependence on electron temperature is obtained. Te = 4eV is chosen in Fig. 4.3. 

Intensities and Statistical Weights. The absolute absorption intensity of a vibrational-rotational transition is proportional to the square of the transition moment Py times the population in the lower state. Py varies only slightly for different rotational levels, so the principal factors determining the relative intensity are the degeneracy and the Boltzmann weight for the lower level,... 

Within the Mtuliiov approximation, the intermolecular dephasing constant associated with the coherence decay between i<->j and i ->j vibrational Raman transitions is expressed in terms of the population decay constant from each state and intermolecular pure dephasing constant as ... 

To determine the nascent distribution, we examined 4 produced by reaction (10) under low pressure conditions. Pulsed photolysis of I2 at 496 nm was used to generate I. As only a fraction of the I2 was dissociated, 4 then appeared due to I + I2 collisions. The excited vibrational levels were probed using LIF of the D X transition with full rotational resolution. The nascent vibrational population distribution extracted from this spectrum is shown in Fig. 6, which reveals a strong preference for near resonant E-V transfer. 

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