Initial state population

The total absorption cross section represents essentially the probability of forming the product AB at all. It is obtained from state to state cross sections by summing over all initial states populated in the parent molecule - weighted with their corresponding probabilities - and by summing also over all final states in which the AB product is formed... 

The above picture was theoretically assumed by Fermi and Teller in 1947 and experimentally proven in the 1990s by a measurement of the initial state populations of antiprotonic helium (Yamazaki et al. 2002 Hayano et al. 2007). 

The initial state populates both types of resonance states of Interference between the vibrational discrete and the vibrational continuum autoionization resonances takes place although the resonance positions of the vibrationally-discrete autoionization-resonance (disc-res) states and the vibrationally-continuum autoionization-resonance states (cont-res) are very far from one another (as compared to their width). One may think that when E en(disc — res) there is only one dominant term in the series resonance expansion of tres(E) (see Eq. 33). This is however not the case. The numerators associated with the branch-cut resonances, an(cont — res), get complex values where both the real and the imaginary parts are larger than the corresponding ones of an(disc — res) by several orders of magnitude. In the numerical calculations the ampHtudes of the continuum t3q>e resonances... 

Fig. 11, Comparison of initial state population distributions for AJ = 2 transitions of a Raman rotational/vibrational band.

The number of molecules Ni in the initial state depends on the total number of molecules, the distribution of energy levels, the degeneracy of individual levels (number of levels of identical energy), and the temperature of the gas. In equilibrium the initial state population is... 

Therefore, by observing the rotational line structure an estimate of the temperature in the line forming region may be obtained. The temperature so derived is called the rotational temperature. The strengths of emission and absorption lines are obtained by substituting the initial state population [Eq. (3.5.11)], in Eqs. (3.5.1) and (3.5.2) ... 

It follows that there are two kinds of processes required for an arbitrary initial state to relax to an equilibrium state the diagonal elements must redistribute to a Boltzmaim distribution and the off-diagonal elements must decay to zero. The first of these processes is called population decay in two-level systems this time scale is called Ty The second of these processes is called dephasmg, or coherence decay in two-level systems there is a single time scale for this process called T. There is a well-known relationship in two level systems, valid for weak system-bath coupling, that... 

B. Averaging Over Equilibrium Boltzmann Population of Initial States... 

The intensity distribution among rotational transitions in a vibration-rotation band is governed principally by the Boltzmann distribution of population among the initial states, giving... 

Quite apart from the necessity for Franck-Condon intensities of vibronic transitions to be appreciable, it is essential for the initial state of a transition to be sufficiently highly populated for a transition to be observed. Under equilibrium conditions the population 1, of any v" level is related to that of the u" = 0 level by... 

Fig. 35). The potential energy curves and the transition dipole moment are taken from [117]. The time evolution of the populations on the ground and excited states is shown in Fig. 36 More than 86% of the initial state is excited to the B state within the period shorter than a few femtoseconds. The integrated total transition probability V given by Eq. (173) is P = 0.879, which is in good agreement with the value 0.864 obtained by numerical solution of the original coupled Schroedinger equations. This means that the population deviation from 100% is not due to the approximation, but comes from the intrinsic reason, that is, from the spread of the wavepacket. Note that the LiH molecule is one of the...

Fig. 8. Scattering the transition state from the surface. Measured vibrational distribution of NO resulting from scattering of laser-prepared NO(v = 15) from Au (111) at incidence = 5 kJ mol-1. Only a small fraction of the laser-prepared population of v = 15 remains in the initial vibrational state. The most probable scattered vibrational level is more than 150 kJ mol-1 lower in energy than the initial state. Vibrational states below v = 5 could not be detected due to background problems. These experiments provide direct evidence that the remarkable coupling of vibrational motion to metallic electrons postulated by Luntz et al. can in fact occur. (See Refs. 44 and 59.)...

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