Vibrational quantum number 590 INDEX

At any total scattering energy E, elements of the multichannel S matrix In the RLM are labelled by the total angular momentum Index I, and by the Initial and final vibrational quantum numbers v and v. Equations for physical observables in the BCRLM have been given previously (24-26), and we only summarize the final results here, In order to establish a common notation. The opacity function gives the Impact parameter dependence of the reaction probabilities. 

In (35) the first index (M + 2i — 1) gives the vibrational quantum number and the second index M > 0 the total angular momentum the aUowed values for the vibrational levels i = 0,1,2,... For t = 0 the perturbation disappears in first order. While the perturbation in first order leads to a splitting of the energy terms E and E, the perturbation through second order in e for both cases yields the same value as the same sign. In general... 

The excited-state wavepacket spontaneously emits photons while undergoing transitions to any of the electronically-ground vibrational wavefunctions t (where we have lumped the final state quantum numbers i>/, jf in a single index f). The rate of emission from a given 4% component of the excited wavepacket to a given ground state is given in terms of the Einstein A-coefficient [9],... 

A more compact notation [58] may be used to label vibronic (or vibrational) transitions in polyatomic molecules with many normal modes, in which each vibration index r is given a superscript v r and a subscript v, indicating the upper and lower state values of the quantum number. When v r = v, = 0 the corresponding index is suppressed. 

Let us denote the excited state after initial excitation by x,) with quantum numbers denoted by the composite index i, which is assumed to be in a particular vibrational state v,. The continuum eigenstate of the full Hamiltonian H is denoted as whose quantum numbers are given by the composite index /. The probability per unit energy that the system will end up in the continuous state / is given by... 

Cartesian coordinates and momenta, the kt are quantum numbers, and m( is an even integer known as the Maslov index, [51] 2, for vibrational motion. Most successful applications of Eq. (3.36) require quasi-periodic motion... 

CO2 Laser A section of the level diagram is illustrated in Fig. 5.31. The vibrational levels (i>i, I s) are characterized by the number of quanta in the three normal vibrational modes. The upper index of the degenerate vibration V2 gives the quantum number of the corresponding vibrational angular momentum / [5.45]. Laser oscillation is achieved on many rotational lines within two vibrational transitions (vi, =... 

The index n is used to specify a particular a, v, j, ( channel where v, j, and t are vibrational, rotational, and orbital quantum numbers the index m is used to specify a particular transitional basis function, and P denotes a particular pair of n and m. Note that sometimes for clarity we will label quantities by both a and n although the specification of a is redundant. In addition we use ajjn> to denote a... 

Here, we are using the summation index i as the index on the quantum number v. Although a real molecule will fall apart if v, gets too large, we can assume that the summation goes to infinity. We also know that the degeneracies of vibrational levels are 1 as long as they are counted individually—a circumstance we shall meet in polyatomic molecules. 

The index 3 has to summarise the quantum numbers of the nuclear vibrations. Pnai ) is undetermined function of the introduction of which is neces-... 

Here, Xni l) denotes the harmonic oscillator wave-functions, (pa(r) and (pb(r) correspond to the states of electrons localized on a and b ions, the index v numbers the hybrid cluster states in the molecular field. It should be noted that, within the scope of the adopted approach, the quantum properties of the vibronic states in a self-consistent field are taken into account. Therefore, it is reasonable to call the proposed approximation quasidynamical. The vibronic states obtained within the scope of the quasidynamical approach are hybrid, i.e. retaining the quantum properties of both electronic and vibrational states. In the case of strong vibronic coupling, i.e. in the case of adiabatic potentials possessing deep minima both the... 

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