Transition intensity

A related measure of the intensity often used for electronic spectroscopy is the oscillator strengdi,/ This is a dimensionless ratio of the transition intensity to tliat expected for an electron bound by Hooke s law forces so as to be an isotropic hanuonic oscillator. It can be related either to the experimental integrated intensity or to the theoretical transition moment integral ... 

Transition intensities are detennined by the wavefiinctions of the initial and final states as described in the last sections. In many systems there are some pairs of states for which tire transition moment integral vanishes while for other pairs it does not vanish. The temi selection rule refers to a simnnary of the conditions for non-vanishing transition moment integrals—hence observable transitions—or vanishing integrals so no observable transitions. We discuss some of these rules briefly in this section. Again, we concentrate on electric dipole transitions. 

The transition intensity is proportional to the square of the transition moment, which is given by... 

From Figure 5.3 it is apparent that transition intensities are not equal and, from Table 5.1, that the transition spacings show a slight decrease as J" increases. We will now consider the reasons for these observations. 

All bands with v" 0 are referred to as hot bands because, as indicated by Equation (6.10), the populations of the lower levels of such transitions, and therefore the transition intensities, increase with temperature. 

The transition intensities are proportional also to and therefore, according to... 

The vibrational transition intensity is proportional to R, the square of the vibrational transition moment R where... 

It is important to remember that selection mles, in general, tell us nothing about transition intensities other than their being zero or non-zero. It is possible that, even though it is nonzero, it may be so small that the transition escapes observation. 

Cohen et al. [49] obtained the following relations for the transition intensities... 

From Figure 6.1 it is easy to see that microwave saturation of the t -tz transition of pyrazine should decrease the v = i transition intensity and increase the v = j + k transition intensity. Microwave saturation of the rx—Ty transition should have no effect on v = i, but decrease the intensity of v =j + k. 

When the field is along the z-axis, transition intensities are proportional to the square of the Sz2 matrix element. The. S -2 matrix for B = 1000 G is ... 

For many synthetic copolymers, it becomes possible to calculate all desired statistical characteristics of their primary structure, provided the sequence is described by a Markov chain. Although stochastic process 31 in the case of proteinlike copolymers is not a Markov chain, an exhaustive statistic description of their chemical structure can be performed by means of an auxiliary stochastic process 3iib whose states correspond to labeled monomeric units. As a label for unit M , it was suggested [23] to use its distance r from the center of the globule. The state of this stationary stochastic process 31 is a pair of numbers, (a, r), the first of which belongs to a discrete set while the second one corresponds to a continuous set. Stochastic process ib is remarkable for being stationary and Markovian. The probability of the transition from state a, r ) to state (/i, r") for the process of conventional movement along a heteropolymer macromolecule is described by the matrix-function of transition intensities... 

The relative transition intensities of the spectrum are a good measure of the local temperature of the molecule. This raises the interesting question of whether the relative intensities of R- and P-branch transitions have the same rotational temperature and whether molecules in the same parts of space tell the same temperature. 

The observed transition intensity ratio for R(1)/R(0) of CO in a molecular cloud is 1.10. Calculate the temperature of the molecular cloud. 

Maser The microwave equivalent of a laser that represents some of the strongest transition intensities in the radio region of the electromagnetic spectrum, e.g. the water maser at 22.235 GHz. 

In the Hartree-Fock, frozen-orbital case, Pp acquires its maximum value, unity. Final states with large correlation effects are characterized by low pole strengths. Transition intensities, such as those in Eq. (2.7), are proportional to Pp. 

Complexes containing the 3,5-dinitrosalicylate ion, e.g. [Ln2(C2H202N2)3],- H20 (u = 7 -> 15), and methylsalicylate (MesaP ), e.g. [Ln(Mesal)2(OH)-(H2O)] (Ln = La, Pr, Nd, Sm, Gd, Dy, Er, Yb and have been reported. Tris-salicylaldehydato (said ) complexes, Ln(sald)3 (La, Pr, Nd, Sm, Eu, or Tb) form 1 1 adducts with o-phenanthroline (o-phen), aa -bipyridyl, quinoline, and pyridine. The luminescence spectrum of the Eu " complexes showed that, in the solid state, the symmetrically forbidden electric dipole transition intensity was much enhanced for the o-phen adduct when compared to its salicylate analogue. The simple said" complexes were very poor emitters. 

In order to consider the inversion of Qx(0,0) and Qy(0,0) electronic transition intensities in NH-tautomers of non-symmetrical free-base porphyrins we calculated the ground-state orbital energies of the investigated molecules by a CNDO/2 method using the symmetrized crystal geometry of porphyrin molecule (37,38). On the basis of the above experimental results we must introduce a motionless system of molecular X and Y axes, identically fixed in both tautomers. Then using theoretical MO calculations and the analysis... 

The a-transition intensity increases with dose (tan =0.40 for the control tan S=0.54 at 10,000 Mrads). This increase indicates a "loosening" of the network structure. 

Plasticizers, ie. degradation products, are known to "freeze out" the molecular motions which constitute this transition. The discrepancy between further cure due to ionizing radiation and a lower transition intensity may be due to degradation products interfering with the molecular motions of the transition. 

For the singlet ground state, the first term is zero but the second term contributes. The transition intensity is proportional to A. From expression (3.82) and (3.84)... 

Torque constant, 245 Totally symmetric representation, 402 Totally symmetric symmetry species, 60-61 Totally symmetric vibrations, 247 Townes, C., 137 Trace, 82-83 Transition, 114 Transition intensity, 122 Transition moment, 120, 297-298, 299-301... 

K f. U, + Ix2 tj) 2. (It might be thought necessary to consider also the effect of the relative populations of the levels on the transition intensities, but the separation between nuclear-spin energy levels is much less than kT, so that the very slight differences in population can be ignored here.)... 

From the point of view of optimizing selectivity, this transition, which shows well-resolved P, R, and S branches, is most likely to be a preferable starting point compared to the B-X or C-X bands of this molecule the two-photon transition intensity for the latter bands would be completely concentrated in the O -branch lines, which would not be well resolved. 

---