Dipole-allowed transition, oscillator

The dipole oscillator strength is the dominant factor in dipole-allowed transitions, as in photoabsorption. Bethe (1930) showed that for charged-particle impact, the transition probability is proportional to the matrix elements of the operator exp(ik r), where ftk is the momentum transfer. Thus, in collision with fast charged particles where k r is small, the process is again controlled by dipole oscillator strength (see Sects. 2.3.4 and 4.5). 

The account of the dependence of the generalized oscillator strength on the wave vector q leads to a more complicated behavior of the cross section cr0n (see Refs. 113 and 135). For the dipole-allowed transitions the leading term in data processing, is traditionally presented in the form (taking into account relativity)... 

Figure 2.14. The coupling scheme by which the spin-forbidden a 3A2(rc,7t ) <— X Ai(n2) transition borrows oscillator strength from the B 1A1(jt,jt ) <— X iAi(n2) electric dipole allowed transition.

We have also measured the intensity of the optically allowed transition relative to the other valence excitations in the loss function. As q increases, the intensity decreases rapidly along [100], while the intensity along [110] changes little. This indicates that even the oscillator strength of the dipole-allowed transition is anisotropic. 

Table 6 Performance of Density Functional and Correlated Wave Function Methods for Oscillator Strengths of First Three Dipole-Allowed Transitions of Naphthalene...

Figure 3.3 displays the calculated HOMO HOMO-3 and Rydberg 3py of n-hexane. Among these MOs, HOMO-l(Tt) and HOMO-2(a) are relevant to the electronic dipole-allowed transitions. Transitions from these MOs to Rydberg 3py and 3px have large oscillator strength as noted above, while those from HOMO (ag) have small intensities and those from HOMO-3 (au) are dipole forbidden. 

The strength or intensity of absorption is related to the dipole strength of transition D or square of the transition moment integral M m , and is pressed in terms of oscillator strength / or integrated molar extinction jfe Jv. A transition with /= 1, is known as totally allowed transition. But the transitions between all the electronic, vibrational or rotational states are not equally permitted. Some are forbidden which can become allowed under certain conditions and then appear as weak absorption bands. The rules which govern such transitions are known as selection rules. For atomic energy levels, these selection rules have been empirically obtained from a comparison between the number of lines theoretically... 

---