Charge oscillator strength

Inelastic collisions of swift, charged particles with matter are completely described by the distribution of generalized oscillator strengths (GOS s) characterizing the collision. These quantities, characteristic of excitation in the N-electron target (or, in fact, of a dressed projectile as well [1]) from some initial state 0) to a final state n) and concomitant momentum transfer, can be written... 

Here Z is the charge of the projectile with velocity v. In order to calculate stopping powers for atomic and molecular targets with reliability, however, one must choose a one-electron basis set appropriate for calculation of the generalized oscillator strength distribution (GOSD). The development of reasonable criteria for the choice of a reliable basis for such calculations is the concern of this paper. 

Molecular structures for CNDO/S calculations were optimized using HP/3-21G shown in Fig, 1, Dominant charge transfers at some selected states and their oscillator strength " /l(E-30 esu). 

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). 

Therefore, fast-charged-particle impact resembles optical transition to some extent. The oscillator strength introduced in Chapter 2 corresponds to this kind of transition, whereas that for the entire operator exp(ik r) is called the generalized oscillator strength, which also has some interesting properties (Inokuti, 1971). 

The authors also calculated the band structure expected for the fully oxidised form, taken as 33% doping or 2 charges per 6 rings, and the result is depicted in Figure 3.72(c). Continued removal of the states from the valence and conduction bands widens the gap to 3,56eV, with the two intense absorptions in the gap observed in the optical spectra now accounted for by the presence of wide bipolaron bands. The authors stated that, on the basis of other workers calculations, the lowest energy absorption should have the most intense oscillator strength, as is indeed observed. 

When located at opposite ends (or at conjugated positions) in a molecular system, a donor and an acceptor do more than simply add up their separate effects. A cooperative phenomenon shows up, involving the entire disubstituted molecule, known as charge transfer (C.T.). Such compounds are colored (from pale yellow to red, absorption from 3,000 to 5,000 A) and show high U.V. absorption oscillator strength. "Figure 2 helps understand the enhancement of optical nonlinearity in such a system. 

Notes Oscillator strengths are given within parentheses. Q(Re) gives the Mulliken charge on one Re atom. 

A2g transitions, respectively. Besides being able to correlate jS with oscillator strength,/, of transitions the values may be employed 42) to evaluate the effective charges on the Cr(III) ions in various complexes. Fig. 4 provides plots of the effective metal charge vs. /3, the nephelauxetic parameter and B, the Racah interelectronic repulsion parameter for chromium(III). Jorgensen... 

The shorter wavelength bands (200-300 mp) could be similar (but less forbidden) charge-transfer transitions or homoannular ring-localized transitions. For instance, Nesmeyanov10 concludes, from an inspection of oscillator strengths, that the strong 200 mp band is a -n -s- tt transition in the ring. 

Figure 17. Oscillator-strength spectra for argon L-shell ionization, leading to charge states 1 to 4.149...

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