Dipole oscillator strengths

Many methods for the evaluation of from equation ( Al.5.20) use moments of the dipole oscillator strength distribution (DOSD) defined, for molecule A, by... 

Kumar A and Meath W J 1992 Dipole oscillator strength properties and dispersion energies for acetylene and benzene Mol. Phys. 75 311... 

Meath W J and Kumar A 1990 Reliable isotropic and anisotropic dipole dispersion energies, evaluated using constrained dipole oscillator strength techniques, with application to interactions involving H2, N2 and the rare gases Int. J. Quantum Chem. Symp. 24 501... 

The BEB model was developed to overcome this problem. The dipole oscillator strength is assumed to have a simple form based on the approximate shape of the function for ionization of ground-state hydrogen ... 

Here/(q) is the dipole oscillator strength distribution at q and e is the base of natural logarithm. The lowest excitation potential may be taken for qmin, whereas qmax = (E + EB)/2 with EB a defined mean electron binding energy (Mozumder and La Verne, 1984). 

To further reduce of the cross section formula (4.11), we note that it is proportional to the area of the curve of Fn(K)/en plotted against In (Kag)2 between the maximum and minimum momentum transfers. Since T is large and the generalized oscillator strength falls rapidly with the momentum transfer, the upper limit may be extended to infinity. In addition, the minimum momentum transfer decreases with T in such a manner that the limit Fn(K) may be replaced by /, the dipole oscillator strength for the same energy loss. This implies that a mean momentum transfer can be defined independently of T such that the relevant area of the curve of Fn(K)/ n is equal to (// ) [ (In Kag)2 - (In Ka0)2]. Thus, by definition (Bethe, 1930 Inokuti, 1971),... 

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). 

It is not easy to calculate oscillator strengths from first principles except in some very simple cases. On the other hand, the oscillator strength distribution must fulfill certain sum rules, which in some cases help to unravel their character. Referring the (dipole) oscillator strength for the transition from the ground state with excitation energy n to state n as fn, a sum may be defined by... 

Oddershede s earlier results [3-5] calculate the directional values of the dipole oscillator strength distribution for use in the Bethe theory [9], which is valid for high-energy projectiles. Our approach, since we have not implemented the possibility of treating unbound electrons, is restricted to calculating stopping cross... 

Instead of one resonance frequency per individual electron, Bethe recovered the spectrum of resonance frequencies for the atom, weighted by dipole oscillator strengths satisfying the sum rule... 

Dipole oscillator strengths form important input into all stopping models based on Bethe or Bohr theory. Emphasis has frequently been on total /-values which show only little sensitivity to the specific input. More important are differential oscillator-strength spectra, in particular at projectile speeds where inner-shell excitation channels are closed. Spectra bundled into principal or subshells [60] are sufficient for many purposes, but the best available tabulations are based on analysis of optical data rather than on theory, and such data are unavailable for numerous elements and compounds [61]. 

Figure 2 Dipole oscillator strength distribution in gaseous water [29, curve. A], in liquid water [31, curve, B] and in gaseous cyclohexane [32, curve, C]. Data in liquid water are obtained from an analysis of UV-reflectance and that in cyclohexane, from synchrotron-UV absorption. The Thomas-Kuhn sum rule is satisfied approximately in each case.

This relationship becomes very useful because dipole oscillator strengths are available for a wide selection of atoms and molecules. The authors also provide a means of modifying this equation for use when oscillator strengths are not available the interested reader is directed to their work [39] for additional details. The strength of their work is also evident in that it provides a functional relationship for the determination of total cross section as well. By integration of the single dilferential cross sections, one obtains... 

Figure 4 Relative dipole oscillator strength distribution,/( ), for liquid water [63] and frequency of a given energy loss by 1-MeV electrons in liquid water [64].

The pioneering studies of electron-ion coincidence at small momentum transfer by Van der Wiel and his co-workers provided the first approximate data for dipole oscillator strengths for the multiple ionization of helium and neon,8-11 argon,149 and krypton and xenon141 in both valence... 

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