Dipole length

The oscillator strength of the transition in eh, obtained by the dipole length formulation, is 1.1 the experimental value is >0.7. This overestimation seems to be common among all continuum models. No information on line shape is obtained in this simple model. 

He cites work including Paul Langevin s on the theory of the Kerr Phenomenon. He also calculates that the average calculated dipole length is on the order of tenths of an angstrom, compatible with the estimated distance of an angstrom between atoms, e g., in hydrogen chloride (602). 

In Tables -A, we report oscillator strengths for some fine structure transitions in neutral fluorine, chlorine, bromine and iodine, respectively. Two sets of RQDO/-values are shown, those computed with the standard dipole length operator g(r) = r, and those where core-valence correlation has been explicitly introduced, Eq. (10). As comparative data, we have included in the tables /-values taken from critical compilations [15,18], results of length and velocity /-values by Ojha and Hibbert [17], who used large configuration expansions in the atomic structure code CIVS, and absolute transition probabilities measured through a gas-driven shock tube by Bengtson et al. converted... 

In Eq. (14), /max is the maximum of the orbital angular momentum quantum numbers of the active electron in either the initial or final states, I nl, n l ) is the radial transition integral, that contains only the radial part of both initial and final wavefunctions of the jumping electron and a transition operator. Two different forms for this have been employed, the standard dipole-length operator, P(r) = r, and another derived from the former in such a way that it accounts explicitly for the polarization induced in the atomic core by the active electron [9],... 

As in the case of LS coupling, when there are N equivalent electrons in the outer shell, both the line strength and the oscillator strength should be multiplied by N as well as by the corresponding CFP [ 10,12]. As in the LS scheme the two forms of the electric dipole length transition operator have been employed here in the calculation of the radial transition integral, I nl, n l ). 

Closely related to ferroelectricity is piezoelectricity in which polarization is induced and an electric field is established across a specimen by the application of external force (see Figure 6.28a,b). Reversing the direction of the external force, as from tension to compression, reverses the direction of the field. Alternatively, the application of an external electric field alters the net dipole length and causes a dimensional change, as in Figure 6.28c. Piezoelectric materials can be used as transducers—devices that... 

Covalent Adsorption with Ionic Character). If it is assumed that metallic conduction starts at the metal surface, the effective dipole length is diiJkl I , where duA is equal to the distance between the adsorbate and metal atoms as shown in Fig. 9c. Thus, for a dipole moment M = eduA, ... 

Dipole moment lf(D) Dipole Length 0 A. Bond energy Bond energy B A ) Ionisation potential ely kcal./ mole Electron affinity ea, kcal./ mole Bond energy E M- A) E Initial heats ... 

Unfortunately, the work function is a rather complicated (and not fully understood) function of the surface composition and geometry. The work function change is usually attributed to the formation of a dipole layer on the surface, such as occurs when charge flows from a substrate to an adsorbate, or vice versa. If a is the dipolar charge density, d the dipole length (perpendicular to the surface) and e the electronic charge, then one can write... 

COS 0 47re0x2 ix = dipole moment, d = angle between line of centers and axis of dipole length of dipole small compared to x (sign depends on z and orientation) Coulomb 2... 

In eq. (13-1) the first equality gives the definition of the oscillator strength in the dipole-length representation, while the second equality gives the definition in the momentum (or velocity) representation. As usual, and T, are the total molecular wavefunctions for the final and initial states, and Ef and Et are the energies of the final and initial states, respectively. 

Dipole length, 65 Dipole moments, excited states, 103 operator, 131 oscillating, 49... 

Oscillator strengths can be defined either as dipole velocity quantities or dipole lengths,... 

Molecular dipole moments are often expressed in the non-SI unit debye, where D 3.335 64 x 10"30 C m. The SI unit C m is inconvenient for expressing molecular dipole moments, which results in the continued use of the deprecated debye (D). A convenient alternative is to use the atomic unit, ea0. Another way of expressing dipole moments is to quote the electric dipole lengths, lp = p/e, analogous to the way the nuclear quadrupole areas are quoted (see pp.21 and 98). This gives the distance between two elementary charges of the equivalent dipole and conveys a clear picture in relation to molecular dimensions. 

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