Multipole moments ground state

For a determination of the permanent multipole moments, Eq. 2.42 must be averaged over the ground state nuclear vibrational wavefunction transition elements are also often of interest which are matrix elements between initial and final rotovibrational states. For example, for a diatomic molecule with rotovibrational states vJM), the transition matrix elements (v J M Q(m vJM) will be of interest a prime designates final states. 

Table 3.3. Limiting values of the ratio aPo/aPo °f various rank ground state multipole moments aPo and the population aPo for an infinitely large parameter X — 00...

Thus, in this section we have described the manner in which absorption of light by a molecule leads to polarization of the angular momenta of the absorbing level. We have also shown how to calculate the multipole moments created on the lower level. It is important to stress that the adopted model of description enables us to obtain precise analytical expressions for the multipole moments, including both cases, namely those for arbitrary values of angular momenta and those for the classic limit J — oo. Our subsequent discussion will concern problems connected with the manifestation of ground state angular momenta anisotropy in experimentally observable quantities. 

In order to describe a signal by this method we will first use the classical approach. At the beginning we will ascertain how either probability density Pb(9, multipole moments ipq of the excited state 6, entering into the fluorescence intensity expressions (2.23) or (2.24), are connected to the corresponding magnitudes pa(9, ground state a. The respective kinetic balance equation for probability density and its stationary solution, assuming that the conditions supposed to hold in Eq. (3.4) are in force, is very simple indeed ... 

Let the cw exciting light be weak in the sense that one may neglect all the multipole moments in the ground state, except for the equilibrium... 

For a description of the ground state magnetic quantum beats one might conveniently use the solution of Eq. (4.10) for multipole moments aPq-Assuming that the excitation takes place by a 6-pulse at time t = 0, one may write its solution for t > 0 in the form ... 

If the two subsystems do not possess any permanent multipole moments neither the electrostatic nor the inductive interaction can exist. Nevertheless, there is always an attraction due to mutually induced multipole moments. This interaction is generally referred to as Van der Waals interaction or London-type dispersion or simply dispersion . The explanation of the origin of this interaction goes back to F. London [16,17]. In the very simplest case of the interaction between two closed shell atoms, e.g., two He atoms in their electronic S ground states, the leading terms of the van der Waals interaction are given by... 

The table here reports which multipole moments (in the center-of-mass coordinate system) are zero and which are nonzero for a few simple chemical systems. All of this follows from the symmetry of their nuclear framework in the electronic ground state. 

Higher-order multipole moments enhance the forces between particles at short distances and their neglect is extremely questionable, especially if fine effects are looked at, as for instance the ground-state properties of close-packed lattice structures [244,246-251] or the viscosity To go beyond the point dipole approximation Klingenberg and co-workers [ 173,252] developed an empirical force expression for the interaction between two dielectric spheres in a uniform external field from the munerical solution of Laplace s equation [253]. Recently, Yu and co-workers [254,255] proposed a computationally efficient (approximate) dipole-induced-dipole model based on a multiple image method which accounts partially for multipolar interactions. 

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