Dipole interaction matrix

Where a is the unit vector defined by the local frame defining the axial quadupole, r is the vector oriented towards r from the monopole to the axial quadupole. Qa is the corresponding matrix element. Following the modification of the charge-dipole interaction, we introduced a modified mono-quad interaction, namely I -mono-quad1 ... 

Remembering that each of these is further split by the hyperfine interaction, there are obviously several possible transitions among these four energy levels. To find out which are important, we must evaluate the transition dipole moment matrix elements, (i Sx j), since the absorption intensity is proportional to the square of these matrix elements. The operator Sx can be written ... 

Values of the force matrix components On and 0)2 are specified by the corresponding Fourier components of the dipole-dipole interaction tensors F P(k)... 

The cfata presented in Table I show that the kinetic features of the bulk polymerization of acrylonitrile are very similar to those observed with acrylic acid. It therefore seems pertinent to query whether atrix effect could not arise in the polymerization of acrylonitrile through a regular orientation of monomer molecules along the polymeric matrix involving dipole interaction of the -CsN groups (structure IV). 

Figure 15 Calculated total and state-to-state excitation transfer cross sections in the de-excitation of He(2 P)-Ne. (From Ref. 151.) Both electron exchange and dipole-dipole interactions are included in the coupling matrix elements. The threshold energy into each exit channel is shown on the upper axis.

This result is an exact expression for the transition matrix element. Physically we have a dipole interaction with the vector potential and a dipole interaction with the magnetic field modulated by a phase factor. The problem is that this integral is difficult to compute. An approximation can be invoked. The wavevector has a magnitude equal to 1 /X. The position r is set to the position of an atom and is on the order of the radius of that atom. Thus K r a/X. So if the wavelength of the radiation is much larger than the radius of the atom, which is the case with optical radiation, we may then invoke the approximation e k r 1 + ik r. This is commonly known as the Bom approximation. This first-order term under this approximation is also seen to vanish in the first two terms as it multiplies the term p e. A further simplification occurs, since the term a (k x e) has only diagonal entries, and our transition matrix evaluates these over orthogonal states. Hence, the last term vanishes. We are then left with the simplified variant of the transition matrix ... 

The dipole interaction couples higher sublevel channels too, for which the order of the coefficient matrix on R 2 is larger than for the 2s 2p channel coupling. Numerical values of a and/or (or e () for the decoupled higher sublevel channels are tabulated for some three-body systems [44,53, 66,77-79],... 

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