Strength function symmetrical

The first term in (53) is contribution of the residual two-body interaction while the second term is the unperturbed (purely Iph) strength function. Further, F z) is determinant of the RPA symmetric matrix (35) of the rank 2K, where K is the number of the initial operators Qk- The symmetric matrix B of the rank 2K + 1) is defined as... 

For the purpose of taking the classical limit we consider a more symmetric strength function Y(E,E ), where the initial states at energy E and the final states at the energy E are treated on equal footing ... 

In this paper we amplify Powell s discussion, which is in some respects misleading. For example, Powell made the following statement Unlike the familiar four-lobed cubic d orbital, the pyramidal d orbital has only rather inconspicuous lobes of opposite sign. Each orbital is not quite cylindrically symmetrical about its own axis of maximum probability. In fact, the pyramidal d orbital that he discusses in detail is far from cylindrically symmetrical about its own axis of maximum probability, and the other pyramidal d orbital is also far from cylindrically symmetrical. In the equatorial plane about the axis of maximum probability the functions of Powell s first set (which we shall call II) vary from —0.3706 in two opposite directions to —1.7247 in the orthogonal directions. Each of these functions has almost the same value (strength) in the latter directions as in the principal directions, for which its value is 2.0950. The functions of the other set (which we call I) vary in this plane from —0.7247 to —1.4696, their value in the principal direction being 2.1943. 

Without the external field, the Stockmayer fluid near the wall exhibits symmetric density oscillations that die out as they reach the middle of the film. Near the surface, the fluid dipoles are oriented parallel to the walls. Upon turning on the electric field, the density profile of the Stockmayer fluid exhibits pronounced oscillations throughout the film. The amplitude of these oscillations increases with increasing field strength until a saturation point is reached at which all the fluid dipoles are oriented parallel to the field (perpendicular to the walls). The density profile remains symmetric. The dipole-dipole correlation function and its transverse [] and longitudinal [] com-... 

The complete diagram is often called a correlation diagram. It shows how the energy levels of the ion behave as a function of the strength of the chemical interaction with an octahedrally symmetric environment. 

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