Anisotropy strength functions

Effective anisotropy strength functions for the H2 Ar potential surface of Table I, corresponding to different (fixed) values of the diatom stretching coordinate Reproduced with permission... 

Here the vlbratlonally averaged anisotropy strength functions Vi(v,j R) are defined by (X=0,2)... 

The vlbratlonally averaged anisotropy strength radial functions V,(v,j r) for the case of Interest here (v=l, j=2) are plotted In Figure 9. 

Figure 9. The diagonal vibrationally averaged anisotropy strength radial functions Vj (v,j r) for Ar-HD(v l, j=2). Reproduced with permission from Ref. 20. Copyright 1983, North-Holland Physics Publishing.

Figure 2. The nearest-neighbor concurrence C(l,2) for different values of the anisotropy parameter y = 1, 0.7, 0.3, 0 with an impurity located at = 3 as a function of the reduced coupling constant A = 7/2/i, where J is the exchange interaction constant and h is the strength of the external magnetic field. The curves correspond to different values of the impurity strength a = 0,0.5,1,1.5 with system size iV = 201.

Figures 2 and 3 contain plots of the two non-zero RFs for M = A and T2, respectively, as a function of the coupling strength KT. Also included in each figure are the original analytical calculations of Bates et al. [3] (who also included corrections due to anisotropy) and the numerical results of O Brien [9] (The key is shown as an insert in each figure.) It should be emphasized that, even though the results shown cover the range KT = 0-2.5, all but the numerical results of O Brien [9] are only strictly valid in the strong coupling limit (KT larger than unity).

FIGURE 26 Nomogram of the dimensionless alignment parameter A > as a function of laser intensity, field strength, and polarizability anisotropy. [Reproduced with permission from Freidrich, B., and Herschbach, D. R. (1995). J. Phys. Chem. 99,15686. Copyright American Chemical Society.]... 

The simplified schematic in Figure 2a shows the essential features of the effect. Optically anisotropic molecules in the solution are preferentially oriented by the applied field E(t), resulting in a difference of refractive indices for components of polarized light parallel and perpendicular to the bias field which is measured as a birefringence. The basic theoretical problem is to evaluate this effect in terms of anisotropies of polarizability Aa. referred to molecular axes which produce a time dependent effect when the molecules are preferentially oriented by the field. For no anisotropy in absence of the field, the effect must be an evgn function of field strength, and at low fields proportional to E. A remarkable feature of the effect is that for molecules with permanent dipole moments the response af-... 

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