Field strength parameter

By treating H as of zeroth order (in the field strength Ao ), expanding P order-byorder in the field-strength parameter ... 

Fe(II) salts cannot readily be explained probably spin-forbidden transitions at = 730 nm are also responsible in this case. The field strength parameters can be calculated using the ligand field model if the influence of the sulfate ions on the ligand field is neglected these are a measure of the stability of the aqua complexes in this series. The values of A = 10 Dq are as follows (in the sequence of the test tubes 1-7) 12,350 cm", 13,900 cm, 7,800 cm , 10,400 cm , 9,300 cm and 12,600 cm . ... 

The ground state density will depend on the field strength parameter x, which is denoted by a subscript. The functional has both an explicit and an implicit dependence on x and the first-order energy correction, the total derivative is formed by a partial derivative and a functional derivative... 

Figure 3. The parallel relaxation time T /t as a function of the field strength parameter, = vHMs/kT. The dotted line is the result obtained from the iteration of the continued fraction, Eq. (3.26). The solid line is the closed form expression of Eq. (4.46).

Figure 29. Same as Fig. 28 but for a different combination of field strength parameters. In this way, the branching ratio between the two exit channels can be varied. 

In Fig. 47, we show the expectation values of the ion (upper panel) and the electron (lower panel) for two values of the field strength parameter where in... 

From the above formulae it is evident that the splitting of an atomic term is a linear function of the crystal field strength parameter A. For larger values of A, however, the energies of certain states originating in different atomic terms tend to cross over. For example, the states T g(3F) and Tig(3P) of the electron configuration d2 approach each other at the higher A. In such a case the approximation of the weak crystal field loses its battle and the correct treatment is represented by the intermediate crystal field. 

Table 8. Effect of pressure on the crystal field parameters B q (cm ) for Eu + in several lanthanide oxyhalide systems. S (cm ) is an average crystal field strength parameter (see text). P denotes pressure in kbar and represents the maximum pressure achieved in each study. The linear shifts given in the table are good approximations of data given in graphical or tabular...

Figure 5-13. Evolution of the crystal field strength parameter Ny in the RE203 Em series. (Reproduced with permission from ref. 35. Copyright 2002 Elsevier Science B.V.)...

For a given central ion the field strength parameter Dq depends on the central ion-ligand distance R) and on the charge distribution within the ligands q, fi). The value of Dq is determined from experimental data. 

Figure 2. The evolution of the total energy as a function of within the uniform approximation for three different field strengths. Parameters x = l-6> o = 0.0049 Nm , L = 1 mm, (f> = 0.5.

In the diagram of energy levels versus crystalline field strength parameter A, whereas the curves corresponding to the states having the same configuration are parallel to each other,... 

The parameter X has been introduced so that an expansion can be made, but it can also be considered as a field strength parameter. 

Formally, we have made an expansion in X. To arrive at the properties, both first- and second-order, we differentiated with respect to the field strength. We can consider X as a field strength parameter, taking the scale factor out of A. However, the transformation is also an expansion in powers of 1/c, which appears in the perturbation operator. 

The vector of electric field strength parameters and the geometric... 

In these equations, m (Eq. 2.1) and mj (Eq. 2.2) indicate the circular frequencies associated with the perturbing field, is a small positive number that ensures that the perturbation vanishes for t —> —oo, e icoj) is the field strength parameter and B the associated perturbation operator. The expectation value of the time-independent operator A is written as [1]... 

Several authors have tried to simplify the description of the crystal field by reducing the number of parameters. Auzel (Auzel 1979, Auzel and Malta 1983) has defined a scalar crystal-field strength parameter... 

The relation betw een the maximum crystal-field splitting AE of a multiplet and the scalar crystal-field strength parameter is ... 

Kibler (1983) has proposed another crystal-field strength parameter ... 

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