General restrictions for the relaxation rates of polarization moments

8 General restrictions for the relaxation rates of polarization moments 

As can be seen, for any isotropic relaxation process different rank polarization moments change independently. The question arises can the relaxation constants 7 and Tk be arbitrary The following simple example [135] shows that this is not the case. Let us assume that the angular momentum J = 1 and the initial state are such that only level M = 1 

In the general case of arbitrary J values it is not easy to present, in (2 J — l)-dimensional space, the area of allowed Tk/T values. In order to characterize this area, it is possible to propose the following approach. Of all permitted Tk/T values it is necessary to determine the minimal and the maximal value for each rank K. Here it is necessary to take into consideration the fact that all maximum or all minimum values of Tk/T cannot always be reached simultaneously. This assertion may be illustrated by Fig. 5.14 in the case of the system of inequalities (5.98). The minimum value f /fi = 0 is attained when Ts/Fi = 1, but the minimum value rs/fi = 1/6 is attained when f /Ti = 1/2. 

An analysis of (5.98), in the case where the number of inequalities considerably exceeds the number of constants Tk/T, shows [42] that it is possible to make use of the Monte-Carlo method, i.e. one must generate by 

In the analysis of (5.99), when the number of inequalities is equal to 2 J it is possible to use another method of examination of the permitted region for Tk/Ti. One can turn from the system of inequalities to a system of equalities and solve it by alternately switching off one equality. In this way we will find in the (2J — l)-space corner point coordinates (see Fig. 5.14 in the case of inequalities (5.99)), it means the coordinates for the region of allowed values of Tk/T. From all coordinates of these corner points we must select those which correspond to the minimal and the maximal values of Tk/T for each rank K. 

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