Correlation function dipole auto

Simultaneous Rotation and Fluctuation. The scalar product p(0)-(r(t) has the value /n(0) /x(/) cos 6(0 so the dipole auto-correlation function is (fdP) MO cos 6(/)>, where 6(t) is the angular displacement of the dipole axis and MO), MO the relevant magnitudes. The correlation function will separate into free rotation. If the variation of dipole moment and molecular size is relatively small, the correlation between that and the rotation may be negligible. In that case, if is independently known, may be obtained from an experimentally determined -... 

Furthermore, the lack of correlation of the different spins results in a decoupling of the different spin dipole-dipole interactions experience by the nuclear spin, Thus, even though there in general exists a correlation of the different dipole-dipole interaction tensors, the final expression for intermolecular relaxation time only consists of a sum of auto correlation functions of the individual interactions. 

As a result of the intermolecular origin of the field gradients it is much more difficult to calculate the spectral densities for ions than for the cases considered in Chapter 2. Let us first consider the situation which appears to best rationalize the experimental results, i,e, we assume that there is a random orientation of the water molecules around the relaxing ion. This corresponds to a weakly hydrated ion and would be approximately valid for chloride, bromide and iodide ions. The total auto-correlation function is for the case of random orientational dipole distribution around the relaxing ion obtained by integration to be... 

The spectral density is related to the time Fourier transform of the sample total dipole moment auto-correlation function (a.c.f.)... 

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