Using REDFIELD'S theory of relaxation and SILLESCU'S master equation treatment of molecular reorientation, the longitudinal and transverse nuclear spin relaxation functions have been calculated in a two phase system with different magnetic interaction energies. The interaction HAMILTONian represents the dipolar coupling amongst the nuclei in region (a, 1) and between a nucleus and a paramagnetic ion in region (b, 2). Assuming a strong electron spin relaxation which is statistically independent from the nuclear relaxation, a situation realized in paramagnetic solutions and adsorbate systems, the problem simplifies considerably.
If some correlation, expressed by a correlation coefficient c, is lost in each transfer between the regions, a longitudinal relaxation time T(c)1m can be defined, as long as the life time Tb in the region with the lower mobility is not comparable with the correlation time T1 in the other phase. Without any restriction, however, one time constant T(c)2m should characterize the decay of transverse magnetization as a good approximation. The apparent correlation times, determined from experimental data without any knowledge of the coefficient c, differ only slightly from the effective correlation times (in general less than 10%), in contrast to the case of equal interaction energies in both regions. If the interaction HAMILTONian does not vary under the exchange (e. g. dipolar interaction between the nuclei in both regions) the results of the wellknown statistical treatment of BECKERT and PFEIFER are obtained.
Neglecting any correlation at each transfer (i.e. c = 0) the relaxation rates are weighted averages, which correspond to the fast exchange case in the theory of ZIMMERMAN and BRITTIN with the effective correlation times