Zur Theorie der Kernspinrelaxation bei einem Austausch zwischen zwei Bereichen

Using R EDFIELD 's theory of relaxation and S ILLESCU '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 H AMILTON ian 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 τ b in the region with the lower mobility is not comparable with the correlation time τ 1 in the other phase. Without any restriction, however, one time constant T ( c ) 2 m 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 H AMILTON ian does not vary under the exchange (e. g. dipolar interaction between the nuclei in both regions) the results of the wellknown statistical treatment of B ECKERT and P FEIFER 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 Z IMMERMAN and B RITTIN with the effective correlation times τ ca = τ a • τ 1 / τ a + τ 1 and τ cb = τ b • τ 1 / τ b + τ 1 .