Irreversibility in Paramagnetic Spins Systems. II. Non-Markovian Processes and Spin-Spin Relaxation

The kinetic equations which were derived recently by the authors for the spin density matrix of a weakly ordered paramagnetic system are solved for short and long times. During the non-Markovian period, the evolution of the thermodynamical observables (the magnetization and the secular and nonsecular energies) shows strong oscillations, as expected. The time-dependent magnetization is compared with the experimental data of Strombotne on Ca${\mathrm{F}}_2$, the agreement is good over the whole time scale. In the long time limit, Hartmann and Anderson's coupled equations describing the Zeeman-to-dipole cross-relaxation are recovered in the lowest-order approximation. The dependence of the relaxation time upon the field is similar to that which has already been obtained by other authors. However, neither in the computation of the time evolution of observables nor in the calculation of relaxation times is it necessary to introduce hypotheses about the line shapes, as these may be calculated consistently within the theory.