On the quantum statistical theory of relaxation in isolated spin systems II

Abstract

The investigation of the irreversible behaviour of an isolated spin system, under taken in a previous paper, is continued. The question is studied in how far and in which way the transverse magnetic moments have to be taken into account for a correct description of the long time behaviour of the spin system. All the results obtained previously for the longitudinal magnetic moment are reproduced under the condition that the perturbation is spherically symmetrical in space.

In order to determine the time corrections on the long time behaviour a formal solution is derived for the correlation tensor, valid for all times. It is shown that in the limit t → ∞ this expression yields a value, which is well in accordance with the predictions of microcanonical theory. In this connection the problem of the equivalence of the isolated and adiabatic susceptibilities is discussed. Furthermore, with the help of the formal solution for the correlation tensor, the line spectrum and line shapes are determined in parallel and perpendicular fields for several special cases.