Spin Relaxation Processes in a Two-Proton System

The general theory of nuclear spin relaxation, based on the Boltzmann transport equation for the density matrix, is applied to the very simple, nontrivial system of two identical spins $I=\frac{1}{2}$. A proton pair undergoing hindered rotation around one axis shows a resolvable doublet. The relaxation processes in this doublet are investigated. Explicit formulas for the longitudinal and transverse relaxation times are derived, which display a dependence on the angles of the axis of rotation with the external magnetic field and the radius vector. Experimental evidence for this dependence is discussed. General expressions for the Overhauser and saturation effects with two applied radio-frequency fields are given, which may also be applied to a magnetic ion or nucleus with $I=1\mathrm{}$ and crystalline field splitting.