Note on the Theory of Nuclear Spin Relaxation Exact Formulae in the Weak Collision Limit

A general relation exists between the relative magnitude of the power spectra J ( m ) (ω) that appear in the expressions of nuclear spin relaxation times T 1 , T 2 and T 1ρ of powdered specimen, i.e. J (0) (ω): J (1) (ω): J (2) (ω)=6:1:4. the relation holds exactly in the weak collision case irrespective of the modes of motion responsible for the relaxation. The proof is based on the symmetry properties of the spherical harmonics of rank two and therefore applicable not only to dipole-dipole but also to quadrupole coupling interaction and other problems. The reduction factor of the second moment of the nuclear magnetic resonance that results from a type of molecular motion also bears a simple general relation to the minimum value of T 1 due to the motion.