Spectral densities of spherical harmonics for rotational Brownian motion

Spectral densities of spherical harmonics arising from the rotational Brownian motion of molecules are calculated. The molecules are supposed to be spherical or linear, and account is taken of the influence of their inertia. When the results for a spherical molecule are applied to nuclear magnetic resonance, an expression for spin-lattice relaxation time is deduced and this is shown to provide a small correction to one calculated by Bloembergen, Purcell and Pound8). It is pointed out that the theory may be extended to nuclear magnetic processes when the thermal molecular motion is anisotropic.