The theory of spin–lattice relaxation of Van Kranendonk and Walker is adapted to the α phase of solid nitrogen. The quadrupolar relaxation of the 14N nucleus by the 'anharmonic Raman process' is calculated for the cubic anharmonic terms obtained from the theory presented in the first paper of this series. Different approximations to the Raich–Mills intermolecular potential are employed. When the expansion of the potential in spherical harmonics is truncated at l = 2, the calculated temperature dependence of T1 is in satisfactory agreement with the experimental measurements of DeReggi, Canepa, and Scott between 20 and 35 K. Below 15 K the calculated results for T1, are too long, probably due to the neglect of mixing between the librons and acoustic phonons. When the Raich–Mills potential includes the spherical harmonic terms with l = 4 and l = 6, the relaxation is found to increase by more than a factor of 40, resulting in T1, becoming much shorter than the experimental results over the high-temperature region. This arises mainly from single-molecule terms of three-fold symmetry in the potential, leading to the suspicion that these terms are unrealistically large.