Nuclear Spin Relaxation and Nuclear Electric Dipole Moments

Proposals that nuclear spin relaxation in an appropriate system could serve as a test for the existence of a nuclear electric dipole moment are examined with attention to the consequences of the fact that the electric field at the nucleus is proportional to the nuclear acceleration. It is found that low-frequency fluctuations of the local electric field are suppressed. In particular, the necessarily negative correlation of the momentum transferred in consecutive collisions of an atom in a gas alters the spectral density of the perturbation, from that of uncorrelated pulses, by the factor $\frac{{\omega }^2{{\tau }_c}^2}{(1+{\omega }^2{{\tau }_c}^2)}$, where ${\tau }_c$ is the mean time between collisions. It follows that fairly low gas density is preferable to high. At optimum density a light gas at room temperature carrying electric dipole moments of magnitude $e\times {10}^{-14\mathrm{}}$ cm should have a spin relaxation time, in the absence of competing processes, of around 10 minutes. A formula is given for the electrically induced spin relaxation rate in a crystal. The process is hopelessly slow. In the electric coupling of the lattice vibrations to the spin the ordinarily dominant "two-phonon" or "Raman" process is absent, because of the linearity of the connection between local electric field and nuclear motion.