Measuring the depolarization rate of a $^3$He hyperpolarized gas is a sensitive method to probe hypothetical short-range spin-dependent forces. A dedicated experiment is being set up at the Institute Laue Langevin in Grenoble to improve the sensitivi
ty. We presented the status of the experiment at the 10th PATRAS Workshop on Axions, WIMPs and WISPs.
A bounded random walk exhibits strong correlations between collisions with a boundary. For an one-dimensional walk, we obtain the full statistical distribution of the number of such collisions in a time t. In the large t limit, the fluctuations in th
e number of collisions are found to be size-independent (independent of the distance between boundaries). This occurs for any inter-boundary distance, including less and greater than the mean-free-path, and means that this boundary effect does not decay with increasing system-size. As an application, we consider spin-polarized gases, such as 3-Helium, in the three-dimensional diffusive regime. The above results mean that the depolarizing effect of rare magnetic-impurities in the container walls is orders of magnitude larger than a Smoluchowski assumption (to neglect correlations) would imply. This could explain why depolarization is so sensitive to the containers treatment with magnetic fields prior to its use.
