Relaxation of Electron Velocity in a Rotating Neutron Superfluid: Application to the Relaxation of a Pulsar's Slowdown Rate

We estimate the relaxation time $\tau$ of an average electron velocity relative to a dilute array of vortex cores in a rotating, $s$-wave-paired neutron superfluid. At low temperatures, $\tau$ is found to vary exponentially with $\frac{{\Delta }^2}{{\epsilon }_F}$, the energy scale of vortex core excitations, where $\Delta$ is the gap parameter and ${\epsilon }_F$ is the neutron Fermi energy. For reasonable choices of $\Delta$ and ${\epsilon }_F$, we find values of $\tau$ which include the values of a year and of several days observed, respectively, in the post-speedup relaxation of the Vela and Crab pulsars' slowdown rates.