Calculation of parity non-conserving optical rotation in iodine at 1315 nm

We examine the feasibility of a parity non-conserving (PNC) optical rotation experiment for the $^2$P$_{3/2}\rightarrow ^2$P$_{1/2}$ transition of atomic iodine at 1315 nm. The calculated $E1_{\rm PNC}$ to $M1$ amplitude ratio is $R=0.80(16)\times 10^{-8}$. We show that very large PNC rotations (greater than 10 $\mu$rad) are obtained for iodine-atom column densities of $\sim 10^{22}$ cm$^{-2}$, which can be produced by increasing the effective interaction pathlength by a factor of $\sim 10^4$ with a high-finesse optical cavity. The simulated signals indicate that measurement of the nuclear anapole moment is feasible, and that a 1% PNC precision measurement should resolve the inconsistency between previous measurements in Cs and Tl.