Estimate of Contribution from P-D Mixing in Atomic PNC

We investigate possible contributions to future atomic parity nonconservation (PNC) experiments from parity admixtures between single-electron atomic states with total angular momentum $j = 3/2$. We develop new formalism for studying these admixtures between atomic $p$ and $d$ states, which enter only when finite nuclear size effects are considered and have been neglected in the literature to date. We use analytic approximations to provide an order-of-magnitude estimate of the contribution from these admixtures, and identify a dimensionless ratio which sets the scale of the correction. Using realistic numerical wavefunctions in \baplus we confirm the results of our analytic expressions, and conclude quantitatively that these novel admixtures are likely to be negligible in essentially all cases.