  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.
