  The general end-point of the rp process in rapidly accreting neutron stars is
believed to be a surface distribution of matter whose nuclear composition may
depend on position. Its evolution during compression beyond the neutron-drip
threshold density is determined by the presence of nuclear formation enthalpy
minima at the proton closed shells. At threshold, a sequence of weak
interactions with capture or emission of neutron pairs rapidly transform nuclei
to the most accessible proton closed shell. Therefore, angular asymmetries in
nuclear composition present in accreted matter at neutron drip are preserved
during further compression to higher densities provided transition rates
between closed shells are negligible. Although it has been confirmed that this
condition is satisfied for predicted internal temperatures and for the
formation enthalpy distribution used in this work, it would not be so if the
true enthalpy differences between maxima and minima in the distribution were a
factor of two smaller. For this reason, it does not appear possible to assert
with any confidence that position-dependent surface composition can lead to
significant angle-dependence of the equation of state and to potentially
observable gravitational radiation. The effect of non-radial internal
temperature gradients on angle-dependency of the equation of state is also not
quantifiable.
