  We derive simple analytic expressions for the (coherent and semi-coherent)
phase metrics of continuous-wave sources in low-eccentricity binary systems,
both for the long-segment and short- segment regimes (compared to the orbital
period). The resulting expressions correct and extend previous results found in
the literature. We present results of extensive Monte-Carlo studies comparing
metric mismatch predictions against the measured loss of detection statistic
for binary parameter offsets. The agreement is generally found to be within ~
10%-30%. As an application of the metric template expressions, we estimate the
optimal achievable sensitivity of an Einstein@Home directed search for Scorpius
X-1, under the assumption of sufficiently small spin wandering. We find that
such a search, using data from the upcoming advanced detectors, would be able
to beat the torque- balance level [1,2] up to a frequency of ~ 500 - 600 Hz, if
orbital eccentricity is well-constrained, and up to a frequency of ~ 160 - 200
Hz for more conservative assumptions about the uncertainty on orbital
eccentricity.
