  The most frequently seen binary companions to millisecond pulsars (MSPs) are
helium white dwarfs (He WDs). The standard rejuvenation mechanism, in which a
low- to intermediate-mass companion to a neutron star fills its Roche lobe
between central hydrogen exhaustion and core helium ignition, is the most
plausible formation mechanism. We have investigated whether the observed
population can realistically be formed via this mechanism. We used the
Cambridge STARS code to make models of Case B RLOF with Reimers' mass loss from
the donor. We find that the range of initial orbital periods required to
produce the currently observed range of orbital periods of MSPs is extremely
narrow. To reduce this fine tuning, we introduce a companion enhanced wind
(CEW) that strips the donor of its envelope more quickly so that systems can
detach at shorter periods. Our models indicate that the fine tuning can be
significantly reduced if a CEW is active. Because significant mass is lost
owing to a CEW we expect some binary pulsars to accrete less than the 0.1Msun
needed to spin them up to millisecond periods. This can account for mildly
recycled pulsars present along the entire Mc-Porb relation. Systems with Pspin
> 30ms are consistent with this but too few of these mildly recycled pulsars
have yet been observed to make a significant comparison.
