  We study the accretion efficiency of neutron stars in long-period binaries,
i.e. with periods longer than about 200d, which accrete from a giant companion.
Using alpha-disc models and taking into account the effect of irradiation of
the accretion disc by the central accretion light source we derive explicit
expressions for the duty cycle and the accretion efficiency in terms of the
parameters of the binary system and the disc instability limit cycle. We show
that the absence of millisecond pulsars in wide binaries with circular orbits
and periods longer than about 200d can be understood as a consequence of the
disc instability if the duration of the quiescent phase between two subsequent
outbursts is at least a few decades.
