  The monotonic increase of the radius of low mass stars during their ascent on
the red giant branch halts when they suffer a temporary contraction. This
occurs when the hydrogen burning shell reaches the discontinuity in hydrogen
content left from the maximum increase in the convective extension, at the time
of the first dredge up, and produces a well known "bump" in the luminosity
function of the red giants of globular clusters. If the giant is the mass
losing component in a binary in which mass transfer occurs on the nuclear
evolution time scale, this event produces a temporary stop in the mass
transfer, which we will name "bump related" detachment. If the accreting
companion is a neutron star, in which the previous mass transfer has spun up
the pulsar down to millisecond periods, the subsequent mass transfer phase may
be altered by the presence of the energetic pulsar. In fact, the onset of a
radio--ejection phase produces loss of mass and angular momentum from the
sytem. We show that this sequence of events may be at the basis of the shortage
of systems with periods between ~ 20 and 60 days in the distribution of
binaries containing millisecond pulsars. We predict that systems which can be
discovered at periods into the gap should have preferentially either magnetic
moments smaller than ~ 2 x10^{26}Gcm^3, or larger than ~ 4x10^{26}Gcm^3. We
further show that this period gap should not be present in population II.
