Radio-ejection and bump-related orbital period gap of millisecond binary pulsars

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.