We present an evolutionary scenario for the spin-up and evolution of binary millisecond pulsars, according to which the companion of the pulsar PSR J 1740-5340, recently discovered as a binary with orbital period of 32.5 hr in the Globular Cluster NGC 6397, is presently in a phase of ``radio-ejection’’ mass loss from the system. At present, Roche lobe overflow due to the nuclear evolution of the pulsar companion and to systemic angular momentum losses by magnetic braking is still going on, but accretion is inhibited by the momentum exerted by the radiation of the pulsar on the matter at the inner Lagrangian point. The presence of this matter around the system is consistent with the long lasting irregular radio eclipses seen in the system. Roche lobe deformation of the mass losing component is also necessary to be compatible with the optical light curve. The “radio-ejection” phase had been recently postulated by us to deal with the problem of the lack of submillisecond pulsars (Burderi et al. 2001, ApJ, 560, L71).

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