Abstract
We present a simple model for the evolutionary states of neutron stars in pre-low-mass X-ray binaries during the main sequence stage of donor stars. It is shown that for typical parameters some of the neutron stars in these systems cannot accrete matter from winds of their companions in a stable way. Accretors are found if neutron stars have magnetic fields about 1013 G and higher and/or in close systems with orbital periods of about a few days and shorter.
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