Neutron-star formation in a binary system must result in an eccentric orbit, whereas the orbits of the X-ray sources Her X-1 and Cen X-3 are circular. It is shown how initially eccentric orbits can be circularized by tidal dissipation in acceptably short times, no more than about 10 million years for Her X-1 and no more than 100,000 years for Cen X-3.
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Lecar et al. (1976) studied this question.