In close binary systems composed of a normal, donor star and an accreting neutron star, the amount of material received by the accreting component is, so far, a real intrigue. In the literature there are available models that link the accretion disk surrounding the neutron star with the amount of material it receives, but there is no model linking the amount of matter lost by the donor star to that falling onto the neutron star. In this paper we explore the evolutionary response of these close binary systems when we vary the amount of material accreted by the neutron star. We consider a parameter beta, which represents the fraction of material lost by the normal star that can be accreted by the neutron star. beta is considered as constant throughout evolution. We have computed the evolution of a set of models considering initial donor star masses (in solar units) between 0.5 and 3.50, initial orbital periods (in days) between 0.175 and 12, initial masses of neutron stars (in solar units) of 0.80, 1.00, 1.20 and 1.40 and several values of beta. We assumed solar abundances. These systems evolve to ultracompact or to open binary systems, many of which form low mass helium white dwarfs. We present a grid of calculations and analyze how these results are affected upon changes in the value of beta. We find a weak dependence of the final donor star mass with respect to beta. In most cases this is also true for the final orbital period. The most sensitive quantity is the final mass of the accreting neutron star. As we do not know the initial mass and rotation rate of the neutron star of any system, we find that performing evolutionary studies is not helpful for determining beta.
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