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 M _ { i } / { M } _ { \odot } between 0.5 and 3.50 , initial orbital periods P _ { i } /days between 0.175 and 12 , initial masses of neutron stars ( M _ { NS } ) _ { i } / { M } _ { \odot } 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 .