Globular clusters (GCs) containing bright X-ray sources (L(x) > 10(36)
ergs s(-1)), commonly associated with low-mass X-ray binaries (LMXBs)
, are found to be significantly denser and more metal-rich than normal
nonX-ray clusters both in the Galaxy and in M31. Within a framework w
here LMXBs in GCs are generated via tidal captures in high-density clu
sters and (2 + 1) encounters in low-density globulars, the higher inci
dence of LMXBs with increasing metallicity is shown to be intrinsic an
d not just a by-product of other effects. Two possible mechanisms are
examined: the first one assumes a dependence of the cluster IMF on met
allicity as recently published in the literature. The number of observ
ed LMXBs, more frequently occurring in metal-rich clusters, agrees wit
h the predicted number of NS only if metallicity accounts for a minor
contribution to the observed variation of the IMF slope. Other alterna
tives explored, such as the total variation of the observed IMF slopes
is due to (1) just metallicity and (2) the combination of metallicity
and position in the Galaxy lead to a clear-cut disagreement with the
data. In turn, this result may indicate a flatter dependence of the cl
uster's IMF on metallicity than that deduced from observed cluster lum
inosity functions. The second mechanism assumes that, at fixed cluster
density, the rate of tidar captures depends on radius and mass of the
capturing star. Based on standard stellar models, stars with higher m
etal content have wider radii and higher masses, hence the rate of tid
al captures increases with increasing metallicity. Moreover, since the
fixed binary separation and masses of the two components, metal-rich
stars fill more easily the Roche lobe, as their radii are larger, ther
e is an additional ''evolutionary'' reason to favor a higher incidence
of LMXBs in metal-rich clusters. From the order of magnitude computat
ions made, the new effect by itself could explain the observed ratio o
f 4 between the frequencies of X-ray clusters in the metal-rich and me
tal-poor groups we observationally determined. However, there is no re
ason to exclude that both mechanisms can be at work.