  We study the problem of rationality of an infinite series of components, the
so-called Ein components, of the Gieseker-Maruyama moduli space $M(e,n)$ of
rank 2 stable vector bundles with the first Chern class $e=0$ or -1 and all
possible values of the second Chern class $n$ on the projective 3-space. The
generalized null correlation bundles constituting open dense subsets of these
components are defined as cohomology bundles of monads whose members are direct
sums of line bundles of degrees depending on nonnegative integers $a,b,c$,
where $b\ge a$ and $c>a+b$. We show that, in the wide range when $c>2a+b-e,\
b>a,\ (e,a)\ne(0,0)$, the Ein components are rational, and in the remaining
cases they are at least stably rational. As a consequence, the union of the
spaces $M(e,n)$ over all $n\ge1$ contains an infinite series of rational
components for both $e=0$ and $e=-1$. Explicit constructions of rationality of
Ein components under the above conditions on $e,a,b,c$ and, respectively, of
their stable rationality in the remaining cases, are given. In the case of
rationality, we construct universal families of generalized null correlation
bundles over certain open subsets of Ein components showing that these subsets
are fine moduli spaces. As a by-product of our construction, for $c_1=0$ and
$n$ even, they provide, perhaps the first known, examples of fine moduli spaces
not satisfying the condition "$n$ is odd", which is a usual sufficient
condition for fineness.
