  There is growing observational evidence that gamma-ray bursts (GRBs) are
powered by black holes accreting rapidly through a disk. The supernova-like
outburst that accompanies some gamma-ray bursts suggest that some long-duration
GRBs may be driven by the accretion of a rotating stellar core onto a central
black hole. Such a system can be produced when a compact remnant spirals into
the helium core of its binary companion. During the inspiral, orbital angular
momentum is injected into the core. By the time the compact remnant reaches the
center of the helium core, it too has gained angular momentum as well as mass,
producing a rapidly accreting black hole (or neutron star) at the center of a
rotating stellar core. In this paper, we use a 3-dimensional smooth particle
hydrodynamics (SPH) code to follow such a merger process and make quantitative
estimates of the initial mass and spin of the central compact remnant, as well
as the angular momentum in the accreting helium core. From these results, we
estimate GRB explosion energies. In all mergers, magnetically driven jets are
expected to produce GRB explosions with energies above 10^{51} ergs. For
neutrino-annihilation-driven explosions, the GRB energy increases dramatically
with helium star mass: the merger of a 2 M_sun compact remnant with a 4 M_sun
helium star only produces a 10^{47} ergs explosion in \sim 500 s whereas the
merger of a 2 M_sun compact remnant with a 16 M_sun helium star produces a
>10^{52} ergs explosion in \sim 65 s. (Abridged)
