  The angular momentum transfer associated to Vela-like glitches has never been
calculated {\em directly} within a realistic scenario for the storage and
release of superfluid vorticity; therefore, the explanation of giant glitches
in terms of vortices has not yet been tested against observations. We present
the first physically reasonable model, both at the microscopic and macroscopic
level (spherical geometry, n=1 polytropic density profile, density-dependent
pinning forces compatible with vortex rigidity), to determine where in the star
the vorticity is pinned, how much of it, and for how long. For standard neutron
star parameters ($M=1.4 M_{\odot}, R_s=10$ km, $\dot{\Omega}=\dot{\Omega}_{\rm
Vela}=-10^{-10}$ Hz s$^{-1}$), we find that maximum pinning forces of order
$f_m\approx10^{15}$ dyn cm$^{-1}$ can accumulate $\Delta L_{\rm
gl}\approx10^{40}$ erg s of superfluid angular momentum, and release it to the
crust at intervals $\Delta t_{\rm gl}\approx3$ years. This estimate of $\Delta
L_{\rm gl}$ is one order of magnitude smaller than what implied indirectly by
current models for post-glitch recovery, where the core and inner-crust
vortices are taken as physically disconnected; yet, it successfully yields the
magnitudes observed in recent Vela glitches for {\em both} jump parameters,
$\Delta\Omega_{\rm gl}$ and $\Delta\dot{\Omega}_{\rm gl}$, provided one assumes
that only a small fraction ($<10%$) of the total star vorticity is coupled to
the crust on the short timescale of a glitch. This is reasonable in our
approach, where no layer of normal matter exists between the core and the
inner-crust, as indicated by existing microscopic calculation. The new scenario
presented here is nonetheless compatible with current post-glitch models.
