  With this paper we introduce the concept of apparent structure of a GRB jet,
as opposed to its intrinsic structure. The latter is customarily defined
specifying the functions epsilon(theta) (the energy emitted per jet unit solid
angle) and Gamma(theta) (the Lorentz factor of the emitting material); the
apparent structure is instead defined by us as the isotropic equivalent energy
E_iso(theta_v) as a function of the viewing angle theta_v. We show how to
predict the apparent structure of a jet given its intrinsic structure. We find
that a Gaussian intrinsic structure yields a power law apparent structure: this
opens a new viewpoint on the Gaussian (which can be understood as a proxy for a
realistic narrow, well collimated jet structure) as a possible candidate for a
quasi-universal GRB jet structure. We show that such a model (a) is consistent
with recent constraints on the observed luminosity function of GRBs; (b)
implies fewer orphan afterglows with respect to the standard uniform model; (c)
can break out the progenitor star (in the collapsar scenario) without wasting
an unreasonable amount of energy; (d) is compatible with the explanation of the
Amati correlation as a viewing angle effect; (e) can be very standard in energy
content, and still yield a very wide range of observed isotropic equivalent
energies.
