  We call "projectile fragmentation" of neutron halo nuclei the elastic breakup
(diffraction) reaction, when the observable studied is the neutron-core
relative energy spectrum. This observable has been measured in relation to the
Coulomb breakup on heavy target and recently also on light targets. Such data
enlighten the effect of the neutron final state interaction with the core of
origin. Projectile fragmentation is studied here by a time dependent model for
the excitation of a nucleon from a bound state to a continuum resonant state in
a neutron-core complex potential which acts as a final state interaction.
  The final state is described by an optical model S-matrix so that both
resonant and non resonant states of any continuum energy can be studied as well
as deeply bound initial states. It turns out that due to the coupling between
the initial and final states, the neutron-core free particle phase shifts are
modified, in the exit channel, by an additional phase.
  Some typical numerical calculations for the relevant observables are
presented and compared to experimental data. It is suggest that the excitation
energy spectra of an unbound nucleus might reflect the structure of the parent
nucleus from whose fragmentation they are obtained.
