  We present a simple 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 is shown 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. The effect of the
additional phase on the breakup spectra is clarified. As an example the
population of the low energy resonances of $^{11}$Be and of the unbound
$^{13}$Be is discussed. Finally, we suggest that the excitation energy spectra
of an unbound nucleus might reflect the structure of the parent nucleus from
whose fragmentation they are obtained.
