  Within the pure Coulomb breakup mechanism, we investigate the one-neutron
removal reaction of the type A(a,b$\gamma$)X with $^{11}$Be and $^{19}$C
projectiles on a heavy target nucleus $^{208}$Pb at the beam energy of 60
MeV/nucleon. Our intention is to examine the prospective of using these
reactions to study the structure of neutron rich nuclei. Integrated partial
cross sections and momentum distributions for the ground as well as excited
bound states of core nuclei are calculated within the finite range distorted
wave Born approximation as well as within the adiabatic model of the Coulomb
breakup. Our results are compared with those obtained in the studies of the
reactions on a light target where the breakup proceeds via the pure nuclear
mechanism. We find that the transitions to excited states of the core are quite
weak in the Coulomb dominated process as compared to the pure nuclear breakup.
