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The one-neutron nuclear breakup from the Carbon isotopes $^{19}$C and$^{17}$C, is calculated as an example of application of the theory of transferto the continuum reactions in the formulation which includes spin coupling.  The effect of the energy sharing between the parallel and transverse neutronmomentum distributions is taken into account thus resulting in a theory whichis more general than sudden eikonal approaches. Both effects are necessary tounderstand properly the breakup from not too weakly bound $l_i>1$ orbitals.Breakup which leaves the core into an excited state below particle threshold isalso considered. The core-target interaction is treated in the smooth cut-offapproximation. By comparing to presently available experimental data we showhow to make some hypothesis on the quantum numbers and occupancy of the neutroninitial state. Possible ambiguities in the interpretation of inclusive crosssections are discussed

Initial state dependence of the breakup of weakly bound carbon isotopes