We investigate the nuclear collective excitations of Wigner-Seitz cells containing nuclear clusters immersed in a gas of neutrons .
This baryonic non-uniform system is specific to the structure of inner crust matter of neutron stars .
The collective excitations are studied in the framework of a spherical Hartree-Fock-Bogoliubov + Quasiparticle Random Phase Approximation , formulated in coordinate representation .
The calculations are done for two representative Wigner-Seitz cells with baryonic density equal to 0.02 fm ^ { -3 } and 0.08 fm ^ { -3 } .
It is shown that the excitations with low multipolarities are concentrated almost entirely in one strongly collective mode which exhausts a very large fraction of the energy-weighted sum rule .
Since these collective modes are located at very low energies compared to the giant resonances in standard nuclei , they may affect significantly the specific heat of baryonic inner crust matter of neutron stars .