  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.
