  We study an interacting electron gas in a quantum wire within the
Hartree-Fock random phase approximation. Vertex corrections to the electron
spin polarizability due to the electronic exchange interaction are important
giving rise to spin-density excitations (SDE) with large oscillator strength
shifted to lower energies with respect to single-particle states. The energy of
intersubband SDE oscillates with the number of subbands occupied and has a
minimum when a subband energy is close to the chemical potential. Intrasubband
SDE have a linear dispersion at small wave-vectors. The corresponding sound
velocity is reduced with respect to the Fermi velocity due to exchange
interaction within the occupied subbands and exchange screening caused by
virtual transitions to upper subbands. For intersubband and intrasubband
charge-density excitations (CDE) vertex corrections are of less importance. For
only a single subband occupied the screening of CDE and SDE in the
Tomonaga-Luttinger model due to virtual transitions to upper subband is
studied, where the virtual transitions are treated within the Hartree-Fock
approximation. The calculations are in good qualitative agreement with
experiments.
