  We propose to investigate the in-medium properties of vector $\omega$ mesons
at the normal nuclear density in Ap(pA) collisions and at higher density in AA
collisions at the ITEP accelerator facility TWAC. Using of the inverse Ap
kinematics will permit us to study the $\omega$ meson production in a wide
momentum interval included the not yet explored range of small meson momenta
relative to the projectile nuclei where the mass modification effect in nuclear
matter is expected to be the strongest. Momentum dependence of the in-medium
$\omega$ meson width will be studied in the traditional pA kinematics. We
intend to use the electromagnetic calorimeter for reconstruction of the
$\omega$ meson invariant mass by detecting photons from the $\omega \to
\pi^{0}\gamma \to 3\gamma$ decay. The model calculations and simulations with
RQMD generator show feasibility of the proposed experiment. Available now
intensity of the ion beams provides a possibility to collect large statistics
and make decisive conclusion about the $\omega$ meson properties at density of
normal nuclei. At the second stage of the investigation the $\omega$ meson
properties will be studied in AA collisions at higher density. Interpretation
of these measurements will be based on the results obtained in Ap(pA)
interactions. Further investigation of the in-medium properties of light
unflavored and charmed mesons can be performed at ITEP and at GSI(FAIR) where
higher ion energies will be accessible in near future.
