  Within the Energy Density Functional (EDF) approach, the use of mean-field
wave-functions deliberately breaking (some) symmetries of the underlying
Hamiltonian is an efficient and largely utilized way to incorporate static
correlations. However, the restoration of broken symmetries is eventually
mandatory to recover the corresponding quantum numbers and to achieve a more
precise description of nuclear properties.
  While symmetry-restored calculations are routinely performed to study
ground-state properties and low-lying excitations, similar applications to the
nuclear response are essentially limited to either formal studies or to
schematic models. In the present paper, the effect of angular momentum
restoration on the monopole and quadrupole responses of doubly open-shell
nuclei is investigated.
  Based on deformed Skyrme-Random Phase Approximation (RPA) calculations, the
exact Angular Momentum Projection (AMP) is implemented in the calculation of
the multipole strength functions, thus defining a projection after variation
(PAV-RPA) scheme. The method is employed for the first time in a realistic
study to investigate the effect of AMP on the coupling of monopole and
quadrupole modes in $^{24}$Mg resulting from its intrinsic deformation.
