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Within the Energy Density Functional (EDF) approach, the use of mean-fieldwave-functions deliberately breaking (some) symmetries of the underlyingHamiltonian is an efficient and largely utilized way to incorporate staticcorrelations. However, the restoration of broken symmetries is eventuallymandatory to recover the corresponding quantum numbers and to achieve a moreprecise description of nuclear properties.  While symmetry-restored calculations are routinely performed to studyground-state properties and low-lying excitations, similar applications to thenuclear response are essentially limited to either formal studies or toschematic models. In the present paper, the effect of angular momentumrestoration on the monopole and quadrupole responses of doubly open-shellnuclei is investigated.  Based on deformed Skyrme-Random Phase Approximation (RPA) calculations, theexact Angular Momentum Projection (AMP) is implemented in the calculation ofthe multipole strength functions, thus defining a projection after variation(PAV-RPA) scheme. The method is employed for the first time in a realisticstudy to investigate the effect of AMP on the coupling of monopole andquadrupole modes in $^{24}$Mg resulting from its intrinsic deformation.

Symmetry-restored RPA calculations of the monopole strength in deformed nuclei