| We study the couplings between collective vibrations such as the isovector dipole (GDR) and isoscalar quadrupole (GQR) giant resonances in tin isotopes in the framework of the time dependent Hartree-Fock theory with a Skyrme energy density functional. These couplings are a source of anharmonicity in the multiphonon spectrum. In particular, the residual interaction is known to couple the GDR with the GQR built on top of the GDR,
inducing a non linear evolution of the quadrupole moment after a dipole boost. This coupling also affects the dipole motion in a nucleus with a static or dynamical deformation induced by a quadrupole constraint or boost respectively. We propose three methods associated to these different manifestations of the coupling to extract the corresponding matrix elements of the residual interaction. Numerical applications to $^{120}$Sn are in good agreement. Finally, several tin isotopes are considered to investigate the role of isospin and mass number on this coupling.
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