Couplings between dipole and quadrupole vibrations in tin isotopes

Abstract

We study the couplings between collective vibrations such as the isovector giant dipole and isoscalar giant quadrupole 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 isovector giant dipole resonance with the isoscalar giant quadrupole resonance built on top of it, inducing a nonlinear 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. Three methods associated with these different manifestations of the coupling are proposed to extract the corresponding matrix elements of the residual interaction. Numerical applications of the different methods to $^{132}\mathrm{Sn}$ are in good agreement with each other. Finally, several tin isotopes are considered to investigate the role of isospin and mass number on this coupling. A simple $1/A$ dependence of the residual matrix elements is found with no noticeable contribution from the isospin. This result is interpreted within the Goldhaber-Teller model.