Giant resonance splitting in deformed nuclei

We describe the giant resonances as simple scaling solutions of a linearized Vlasov equation obtained from a time-dependent Hartree-Fock theory in phase space. For ellipsoidal deformed nuclei we get a splitting of the isoscalar giant quadrupole resonance proportional to the ground state charge quadrupole moment. The lower energy state ($\hslash {\omega }_{\parallel }$ for prolate nuclei, $\hslash {\omega }_{\perp }$ for oblate) always gets the larger electromagnetic strength.