Isovector giant monopole and quadrupole resonances in a Skyrme energy density functional approach with axial symmetry

Background: Giant resonance (GR) is a typical collective mode of vibration. The deformation splitting of the isovector (IV) giant dipole resonance is well established. However, the splitting of GRs with other multipolarities is not well understood.Purpose: I explore the IV monopole and quadrupole excitations and attempt to obtain the generic features of IV giant resonances in deformed nuclei by investigating the neutral and charge-exchange channels simultaneously.Method: I employ a nuclear energy-density functional (EDF) method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase approximation are used to describe the ground state and the transition to excited states.Results: I find the concentration of the monopole strengths in the energy region of the isobaric analog or Gamow-Teller resonance irrespective of nuclear deformation, and the appearance of a high-energy giant resonance composed of the particle-hole configurations of $2\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$ excitation. Splitting of the distribution of the strength occurs in the giant monopole and quadrupole resonances due to deformation. The lower $K$ states of quadrupole resonances appear lower in energy and possess the enhanced strengths in the prolate configuration, and vice versa in the oblate configuration, while the energy ordering depending on $K$ is not clear for the $J=1$ and $J=2$ spin-quadrupole resonances.Conclusions: The deformation splitting occurs generally in the giant monopole and quadrupole resonances. The $K$ dependence of the quadrupole transition strengths is largely understood by the anisotropy of density distribution.