Roles of deformation and neutron excess on the giant monopole resonance in neutron-rich Zr isotopes

We investigate the roles of deformation on the giant monopole resonance (GMR), particularly the mixing of the giant quadrupole resonance (GQR) and the effects of the neutron excess in the well-deformed nuclei around $^{110}$Zr and in the drip-line nuclei around $^{140}$Zr by means of the deformed quasiparticle-random-phase-approximation employing the Skyrme and the local pairing energy-density functionals. It is found that the isoscalar (IS) GMR has a two-peak structure, the lower peak of which is associated with the mixing between the ISGMR and the $K^{\pi}=0^{+}$ component of the ISGQR. The transition strengths of the lower peak of the ISGMR grows as the neutron number increases. In the drip-line nuclei, the neutron excitation is dominant over the proton excitation. We find for an isovector (IV) excitation the GMR has a four-peak structure due to the mixing of the IS and IV modes as well as the mixing of the $K^{\pi}=0^{+}$ component of the IVGQR. Besides the GMR, we find the threshold strength generated by neutrons only.