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 ${}^{110}\mathrm{Zr}$ and in the drip-line nuclei around ${}^{140}\mathrm{Zr}$ 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 strength 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 that 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. In addition to the GMR, we find that the threshold strength is generated by neutrons only.

Figure 1

Isoscalar (IS) and isovector (IV) monopole and quadrupole transition strengths in ${}^{90,100,108,110,112}$Zr. The neutron and proton transition strengths are also shown for the monopole excitation. The arrows indicate the one-quasineutron continuum threshold $E_{\mathrm{th},1n}=\left|\lambda \right|+min{E}_{\alpha }$ and the two-quasineutron continuum threshold $E_{\mathrm{th},2n}=2\left|\lambda \right|$. Only the one-neutron continuum thresholds for ${}^{90,100,112}\mathrm{Zr}$, the normalfluid systems, are shown.

Figure 2

Same as Fig. 1 but in ${}^{136,138,140}\mathrm{Zr}$.

Figure 3

(a) Mean energy of the ISGMR in Zr isotopes. The energies of the upper and lower peaks are denoted by triangles and squares, respectively. (b) Fraction of the EWSR value for the upper and lower peaks. The mean energy of the upper and lower peaks is calculated as $m_1/m_0$ for the energy interval of $5$ MeV $<E<E_c$ and $E_c<E<25$ MeV, and the fraction is calculated for each interval. The lines represent the results obtained in the scaling model [26].