Emergent soft monopole modes in weakly bound deformed nuclei

Based on the Hartree-Fock-Bogoliubov solutions in large deformed coordinate spaces, the finite amplitude method for the quasiparticle random-phase approximation (FAM-QRPA) has been implemented, providing a suitable approach to probing collective excitations of weakly bound nuclei embedded in the continuum. The monopole excitation modes in magnesium isotopes up to the neutron drip line have been studied with the FAM-QRPA framework on both the coordinate-space and harmonic oscillator basis methods. Enhanced soft monopole strengths and collectivity as a result of weak-binding effects have been unambiguously demonstrated.