Effects of the γ -soft isomeric states on the giant monopole resonances in even-even cadmium isotopes Cd110,112,114,116

Abstract

The shape evolutions of the even-even cadmium isotopes $^{110--116}\mathrm{Cd}$ are investigated in this work. The giant monopole resonances built on different shape isomeric states are studied using the quasiparticle random phase approximation, which is implemented with a finite amplitude method. We find the local minima corresponding to the prolate, oblate, and triaxial-deformed isomeric states in the even-even cadmium isotopes. Their responses to external monopole perturbations are quite different. Larger deformation tends to make the energy of the giant monopole resonance to shift lower. It is well known that the density functional models have some difficulties in predicting the right positions of the monopole resonances in cadmium isotopes: the centroid energies always seem too large compared to the experimental results. Our calculations show the giant monopole resonances built on the $\ensuremath{\gamma}$ soft isomeric states in the cadmium isotopes have centroid energies even lower than the experimental measurements. Therefore, if the isomeric branching of these $\ensuremath{\gamma}$ soft isomeric states turns out to be prominent, isomer mixing may be a good explanation to the longstanding puzzle.