Evolution of soft monopole mode in the even-even nickel isotopes ${}^{58\text{–}68}\mathrm{Ni}$

The finite amplitude method is implemented for covariant density functional theory with the point-coupling functional PC-PK1 for deformed nuclei. The giant monopole resonances for even-even nickel isotopes ${}^{58\text{–}68}\mathrm{Ni}$ are studied. The experimentally reported soft monopole mode, a distinct form of nuclear compressional mode, for the unstable nucleus ${}^{68}\mathrm{Ni}$ is well reproduced. The evolution of the soft monopole mode in neutron-rich nickel isotopes is shown. Microscopic analysis of the transition density shows that the soft monopole mode is dominated by neutron vibrations.

Figure 1

Monopole strength functions for ${}^{68}\mathrm{Ni}$ calculated by using PC-PK1: (a) comparison between the direct variation approach (solid line) and the numerical differentiation approach (circles); (b) effect of the smearing width $\mathrm{\Gamma }$.

Figure 2

Calculated strength functions by PC-PK1 for ${}^{58}\mathrm{Ni}$ (a) and ${}^{60}\mathrm{Ni}$ (b) with (solid line) and without (dashed line) currents are shown, in comparison with the experimental data (blue error-bars) scaled on right in terms of EWSR fractions.

Figure 3

Normalized transition density for ${}^{68}\mathrm{Ni}$ at $\omega =19.0$ MeV for neutron (a) and proton (b), and at $\omega =13.2$ MeV for neutron (c) and proton (d). In each panel, the dashed line represents the root-mean-square radius for neutron or proton density distribution.

Figure 4

The calculated monopole strength functions, smeared with $\mathrm{\Gamma }=2$ MeV, by PC-PK1 for ${}^{62\text{–}68}\mathrm{Ni}$ are presented in (a)–(d), with arrows indicating the soft monopole modes. The corresponding normalized neutron transition densities are depicted in (e)–(h). The fractions of EWSR exhausted by the soft monopole modes (i) and their peak positions $E^s$ (j) are also presented.