Coulomb shift in the mirror pair of ${}^{14}\mathrm{C}$ and ${}^{14}\mathrm{O}$ as a signature of the linear-chain structure

Coulomb shifts of the linear-chain states are theoretically investigated for the mirror pair of ${}^{14}\mathrm{C}$ and ${}^{14}\mathrm{O}$ by using the antisymmetrized molecular dynamics. Energy shift of the $\sigma$-bond linear-chain states is found and it is due to the reduction in the Coulomb energy associated with the spatially extended $\sigma$ orbit. This new signature supports the existence of the linear-chain formation and encourages further experimental investigations.

Figure 1

Left: Positive-parity energy levels of ${}^{14}\mathrm{O}$ up to $J^{\pi }=8^{+}$. The filled circles, triangles, and boxes show the ground, triangular, and linear-chain bands, while lines show the noncluster states. Dashed lines show theoretical threshold energies. Right: Density distributions of intrinsic wave functions in ${}^{14}\mathrm{O}$. Contour lines show the neutron density distribution and blue plots show the single-particle orbit occupied by the most weakly bound proton.

Figure 2

Energy spectra for $J^{\pi }=0^{+}$ of ${}^{14}\mathrm{C}$ (left levels) and ${}^{14}\mathrm{O}$ (right levels). Levels are marked by an excitation energy in units of MeV. Dashed lines show theoretical thresholds.

Figure 3

Energy spectra for $J^{\pi }=2^{+}$ of ${}^{14}\mathrm{C}$ and ${}^{14}\mathrm{O}$.

Figure 4

Energy spectra for $J^{\pi }=4^{+}$ of ${}^{14}\mathrm{C}$ and ${}^{14}\mathrm{O}$.