Observation of the near-threshold intruder $0^{-}$ resonance in ${}^{12}\mathrm{Be}$

A resonant state at $3.{21}_{-0.04}^{+0.12}\mathrm{MeV}$, located just above the one-neutron separation threshold, was observed for the first time in ${}^{12}\mathrm{Be}$ from the ${}^{11}\mathrm{Be}(d,p){}^{12}\mathrm{Be}$ one-neutron transfer reaction in inverse kinematics. This state is assigned a spin-parity of $0^{-}$ according to the systematics of the level scheme of the $N=8$ isotones and decay-width analysis. Gamow coupled-channel and Gamow shell-model calculations show the importance of the continuum coupling, which dramatically influences the excitation energy and ordering of low-lying states. Various exotic structures associated with cross-shell intruding configurations in ${}^{12}\mathrm{Be}$ and in its isotonic nucleus ${}^{11}\mathrm{Li}$ are comparably discussed.

Figure 1

Missing-mass spectra of ${}^{12}\mathrm{Be}$ unbound states, obtained from the protons in coincidence with ${}^{11}\mathrm{Be}$ (blue-solid spectrum) and ${}^{10}\mathrm{Be}$ (blue-dotted spectrum) ions detected at forward angles. The former is fit with resonance peaks plus a simulated background. The identified resonant states are labeled with their corresponding excitation energies. The inset shows in arbitrary units the energy loss versus remaining energy ($\mathrm{\Delta }E-E$) spectrum of Be ions obtained from the zero-degree telescope in coincidence with the protons detected in the annular silicon array.

Figure 2

Differential cross sections of the ${}^{11}\mathrm{Be}(d,p){}^{12}\mathrm{Be}$ reaction populating the (a) $3.{21}_{-0.04}^{+0.12}\text{−}\mathrm{MeV}$ and (b) $4.{44}_{-0.15}^{+0.15}\text{−}\mathrm{MeV}$ states of ${}^{12}\mathrm{Be}$ and the corresponding DWBA calculations. The error bars are statistical only.

Figure 3

Excitation energies (located at the thin red solid vertical lines) of the negative-parity states and the corresponding $S$ values (height of the red bars) calculated by the GCC, GSM, and shell-model approaches in comparison with the present and previous experimental result. In addition, these three models predict the $0_3^{+}$ state at 4.8, 4.7, and 5.6 MeV (not plotted in the figure), respectively.

Figure 4

Two-nucleon density distributions (in ${\mathrm{fm}}^{-2}$) in Jacobi coordinates predicted by GCC for the g.s. and low-lying states in (a)–(d) ${}^{12}\mathrm{Be}$ and (e), (f) ${}^{11}\mathrm{Li}$.

Figure 5

The binding energies of the $1^{-}$ and $0^{-}$ (or $5/2^{+}$ and $3/2^{+}$) 1p-1h states as a function of $Z$, for $N=8$ isotones. The $3/2^{+}$ state in ${}^{13}\mathrm{B}$ has not been found experimentally and is marked by the theoretical value [24, 25].