The spectra of mass-11 nuclei are unusual, and so pose a challenge for nuclear-structure theory. Relating to nucleon emission, the set of isobars range from being well-bound (11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}B,11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}C) through weakly bound (11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}Li, 11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}Be), to being proton unstable (11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}N,11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}O). To add complexity, the weakly bound 11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}Li takes the form of a two-nucleon halo nucleus. A self-consistent approach to understand this set of nuclei is especially important as the mirror pair 11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}Be-11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}N exhibit a parity-inverted ground state compared to their neighboring nuclei. Herein, the Multi-Channel Algebraic Scattering method (MCAS) has been used to describe the low excitation spectra of those isobars in terms of nucleon-nucleus clusters. A collective model description of the low-excitation states of the mass-10 mass-10 core nuclei has been used to form the coupled-channel interactions required in the method. For comparison, and to understand the underlying configurations, a shell model approach has been used to obtain those spectra with no-core (0+2+4)ħω\documentclass[12pt]{minimal}
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\begin{document}$$(0+2+4)\hbar \omega $$\end{document} and (0+2)ħω\documentclass[12pt]{minimal}
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\begin{document}$$(0+2)\hbar \omega $$\end{document} shell-model spaces for the mass 10 and mass 11 nuclei respectively. The results of the calculations suggest the need of a strong coupling in the collective coupled-channel vibrational model. In particular, the strong coupling of the collective 21+\documentclass[12pt]{minimal}
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\begin{document}$$2^+_1$$\end{document} state of 10\documentclass[12pt]{minimal}
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\begin{document}$$^{10}$$\end{document}Be to the valence neutron plays a decisive role in forming the positive parity ground state in 11\documentclass[12pt]{minimal}
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\begin{document}$$^{11}$$\end{document}Be; an effect confirmed by the shell-model results.
