Magnetic dipole ($M1$) transitions of $N=11$ nuclei ${}^{17}\mathrm{C}$ and ${}^{21}\mathrm{Ne}$ are investigated by using shell model and deformed Skyrme Hartree-Fock $+$ blocked BCS wave functions. Shell model calculations predict well observed energy spectra and magnetic dipole transitions in ${}^{21}\mathrm{Ne}$, while the results are rather poor to predict these observables in ${}^{17}\mathrm{C}$. In the deformed HF calculations, the ground states of the two nuclei are shown to have large prolate deformations close to ${\beta }_2=0.4$. It is also pointed out that the first $K^{\pi }=1/2^{+}$ state in ${}^{21}\mathrm{Ne}$ is prolately deformed, while the first $K^{\pi }=1/2^{+}$ state in ${}^{17}\mathrm{C}$ is predicted to have a large oblate deformation close to the ground state in energy, We point out that the experimentally observed large hindrance of the $M1$ transition between $I^{\pi }=1/2^{+}$ and $3/2^{+}$ in ${}^{17}\mathrm{C}$ can be attributed to a shape coexistence near the ground state of ${}^{17}\mathrm{C}$.

• Received 16 July 2008

DOI:https://doi.org/10.1103/PhysRevC.78.041304