Possible shape coexistence and magnetic dipole transitions inC17andNe21

Abstract

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 ${\ensuremath{\beta}}_{2}=0.4$. It is also pointed out that the first ${K}^{\ensuremath{\pi}}=1/{2}^{+}$ state in $^{21}\mathrm{Ne}$ is prolately deformed, while the first ${K}^{\ensuremath{\pi}}=1/{2}^{+}$ 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 ${I}^{\ensuremath{\pi}}=1/{2}^{+}$ and $3/{2}^{+}$ in $^{17}\mathrm{C}$ can be attributed to a shape coexistence near the ground state of $^{17}\mathrm{C}$.