Possible Shape Coexistence and Magnetic Dipole Transitions in ${}^{17}$C and ${}^{21}$Ne

Abstract

Magnetic dipole(M1) transitions of N=11 nuclei, ${}^{17}$C and ${}^{21}$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 ${}^{21}$Ne, while the results are rather poor to predict these observables in ${}^{17}$C. In the deformed HF calculations, the ground states of 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 ${}^{21}$Ne is prolately deformed, while the first $K^{\pi }=1/2^{+}$ state in ${}^{17}$C is predicted to have a large oblate deformation being close to the ground state in energy, We point out that experimentally observed large hindrance of M1 transition between $I^{\pi }=1/2^{+}$ and $3/2^{+}$ in ${}^{17}$C can be attributed to a shape coexistence near the ground state of ${}^{17}$C.

5pages, 1figure. Phys. Rev. C, rapid communications, in press