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

TL;DR

This study investigates shape coexistence and magnetic dipole transitions in $^{17}$C and $^{21}$Ne using shell model and deformed Skyrme Hartree-Fock methods, revealing shape differences and transition hindrance linked to nuclear deformation.

Contribution

It combines shell model and deformed Hartree-Fock calculations to analyze shape coexistence and magnetic transitions in N=11 nuclei, highlighting the role of shape effects in transition hindrance.

Findings

Shell model reproduces spectra and M1 transitions in $^{21}$Ne.

Deformed HF predicts prolate ground states for both nuclei.

Shape coexistence explains M1 transition hindrance in $^{17}$C.

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.