Coulomb excitation of the proton-rich nucleus ${}^{20}\mathrm{Mg}$ was studied using a radioactive ${}^{20}\mathrm{Mg}$ beam at $58A$ MeV impinging on a lead target. The reduced transition probability $B(E2;0_{\mathrm{g}.\mathrm{s}.}^{+}\to 2_1^{+})$ was extracted to be $177(32)\hspace{0.5em}{e}^2$ fm${}^4$, which agrees with the theoretical predictions by a cluster model assuming ${}^{16}\mathrm{O}\hspace{0.5em}+\hspace{0.5em}2p\hspace{0.5em}+\hspace{0.5em}2p$ structure, a mean-field approach based on the angular momentum projected generator coordinate method, and the USD shell model. The ratio of the neutron-to-proton multipole matrix elements $M_{\mathrm{n}}/M_{\mathrm{p}}$ in the mirror nucleus ${}^{20}\mathrm{O}$ was deduced to be 2.51(25) with the $M_{\mathrm{n}}$ value evaluated from the measured $B(E2)$ value for ${}^{20}\mathrm{Mg}$ with the help of isospin symmetry. The results confirm the large $M_{\mathrm{n}}/M_{\mathrm{p}}$ value previously reported in ${}^{20}\mathrm{O}$, leading to the dominant role of the four valence nucleons in the $2_1^{+}$ excitation and persistence of the ${}^{16}\mathrm{O}$ core in ${}^{20}\mathrm{O}$ and ${}^{20}\mathrm{Mg}$.

• Received 16 June 2008
• Publisher error corrected 20 August 2008

DOI:https://doi.org/10.1103/PhysRevC.78.024306