Hindered Proton Collectivity in ${}_{16}{}^{28}\mathrm{S}_{12}$: Possible Magic Number at $Z=16$

The reduced transition probability $B(E2;0_{gs}^{+}\to 2_1^{+})$ for ${}^{28}\mathrm{S}$ was obtained experimentally using Coulomb excitation at $53\mathrm{MeV}/\mathrm{nucleon}$. The resultant $B(E2)$ value $181(31)e^2{\mathrm{fm}}^4$ is smaller than the expectation based on empirical $B(E2)$ systematics. The double ratio $|M_n/M_p|/(N/Z)$ of the $0_{gs}^{+}\to 2_1^{+}$ transition in ${}^{28}\mathrm{S}$ was determined to be 1.9(2) by evaluating the $M_n$ value from the known $B(E2)$ value of the mirror nucleus ${}^{28}\mathrm{Mg}$, showing the hindrance of proton collectivity relative to that of neutrons. These results indicate the emergence of the magic number $Z=16$ in the $|T_z|=2$ nucleus ${}^{28}\mathrm{S}$.

Figure 1

Doppler-shift-corrected $\gamma$-ray energy spectrum in the $\mathrm{Pb}({}^{28}\mathrm{S},{}^{28}\mathrm{S}\gamma )\mathrm{Pb}$ reaction. The fit by the response function (dashed curve) and the exponential background (dotted curve) is shown by the solid curve.

Figure 2

(a) Angular distribution for the $\mathrm{Pb}({}^{28}\mathrm{S},{}^{28}\mathrm{S}\gamma )\mathrm{Pb}$ reaction exciting the 1.5 MeV state in ${}^{28}\mathrm{S}$. The solid curve represents the best fit with ECIS calculation assuming $\Delta L=2$. The dashed and dotted curves show the Coulomb and nuclear contributions, respectively. (b) Detection efficiency calculated by the Monte Carlo simulation.

Figure 3

Plot of the $B(E2;0_{gs}^{+}\to 2_1^{+})$ values (a) the excitation energies of $2_1^{+}$ states and (b) the double ratio $|M_n/M_p|/(N/Z)$ (c) for sulfur ($Z=16$) isotopes. The shell model predictions with the USDB interaction [39] are shown by the dotted curves for each quantity. The shaded region represents the $B(E2)$ predictions by the empirical $B(E2)$ systematics [28]. The present result is represented by the filled circles.