Search for dilute excited states in ${}^{16}\mathrm{O}$

The root mean square radii of ${}^{16}\mathrm{O}$ in the short-lived $0^{+}$ excited states were experimentally deduced for the first time from the analyses of $\alpha +{}^{16}\mathrm{O}$ diffraction scattering. Differential cross sections of the elastic and inelastic $\alpha +{}^{16}\mathrm{O}$ and ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ scattering in the incident energy range from a few MeV/nucleon up to 100 MeV/nucleon were analyzed by the modified diffraction model. No significant radius enhancement in any state in comparison with the ground state was observed. This concerns, in particular, the 15.1-MeV $0_6^{+}$ state of ${}^{16}\mathrm{O}$, located in the vicinity of the four-$\alpha$-particle complete dissociation threshold, for which we did not confirm the “gigantic” size predicted by the $\alpha$-particle condensation model. This result does not support the idea that ${}^{16}\mathrm{O}$ in the $0_6^{+}$ state has a dilute structure and can be considered as an analog of the famous 7.65-MeV $0_2^{+}$ Hoyle state of ${}^{12}\mathrm{C}$.

Figure 1

Energy dependence of the diffraction radii extracted from the $\alpha +{}^{12}\mathrm{C}$ elastic and inelastic scattering populating the 4.44-MeV $2^{+}$ and 7.65-MeV $0_2^{+}$ states (adopted from Ref. [10]). The straight lines show linear approximations of the data at $E/A\lesssim 60$ MeV (solid lines) and $E/A\gtrsim 60$ MeV (dashed lines).

Figure 2

Energy dependence of the diffraction radii extracted by the MDM analysis of $\alpha +{}^{16}\mathrm{O}$ elastic and inelastic scattering data from Refs. [24, 25, 32, 33, 34, 35, 36, 37, 38, 39]. The solid lines represent linear approximations of the elastic scattering data. The diffraction radii for the elastic scattering, $1^{-}$, $2^{+}$, $3^{-}$, and $0^{+}$ states are denoted by filled squares, down triangles, triangles, diamonds, and circles, correspondingly. The extracted diffraction radius for the 15.1-MeV $0_6^{+}$ state is marked by a filled star, while a prediction from Refs. [22, 23] is pointed out by a pentagon. The radii for some states measured at about 100 MeV/nucleon are slightly shifted for convenience of observation.

Figure 3

Cross sections of the elastic and inelastic $\alpha +{}^{16}\mathrm{O}$ scattering plotted vs momentum transfer $q$. Three upper graphs present the elastic scattering data at $E_{\alpha }=400$, 80.7, and 50 MeV (adopted from Refs. [24, 32]). The solid curves in the three upper graphs show the optical model and spline fits. The next three graphs present the inelastic scattering cross sections at $E_{\alpha }=386$ MeV (adopted from Ref. [25]) with an excitation of the 12.0-MeV $0_3^{+}$, 14.0-MeV $0_5^{+}$, and 15.1-MeV $0_6^{+}$ states. The dotted curves show the $L=0$ cross-section components in the multipole decomposition fitted the data. The lower graph presents the inelastic scattering data at $E_{\alpha }=400$ MeV (adopted from Refs. [24]) populating the 13.6-MeV $0_4^{+}$ state. The vertical lines are drawn through the minima and maxima of the same order.