Figure 1

${}^{12}$C excitation energy spectra (with the ${}^{16}$O background subtracted) from $\alpha$-particle inelastic scattering at 386 MeV at ${\theta }_{\mathrm{lab}}=0$ and 3.7${}^{\circ }$. The black-dotted curve characterizes the shape of the 10.3 MeV 0${}^{+}$ state (and any other broad components). The data at ${\theta }_{\mathrm{lab}}=3.7^{\circ }$ have been fitted with two curves. The red dashed line corresponds to all known ${}^{12}$C states. The solid blue curve includes an additional 2${}^{+}$ contribution from an $R$-matrix calculation. The hatched region shows the asymmetric shape of the 2${}^{+}$ state predicted by the $R$-matrix calculation [Eq. (1)], see text for details. Note there is a contaminant from the hydrogen in the target between 5 and 8 MeV (labeled H in Fig. 2.) The black dot-dashed line is the scaled broad 0${}^{+}$ background used in the fit which includes the proposed 2${}^{+}$ contribution.Reuse & Permissions

Figure 2

Analysis of background contributions to the ${}^{12}$C excitation energy spectrum populated in $\alpha$-inelastic scattering at ${\theta }_{\mathrm{lab}}=3.7^{\circ }$. The maroon histogram (labeled “Before Subtraction”) is the data before background subtraction. The hydrogen contaminant is labeled H. The red histogram (labeled “${}^{16}$O”) shows the ${}^{16}$O contaminant spectrum, which when subtracted gives the black histogram (labeled “After Subtraction”). The blue histogram (labeled “${}^{13}$C”) shows a measurement of ${}^{13}$C($\alpha$,${\alpha }^{\prime }$) measured at ${\theta }_{\mathrm{lab}}=3.7^{\circ }$ [19]. The broad feature in the ${}^{12}$C excitation energy spectrum between 9 and 10 MeV cannot be interpreted in terms of target contaminants.Reuse & Permissions

Figure 3

${}^{12}$C excitation energy spectrum from a measurement of proton inelastic scattering for a 66 MeV proton beam and a scattering angle of ${\theta }_{\mathrm{lab}}=$ 16${}^{\circ }$. Contaminants from ${}^{13}$C and ${}^{16}$O target contaminants are labeled C and O, respectively. Two fits are shown. The red dashed line corresponds to all known ${}^{12}$C states. The solid blue curve includes an additional 2${}^{+}$ contribution from an $R$-matrix calculation. The hatched region shows the asymmetric shape of the 2${}^{+}$ state predicted by the $R$-matrix calculation [Eq. (1)], see text for details. The black dot-dashed line is the scaled broad 0${}^{+}$ background used in the fit which includes the proposed 2${}^{+}$ contribution.Reuse & Permissions

Figure 4

The spin-2 strength function $[S_2\left(E_x\right)$] extracted from the multipole decomposition analysis [17] (data points) compared with the $R$-matrix line shapes [Eq. (1)] associated with different channel radii and excitation energies.Reuse & Permissions