${}^{10}\mathrm{C} + \alpha$ elastic scattering: A study of the proton-rich ${}^{14}\mathrm{O}$ nucleus and $\alpha$ clustering

The ${}^{10}\mathrm{C}+\alpha$ elastic cross section was measured to investigate the structure of the proton-rich ${}^{14}\mathrm{O}$ nucleus. A radioactive beam of ${}^{10}\mathrm{C}$ was produced at the RI beam separator CRIB using the ${}^{10}\mathrm{B}(p,n){}^{10}\mathrm{C}$ reaction with a ${}^{10}\mathrm{B}$ beam energy of 6.99 MeV/nucleon. A complex resonant structure is observed in ${}^{14}\mathrm{O}$ in the excitation energy region around 13–18 MeV, improving significantly our knowledge on the structure of this nucleus. An $R$-matrix analysis was performed to determine the properties of resonances. $\alpha$ clustering structure is observed for $J=0^{+}$ and $J=2^{+}$ at 13.44 and 14.88 MeV, respectively. These results are compared with the $\alpha$ clustering structure reported in the mirror nucleus ${}^{14}\mathrm{C}$.

Figure 1

A schematic of the experimental setup for the ${}^{10}\mathrm{C}+\alpha$ elastic scattering measurement. The distance between detector no. 1 and the mylar window was 507 mm. In the figure the relevant distances are indicated in relation to a reference point. The telescope numbers referred to in the text are also indicated (nos. 1, 2, and 3).

Figure 2

$\mathrm{\Delta }E-E$ particle identification plot measured with telescope no. 1 (${\theta }_{\mathrm{lab}}=0-8{}^{\circ }$). The scattered protons and $\alpha$ particles are clearly separated and identified.

Figure 3

Energy ($E_{\mathrm{c}.\mathrm{m}.}$) vs the angular (${\theta }_{\mathrm{c}.\mathrm{m}.}$) distribution of the ${}^{10}\mathrm{C}+\alpha$ scattering measured by telescope no. 1.

Figure 4

Energy ($E_{\mathrm{c}.\mathrm{m}.}$) vs angular (${\theta }_{\mathrm{c}.\mathrm{m}.}$) distributions of the ${}^{10}\mathrm{C}+\alpha$ scattering measured by the telescope nos. 2 (top) and 3 (bottom).

Figure 5

Experimental center-of-mass cross section of the ${}^{10}\mathrm{C}+\alpha$ scattering ${(d\sigma /d\mathrm{\Omega })}_{\mathrm{c}.\mathrm{m}.}$ as a function of $E_{\mathrm{c}.\mathrm{m}.}$ in the bottom axis and as a function of the excitation energy $E_{\mathrm{ex}}$ in the top axis. The DSC data are fitted with the R-matrix calculation using azure2 (lines are the fits, ${\chi }^2/\mathrm{ndof}=337/291$). From top to bottom ${\theta }_{\mathrm{c}.\mathrm{m}.}$ = $169.1{}^{\circ }-172.8{}^{\circ }, 172.8{}^{\circ }-176.4{}^{\circ }$ and $176.4{}^{\circ }-180{}^{\circ }$ respectively.

Figure 6

Excitation energies of the resonances in ${}^{14}\mathrm{O}$ plotted against $J(J+1)$ for the predicted linear chain band [17] (open square) and by the present work (solid circles). The candidate of the linear-chain band in ${}^{14}\mathrm{C}$ proposed in [9] is also plotted for comparison (solid triangle). The lower $4^{+}$ state in the present work is with a tentative $J^{\pi }$ assignment and plotted with parentheses.