Analysis of states in ${}^{13}$C populated in ${}^9$Be $+$ ${}^4$He resonant scattering

Measurements of ${}^9$Be + $\alpha$ resonant scattering have been performed using the thick-target approach with a ${}^4$He gas volume and a large-area silicon strip detector. ${}^9$Be beam energies in the range 12 to 21.4 MeV were used to measure the ${}^{13}$C excitation energy spectrum between 13.2 and 16.2 MeV. An $R$-matrix analysis has been performed to characterize the spins and widths of ${}^{13}$C resonances, some of which have been proposed to be associated with a 3$\alpha +n$ molecular band.

Figure 1

Experimental setup showing the ${}^9$Be beam passing through the Havar window, interacting with a ${}^4$He nucleus to form ${}^{13}$C, with the subsequent emission of an $\alpha$ particle in the forward direction. The $\alpha$ particle is then detected by the silicon strip detector. The gas pressure is then adjusted to stop the beam in the gas before the detector.

Figure 2

The excitation function for ${}^9$Be + $\alpha$ measured at 21.4 MeV (black dots), 20 MeV (red line), 17 MeV (dashed line), and 12 MeV (blue line). The 21.4 MeV data restricted to the central 4$\times$4 pixels are shown by the green line.

Figure 3

$R$-matrix fits [red lines and blue dot-dashed line in (b)] to the 21.4 MeV data (black points). The dotted line shows the estimated background contribution from breakup and inelastic contributions. See the main text for details. Parts (a) and (b) are labeled in terms of the ${}^{13}$C excitation energy and (c) and (d) the center-of-mass energy of the $\alpha$ + ${}^9$Be system. $E_x=E_{\mathrm{c}.\mathrm{m}.}+10.65$ MeV.