New resonances in ${}^{11}\mathrm{C}$ above the ${}^{10}\mathrm{B} + p$ threshold investigated by inverse kinematic resonant scattering

The spectroscopy of ${}^{11}\mathrm{C}$ has been investigated by the resonant scattering of ${}^{10}\mathrm{B}+p$ with the thick target inverse kinematic method. The ${}^1\mathrm{H}({}^{10}\mathrm{B},p){}^{10}\mathrm{B}$ reaction was measured at ${\theta }_{\mathrm{c}.\mathrm{m}.}={180}^{\circ }, {170}^{\circ }, {160}^{\circ }, {150}^{\circ }$, and ${140}^{\circ }$ using a 35.93 MeV ${}^{10}\mathrm{B}$ beam. Resonances in ${}^{11}\mathrm{C}$ between the excitation energy of 9.6 and 11.8 MeV are observed. The excitation functions are compared with previous data using thin target direct kinematics measurements. A multichannel $R$-matrix calculation under the kinematics assumption of resonant elastic scattering is performed and the resonant parameters, such as the resonant energy $E_x$, the spin-parity $J^{\pi }$, and the proton-decay partial width ${\mathrm{\Gamma }}_p$ are extracted.

Figure 1

A schematic of the experimental setup.

Figure 2

Two-dimensional spectrum ($\mathrm{\Delta }E$ vs $E_{\mathrm{residual}}$) measured at ${\theta }_{\mathrm{lab}}=0^{\circ }$. The measured light particles $p,d, {}^3\mathrm{He}$, and ${}^4\mathrm{He}$ are indicated.

Figure 3

Proton spectra excitation function obtained with the plastic target (green) and ${}^{12}\mathrm{C}$ target (blue) (background events) at (a) ${\theta }_{\mathrm{lab}}={10}^{\circ }$ and (b) ${15}^{\circ }$.

Figure 4

The extracted excitation function for the reaction channel ${}^1\mathrm{H}({}^{10}\mathrm{B},p){}^{10}\mathrm{B}$ at indicated laboratory angles.

Figure 5

Energy-level diagram of the ${}^{11}\mathrm{C}$ nucleus above the proton separation energy (indicated with the dotted line). The values in the black color correspond to the levels reported in Ref. [11], in blue are resonances reported in the references tabulated in Table 1, and in red the new resonances observed in the present paper.

Figure 6

Excitation functions measured in the present paper compared with the one obtained in direct kinematic reported by Chiari et al. [12]. The corresponding angles are mentioned in the laboratory frame and the equivalent laboratory angles from inverse to forward kinematics are given inside the square brackets.

Figure 7

$R$-matrix fits to the present data with a simultaneous calculations for including all the measured angles. The resonant energy levels considered above 11.0 MeV are as follows: 11.26, 11.44, and 11.75 MeV. The corresponding spin-parity combinations for these three levels are shown with legends.

Figure 8

The $R$-matrix calculation for ${}^{10}\mathrm{B}(p,p)$ reaction for the data measured at ${\theta }_{\mathrm{c}.\mathrm{m}.}={180}^{\circ }$ in the inverse kinematics. The results with different spin-parity combinations for resonances at $E_x=11.44$ and 11.75 MeV (considered as variable parameters) are shown.

Figure 9

Role of three proposed resonances in the best fit: The results shown are obtained by excluding one at a time as indicated with the legends.

Figure 10

The observed resonant states in ${}^{11}\mathrm{C}$ and together with those obtained with Eq. (1) for the mirror analog to ${}^{11}\mathrm{B}$ states. For each state, $E_x$ in MeV and $J^{\pi }$ are mentioned. The states reported in literature [29] for the ${}^{11}\mathrm{B}$ are shown with red dotted lines, and corresponding resonant parameters are mentioned in red.