$\alpha$-resonance structure in ${}^{11}$C studied via resonant scattering of ${}^7\mathrm{Be}+\alpha$ and with the ${}^7$Be($\alpha ,p$) reaction

Background: The resonance structure in ${}^{11}$C is of particular interest with regard to the astrophysical ${}^7$Be($\alpha ,\gamma$) reaction, relevant at high temperature, and to the $\alpha$-cluster structure in ${}^{11}$C.

Purpose: The measurement was made to determine the unknown resonance parameters for the high excited states of ${}^{11}$C. In particular, the $\alpha$-decay width can be useful information to discuss the $\alpha$-cluster structure in ${}^{11}$C.

Methods: New measurements of ${}^7\mathrm{Be}+\alpha$ resonant scattering and the ${}^7$Be($\alpha ,p$)${}^{10}$B reaction in inverse kinematics were performed for center-of-mass energy up to 5.5 MeV, and the resonances at excitation energies of 8.9–12.7 MeV in the compound ${}^{11}$C nucleus were studied. Inelastic scattering of ${}^7\mathrm{Be}+\alpha$ and the ${}^7$Be($\alpha ,p$${}_1$)${}^{10}$B${}^{*}$ reaction were also studied with a simultaneous $\gamma$-ray measurement. The measurements were performed at the low-energy radioactive ion beam facility CRIB (CNS Radioactive Ion Beam separator) of the Center for Nuclear Study, the University of Tokyo.

Results: We obtained excitation functions of ${}^7$Be($\alpha ,{\alpha }_0$)${}^7$Be (elastic scattering), ${}^7$Be($\alpha ,{\alpha }_1$)${}^7$Be${}^{*}$ (inelastic scattering), ${}^7$Be($\alpha ,p$${}_0$)${}^{10}$B, and ${}^7$Be($\alpha ,p$${}_1$)${}^{10}$B${}^{*}$. Many resonances including a new one were observed and their parameters were determined by using an $R$-matrix analysis.

Conclusions: The resonances we observed possibly enhance the ${}^7$Be($\alpha ,\gamma$) reaction rate but with a smaller magnitude than the lower-lying resonances. A new negative-parity cluster band, similar to the one previously suggested in the mirror nucleus ${}^{11}$B, is proposed.

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Figure 1

Experimental setup of the measurement of ${}^7\mathrm{Be}+\alpha$ elastic scattering and others in inverse kinematics.

Figure 2

$\Delta E$-$E$ plot for the particle identification.

Figure 3

Energy spectrum of $\gamma$ rays for ${}^7$Be-$\alpha$-$\gamma$ triple-coincidence events. The insets show the same spectrum for events with an $\alpha$ particle or $p$ identified, after a beam position selection.

Figure 4

Background subtraction for (a) $\alpha$ and (b) $p$ spectra. Total $\alpha$ and $p$ spectra are the excitation functions of ${}^7$Be($\alpha ,\alpha$)${}^7$Be and ${}^7$Be($\alpha ,p$)${}^{10}$B, but still containing background events. Shaded spectra show the contributions of background $\alpha$ and $p$ as beam contaminations. The spectra of ${}^7$Be($\alpha ,{\alpha }_1$)${}^7$Be${}^{*}$ and ${}^7$Be($\alpha ,p$${}_1$)${}^{10}$B${}^{*}$ are also shown.

Figure 5

Excitation functions, referred to as ${\alpha }_0$, ${\alpha }_1$, $p_0$, and $p_1$ spectra. The best-fit curves from the $R$-matrix analysis are also shown. The labels (A–E) correspond to structures discussed in Sec. 5.

Figure 6

Uncertainty in $E_{\mathrm{c}.\mathrm{m}.}$ and averaged ${\theta }_{\mathrm{c}.\mathrm{m}.}$ for the ${\alpha }_0$ and $p_0$ spectra.

Figure 7

The $p_0$ spectrum compared with previous measurements of the inverse ${}^{10}$B($p,\alpha$)${}^7$Be reaction by (J) Jenkin et al. [12], (C) Cronin [11], and (O) Overley and Whaling [15]. $R$-matrix calculations performed at ${\theta }_{\mathrm{lab}}={90}^{\circ }$ and 164${}^{\circ }$ are also shown. Note that the angles are in the laboratory system of the ${}^{10}$B($p,\alpha$)${}^7$Be reaction.

Figure 8

The ${\alpha }_0$ and $p_0$ spectra from the present work and [26] (solid lines).

Figure 9

Resonant states observed in the present work and our previous work [25]. $E_{\mathrm{ex}}$ in MeV and $J^{\pi }$ in our works are shown for each state, and the states with an $E_{\mathrm{ex}}$ in bold letters were observed as significant resonant peaks. The states with dashed lines were not observed in our measurements but are taken from [38].

Figure 10

Two positive-parity rotational bands in ${}^{11}$C suggested in [24], and a newly proposed negative-parity band.

Figure 11

Resonant reaction rate of ${}^7$Be($\alpha ,\gamma$) for the 8.90-, 9.20-, and 9.97-MeV resonances, calculated by using the analytical formula (see text and Table for the labels). The evaluation by NACRE and NACRE-II are shown for comparison. The contribution by the 8.420-MeV resonance, included in NACRE, is also shown.