Resonances in ${}^{11}$C observed in the ${}^4$He(${}^7\text{Be},\alpha$)${}^7$Be and ${}^4$He(${}^7\text{Be},p$)${}^{10}$B reactions

Measurements of the ${}^4$He(${}^7\text{Be},\alpha$)${}^7$Be and ${}^4$He(${}^7\text{Be},p$)${}^{10}$B reactions were performed using ${}^7$Be beam energies of 7.1 and 23 MeV and a helium-4 target, employing the thick target technique. Resonances were observed between $E_x{(}^{11}\text{C})=8.6$ to 13.8 MeV. An $R$-matrix analysis was performed to characterize the spins and partial widths. This analysis showed that the observed sequence of states was consistent with that found for ${}^7$Li $+$ $\alpha$ resonant scattering populating resonances in ${}^{11}$B. A comparison of the proposed partial widths for decay with the Wigner limit indicates that several of the states are associated with cluster-like structures.

Figure 1

Energy vs time-of-flight spectrum, for all strips of the LEDA array, showing the identification of $\alpha$ particles and protons. The various particle types are labeled.

Figure 2

(a) Proton and (b) $\alpha$-particle laboratory energy spectra from the $E{(}^7\text{Be})=7.1$-MeV data. The vertical dashed lines indicate the maximum energy protons and $\alpha$ particles expected from the resonant scattering reactions. In part (a) the region of the spectrum corresponding to protons knocked out of the Mylar window foil is indicated.

Figure 3

Measured cross sections for the ${}^4$He(${}^7\text{Be},p$)${}^{10}$B (top) and ${}^4$He(${}^7\text{Be},\alpha$)${}^7$Be (bottom) reactions. The red lines show the $R$-matrix fit to the data with $R_0=1.4$ fm. Blue data points indicate the high-energy data measured at ORNL and the black data points are the data from LLN. The error bars indicate statistical errors only. The green line shows the $R$-matrix fit with $R_0=1.3$ fm.

Figure 4

Comparison between resonant scattering of ${}^7$Li $+$ $\alpha$ (top) from Ref. [8] and ${}^7$Be $+$ $\alpha$ (bottom). The red line corresponds to the $R$-matrix fit to the data, described in the text. The vertical dashed lines are associated with the dominant features of the ${}^7$Be $+$ $\alpha$ spectrum and are to guide the eye.

Figure 5

Comparison between excitation energies of ${}^{11}$C and ${}^{11}$B states (lower panel). The red line is a linear fit to the states associated with ${}^{11}$C excitations between 4 and 9 MeV. The top panel shows the deviation from the linear fit. The blue dashed line indicates the locus of the states which are proposed to be linked with excitations to the $sd$ shell (see the text for details).

Figure 6

Excitation energy difference between analog states in ${}^{11}$B and ${}^{11}$C as a function of the spin of the state $J$ (see text for details). The horizontal dashed lines indicate regions associated with different nuclear configurations.