Spectroscopy of high-lying resonances in ${}^9\mathrm{Be}$ by the measurement of ($p,p$), ($p,d$), and ($p,\alpha$) reactions with a radioactive ${}^8\mathrm{Li}$ beam

We measured the ${}^8\mathrm{Li}(p,p){}^8\mathrm{Li}$, ${}^8\mathrm{Li}(p,d){}^7\mathrm{Li}$, and ${}^8\mathrm{Li}(p,\alpha ){}^5\mathrm{He}$ reactions at low energies using the thick target inverse kinematics method, with a polyethylene ${\left[{\mathrm{CH}}_2\right]}_n$ target and a radioactive ${}^8\mathrm{Li}$ beam available at the Radioactive Ion Beams in Brazil facility of São Paulo. By measuring simultaneously several reaction channels $(p,p)$, $(p,d)$, and $(p,\alpha )$, the still uncertain high-lying resonances of ${}^9\mathrm{Be}$, close to the proton threshold, can be studied and their parameters, such as energy, width, and spin parity can be more reliably determined. The experimental excitation functions of the reactions ${}^8\mathrm{Li}(p,p){}^8\mathrm{Li}$, ${}^8\mathrm{Li}(p,d){}^7\mathrm{Li}$, and ${}^8\mathrm{Li}(p,\alpha ){}^5\mathrm{He}$ were analyzed using the $R$-matrix theory, which allows us to infer the properties of the resonances. Multichannel $R$-matrix analysis provides evidence for a significant clustering in the $(p,d)$ channel. The experimental data and the multichannel $R$-matrix analysis will be presented.

Figure 1

Schematic overview of the RIBRAS facility depicting its main components. Blue lines are simulated trajectories of secondary beam transport through the setup.

Figure 2

(a) The yield of the experimental ${}^8\mathrm{Li}+{}^{197}\mathrm{Au}$ angular distribution is presented by black squares. The red line is the Rutherford cross section. (b) Using the effective average scattering angle instead of the geometrical one, the angular distribution agrees with the Rutherford cross section.

Figure 3

Bidimensional identification spectra obtained using a Si telescope at ${\theta }_{\mathrm{lab}}={18}^{\circ }$ in the scattering chamber (3), with the secondary beam of $E_{\mathrm{lab}}=16.0\mathrm{MeV}$. We clearly see well-separated proton, deuteron, triton, and $\alpha$ strips. The beam was focused, respectively, on: the ${\left[{\mathrm{CH}}_2\right]}_n$ target of $6.7{\mathrm{mg}/\mathrm{cm}}^2$ (top), with $4.5\times {10}^8$ incident ${}^8\mathrm{Li}$ beam particles; a ${}^{197}\mathrm{Au}$ target of $5.3{\mathrm{mg}/\mathrm{cm}}^2$ (middle) with $0.85\times {10}^8$ incident ${}^8\mathrm{Li}$ beam particles; a carbon target of $15{\mathrm{mg}/\mathrm{cm}}^2$(bottom) with $8.2\times {10}^8$ incident ${}^8\mathrm{Li}$ beam particles.

Figure 4

The experimental cross section of the reaction ${}^8\mathrm{Li}(p,\alpha ){}^5\mathrm{He}$ before (black dots) and after (blue triangles) the subtraction of the $\alpha$ particles from the decay of ${}^5\mathrm{He}$ (red dots), and of the phase-space three-body breakup (green triangles).

Figure 5

The experimental cross sections of the reactions (a) ${}^8\mathrm{Li}(p,p){}^8\mathrm{Li}$, (b) ${}^8\mathrm{Li}(p,\alpha ){}^5\mathrm{He}$, and (c) ${}^8\mathrm{Li}(p,d){}^7\mathrm{Li}$ measured at ${\theta }_{\mathrm{lab}}={18}^{\circ }$ with the secondary beam of $E_{\mathrm{lab}}=16.0\mathrm{MeV}$. The black dots and red crosses in (a) were obtained, respectively, without and with the subtraction of the background of protons detected with Carbon target.

Figure 6

The superposition of the experimental ${}^8\mathrm{Li}(p,\alpha ){}^5\mathrm{He}$ cross sections measured in three experiments is presented. The red dots represent the cross section of ${}^8\mathrm{Li}(p,\alpha ){}^5\mathrm{He}$ measured at $E_{\mathrm{lab}}=18.7\mathrm{MeV}$ and ${\theta }_{\mathrm{lab}}={10}^{\circ }$ [27]. The black squares correspond to the ${}^8\mathrm{Li}(p,\alpha ){}^5\mathrm{He}$ measurement of Mendes et al. [9] (see also Erratum [10]). The blue triangles represent the cross sections shown on Fig. 5.

Figure 7

(a) The cross section of ${}^8\mathrm{Li}(p,d){}^7\mathrm{Li}$ measured at $E_{\mathrm{lab}}=18.7\mathrm{MeV}$ and ${\theta }_{\mathrm{lab}}={10}^{\circ }$ [27]. (b) The comparison, as a function of $E_{\mathrm{c}.\mathrm{m}.}$, of two measurements of the reaction ${}^8\mathrm{Li}(p,d){}^7\mathrm{Li}$ at different incident energies and angles.

Figure 8

The experimental cross sections of the reactions ${}^8\mathrm{Li}(p,p){}^8\mathrm{Li}$ [in (a)], ${}^8\mathrm{Li}(p,\alpha ){}^5\mathrm{He}$ [in (b)], ${}^8\mathrm{Li}(p,d){}^7\mathrm{Li}$ [in (c)] measured at ${\theta }_{\mathrm{lab}}={18}^{\circ }$ with $E_{\mathrm{lab}}=16.0\mathrm{MeV}$. The red solid line is the result of the best fit $R$-matrix calculation using the resonance parameters presented on Table 1 and was obtained including excitation of the recoiling ${}^7\mathrm{Li}$ in the reaction ${}^8\mathrm{Li}(p,d){}^7\mathrm{Li}$. More details and explanations in the text.