Global study of Be9 + p at 2.72A MeV

Background: In our recent experiment, $^{9}\mathrm{Be}+p$ at $5.67A$ MeV, the breakup decay rates to the three configurations, $\ensuremath{\alpha}+\ensuremath{\alpha}+n, ^{8}\mathrm{Be}^{*}+n$ and $^{5}\mathrm{He}+^{4}\mathrm{He}$ of $^{9}\mathrm{Be}$, were observed and quantified in the proton recoil spectra, in a full kinematics approach. Unfolding step by step the accessibility to the above configurations, it will require similar experiments at lower or/and higher energies. It will also require the interpretation of the data in a theoretical framework. Three-body models for the structure of $^{9}\mathrm{Be}$ have been developed and applied to reactions with heavy targets. Further research on lighter targets is required for the best establishment of the model. Such models are relevant for the calculation of the corresponding radiative capture reaction rate, $\ensuremath{\alpha}(\ensuremath{\alpha},\ensuremath{\gamma})^{9}\mathrm{Be}$ followed by $^{9}\mathrm{Be}(\ensuremath{\alpha},n)^{12}\mathrm{C}$. The last is essential for the $r$-process abundance predictions.Purpose: Investigate the breakup decay rate of $^{9}\mathrm{Be}+p$ at $2.72A$ MeV, where the direct configuration $\ensuremath{\alpha}+\ensuremath{\alpha}+n$ is mainly accessible. Compare and interpret data at this low energy and at the higher energy of $5.67A$ MeV into a four-body continuum discretized coupled-channel formalism. Point out and discuss couplings to continuum.Methods: Our experimental method includes an exclusive breakup measurement in a full kinematic approach of $^{9}\mathrm{Be}$ incident on a proton target at 24.5 MeV ($2.72A$ MeV). Complementary the elastic scattering is measured and other reaction channels are evaluated from previous measurements under the same experimental conditions. The interpretation of present data at $2.72A$ MeV and previous data at $5.67A$ MeV, are considered in a four-body continuum discretized coupled channel (CDCC) approach, using the transformed harmonic oscillator method for the three-body projectile.Results: An elastic scattering angular distribution at $2.72A$ MeV is measured, which compares very well with CDCC calculations, indicating a strong coupling to continuum. At the same energy, the breakup and total reaction cross sections are measured as ${\ensuremath{\sigma}}_{\mathrm{break}}=2.5\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{4pt}{0ex}}\mathrm{mb}$ and ${\ensuremath{\sigma}}_{\mathrm{tot}}=510\ifmmode\pm\else\textpm\fi{}L90\phantom{\rule{4pt}{0ex}}\mathrm{mb}$, in good agreement with the calculated values of 3.7 and 433 mb, respectively. Further on, into the same theoretical framework, the elastic scattering and breakup cross section data at $5.67A$ MeV are found in very good agreement with the CDCC calculations.Conclusions: It was confirmed in a global experimental framework that four-body CDCC calculations can describe very well the data even at low energies. Coupling to continuum is very strong despite the small measured breakup cross section. Moreover, the present results support further our three-body model for the structure of $^{9}\mathrm{Be}$, validating relevant radiative reaction rates obtained previously.