<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts></mml:math> production in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Be</mml:mi><mml:mprescripts/><mml:none/><mml:mn>7</mml:mn></mml:mmultiscripts><mml:mo>+</mml:mo><mml:mspace width="0.16em"/><mml:mmultiscripts><mml:mi mathvariant="normal">Si</mml:mi><mml:mprescripts/><mml:none/><mml:mn>28</mml:mn></mml:mmultiscripts></mml:mrow></mml:math> reaction at near-barrier energies: Direct versus compound-nucleus mechanisms

The production of $\ensuremath{\alpha}$ and $^{3}\mathrm{He}$ particles, the cluster constituents of $^{7}\mathrm{Be}$, in the $^{7}\mathrm{Be}+\phantom{\rule{0.16em}{0ex}}^{28}\mathrm{Si}$ reaction was studied at three near-barrier energies, namely 13, 20, and 22 MeV. Angular distribution measurements were performed at each energy, and the data were analyzed in both statistical model and Distorted-Wave Born Approximation (DWBA) frameworks in order to disentangle the degree of competition between direct and compound channels. The energy evolution of the ratio of direct to total reaction cross section was mapped in comparison with similar data for $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ projectiles on a $^{28}\mathrm{Si}$ target. The results indicate larger transfer contributions for collisions involving the mirror nuclei $^{7}\mathrm{Be}$ and $^{7}\mathrm{Li}$ than in the $^{6}\mathrm{Li}$ case. Fusion cross sections were deduced, taking into account the $\ensuremath{\alpha}$-particle cross sections due to compound-nucleus formation and particle multiplicities deduced from our statistical model framework. It was found that fusion is compatible with systematics and single-barrier penetration cross sections to within an uncertainty band of 10% to 20%. Indications of fusion hindrance for $^{7}\mathrm{Li}$ and $^{7}\mathrm{Be}$ compared to $^{6}\mathrm{Li}$, starting from the barrier and below it, are given. This hindrance is attributed to the existence of large transfer channels. Furthermore, the experimental results, analyzed in the DWBA framework, suggest $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ transfer as the dominant direct reaction mechanism.