Indirect determination of the astrophysical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math> factor for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts/><mml:none/><mml:mn>6</mml:mn></mml:mmultiscripts></mml:math>(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>)</mml:mo><mml:mmultiscripts><mml:mi>Be</mml:mi><mml:mprescripts/><mml:none/><mml:mn>7</mml:mn></mml:mmultiscripts></mml:mrow></mml:math> reaction using the asymptotic normalization coefficient method

Background: The $^{6}\mathrm{Li}(p,\ensuremath{\gamma})^{7}\mathrm{Be}$ cross section influences a variety of astrophysical scenarios, including big-bang and stellar nucleosynthesis. In recent years, conflicting results of direct measurements have been published, reporting contradictory low-energy trends.Purpose: To shed light on the contradiction between the existing data sets, the reaction was studied using the asymptotic normalization coefficient (ANC) technique which was up-to-now never used for this reaction.Methods: To derive the ANC, the $^{6}\mathrm{Li}(^{3}\mathrm{He},d)^{7}\mathrm{Be}$ transfer reaction, studied at the Department of Physics and Astronomy of the University of Catania and at the John. D. Fox Superconducting Accelerator Laboratory at Florida State University, was re-analyzed, focusing on the proton transfer mechanism [the $\ensuremath{\alpha}$ transfer process is discussed by Kiss et al. [Phys. Lett. B 807, 135606 (2020)]. The energy of the $^{3}\mathrm{He}$ beam impinging on a $^{6}\mathrm{Li}$ target was ${E}_{\mathrm{lab}}=3$ MeV and ${E}_{\mathrm{lab}}=5$ MeV. The yield of the emitted deuterons was measured with high precision by using silicon $\mathrm{\ensuremath{\Delta}}E\ensuremath{-}E$ telescopes.Results: From the DWBA analysis of the angular distributions of the emitted deuterons populating the ground (${E}^{*}=0.0$ MeV; ${\frac{3}{2}}^{\ensuremath{-}}$) and the first excited (${E}^{*}=0.429\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$; ${\frac{1}{2}}^{\ensuremath{-}}$) states of $^{7}\mathrm{Be}$, the ANCs for the $^{6}\mathrm{Li}+p\ensuremath{\rightarrow}^{7}\mathrm{Be}$ system were deduced. Furthermore, the recently measured $^{6}\mathrm{Li}(p,\ensuremath{\gamma})^{7}\mathrm{Be}$ reaction cross sections [Piatti et al., Phys. Rev. C 102, 052802 (2020)] were also analyzed within this theoretical framework. Excellent agreement was found between ANC values derived indirectly and those determined from the direct data, which strengthens the conclusion of the present work. The astrophysical $S$ factor---at energies characterizing the Sun---for the $^{6}\mathrm{Li}(p,\ensuremath{\gamma})^{7}\mathrm{Be}$ reaction was calculated using the weighted mean of the experimentally derived ANC values.Conclusions: The result of the present comprehensive study supports the extrapolation of Piatti et al. [Phys. Rev. C 102, 052802 (2020)], Dong et al. [J. Phys. G Nucl. Partic. 44, 045201 (2017)], and Gnech and Marcucci [Nucl. Phys. A 987, 1 (2019)], and thus disfavors the conclusions drawn by He et al. [Phys. Lett. B 725, 287 (2013)] and Xu et al. [Nucl. Phys. A 918, 61 (2013)].