<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi>Si</mml:mi><mml:mprescripts/><mml:none/><mml:mn>26</mml:mn></mml:mmultiscripts><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>)</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">P</mml:mi><mml:mprescripts/><mml:none/><mml:mn>27</mml:mn></mml:mmultiscripts></mml:mrow></mml:math> direct proton capture by means of the asymptotic normalization coefficients method for mirror nuclei
G. D’Agata, A. I. Kilić, V. Burjan, J. Mrázek, В. В. Глаголев, V. Kroha, G. L. Guardo, M. La Cognata, L. Lamia, S. Palmerini, R. G. Pizzone, G. G. Rapisarda, S. Romano, M. L. Sergi, R. Spartá, C. Spitaleri, I. Siváček, А. Туміно
Abstract
The $^{26}\mathrm{Si}(p,\ensuremath{\gamma})^{27}\mathrm{P}$ reaction might be relevant in understanding the $^{26}\mathrm{Si}$ depletion and $^{26}\mathrm{Al}$ production in stars. The asymptotic normalization coefficients (ANC) for the $^{26}\mathrm{Si}(p,\ensuremath{\gamma})^{27}\mathrm{P}$ reaction were extracted earlier from the reanalysis of $^{26}\mathrm{Mg}(d,p)^{27}\mathrm{Mg}$ and $^{26}\mathrm{Mg}(t,d)^{27}\mathrm{Mg}$ reactions, in which the deduced ANC's show significant discrepancies. In this work, a dedicated ($d,p$) measurement is presented: the ANC for the $^{27}\mathrm{Mg}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{26}\mathrm{Mg}+n$ virtual decay is deduced from the $^{26}\mathrm{Mg}(d,p)^{27}\mathrm{Mg}$ reaction populating the ground and the first excited state of $^{27}\mathrm{Mg}$ using the distorted wave Born approximation (DWBA). The charge symmetry properties for mirror nuclei have been used to calculate the ANC for the direct capture $^{26}\mathrm{Si}+p\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{27}\mathrm{P}$ populating the ground state of $^{27}\mathrm{P}$. By means of the same formalism, the ${\mathrm{\ensuremath{\Gamma}}}_{p}$ width for the first excited state has also been deduced. The reaction rate is also updated using recent values for the ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}/{\mathrm{\ensuremath{\Gamma}}}_{p}$ ratio measured by [Sun et al., Phys. Rev. C 99, 064312 (2019); Sun et al., Phys. Lett. B 802, 135213 (2020)].