Si26(p,γ)P27\n direct proton capture by means of the asymptotic normalization coefficients method for mirror nuclei

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)].