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Study of the $^{25}$Mg(d,p)$^{26}$Mg reaction to constrain the $^{25}$Al(p,$γ$)$^{26}$Si resonant reaction rates in nova burning conditions

The rate of the $^{25}$Al($p$,$γ$)$^{26}$Si reaction is one of the few key remaining nuclear uncertainties required for predicting the production of the cosmic $γ$-ray emitter $^{26}$Al in explosive burning in novae. This reaction rate is dominated by three key resonances ($J^π=0^{+}$, $1^{+}$ and $3^{+}$) in $^{26}$Si. Only the $3^{+}$ resonance strength has been directly constrained by experiment. A high resolution measurement of the $^{25}$Mg($d$,$p$) reaction was used to determine spectroscopic factors for analog states in the mirror nucleus, $^{26}$Mg. A first spectroscopic factor value is reported for the $0^{+}$ state at 6.256 MeV, and a strict upper limit is set on the value for the $1^{+}$ state at 5.691 MeV, that is incompatible with an earlier ($^{4}$He,$^{3}$He) study. These results are used to estimate proton partial widths, and resonance strengths of analog states in $^{26}$Si contributing to the $^{25}$Al($p$,$γ$)$^{26}$Si reaction rate in nova burning conditions.