Precise Thermonuclear $^{26}$Si$(p,\gamma)^{27}$P Rate and Its Ultimate Role in Galactic $^{26}$Al Puzzle

The origin of Galactic $^{26}$Al is a long-standing question in nuclear astrophysics. The $^{26}$Si$(p,\gamma)^{27}$P reaction has been thought to be important in the sequence that bypasses the production of this galactic $\gamma$-ray emitter $^{26}$Al. Its reaction rate is dominated by a key $3/2^+$ proton resonance in $^{27}$P at the explosive hydrogen-burning temperature. However, the current recommended rate in REACLIB still has large uncertainties. In this work, the precise $\beta$-decay spectroscopy of the drip-line nucleus $^{27}$S was studied by an implantation-decay method, where the $\beta$-delayed protons and $\gamma$ rays were measured simultaneously. We observed for the first time $\beta$-delayed $\gamma$ ray at 1125(2)~keV from $^{27}$S decay, corresponding to the and exit channel of the astrophysically important $3/2^+$ resonance in $^{26}$Si$(p,\gamma)^{27}$P reaction. To date, the most precise proton-separation energy and mass excess of $^{27}$P is determined, and the ratio between $\gamma$ and proton partial widths is pinned down experimentally for the first time. A precise thermonuclear $^{26}$Si$(p,\gamma)^{27}$P rate is obtained based on these experimental observations. In the temperature region of $0.06\sim0.3$~GK, the reaction rate is significantly lower than the recommended one, up to two orders of magnitude around 0.1~GK. The astrophysical impact of this new rate has been examined by the hydrodynamic simulations of novae outbursts, and it turns out that no significant change in the element production in the Mg-P mass region was found. The well-constrained rate effectively eliminates the uncertainty resulting from $^{26}$Si$(p,\gamma)^{27}$P reaction in the model prediction of the nova contribution to the synthesis of Galactic $^{26}$Al.